alg 1 worksheet pkt. with answers 345 pgs

Regents Exam Questions A.A.45: Pythagorean Theorem 4 Name: ________________________ www.jmap.org

1

A.A.45: Pythagorean Theorem 4: Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides

1 If the length of a rectangular television screen is 20 inches and its height is 15 inches, what is the length of its diagonal, in inches?1) 152) 13.23) 254) 35

2 If the length of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse?

1) 2

2) 2 3

3) 2 6

4) 74

3 The "Little People" day care center has a rectangular, fenced play area behind its building. The play area is 30 meters long and 20 meters wide. Find, to the nearest meter, the length of a pathway that runs along the diagonal of the play area.

4 A cable 20 feet long connects the top of a flagpole to a point on the ground that is 16 feet from the base of the pole. How tall is the flagpole?1) 8 ft2) 10 ft3) 12 ft4) 26 ft

5 A woman has a ladder that is 13 feet long. If she sets the base of the ladder on level ground 5 feet from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the house?1) 82) 93) 114) 12

6 How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will reach a point on the house 36 feet from the ground?

7 An 18-foot ladder leans against the wall of a building. The base of the ladder is 9 feet from the building on level ground. How many feet up the wall, to the nearest tenth of a foot, is the top of the ladder?

ID: A

1

A.A.45: Pythagorean Theorem 4: Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sidesAnswer Section

1 ANS: 3

15, 20, 25 is a multiple of the 3, 4, 5 triangle.

PTS: 2 REF: 060710a 2 ANS: 4

PTS: 2 REF: 010202a 3 ANS:

36.

PTS: 2 REF: 010933a 4 ANS: 3

. 12, 16, 20 is a multiple of the 3, 4, 5 triangle.

PTS: 2 REF: 080707a 5 ANS: 4

PTS: 2 REF: 060115a 6 ANS:

15. . 15, 36, 39 is a multiple of the 5, 12, 13 triangle.

PTS: 2 REF: 080122a

ID: A

2

7 ANS:

15.6.

PTS: 2 REF: 060832a

Regents Exam Questions A.A.16: Rational Expressions 1 Name: ________________________ www.jmap.org

1

A.A.16: Rational Expressions 1: Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms

1 The expression 9x 4 27x 6

3x3 is equivalent to

1) 3x(1 3x)

2) 3x(1 3x 2 )

3) 3x(1 9x 5 )

4) 9x 3 (1 x)

2 Which expression is equivalent to

2x 6 18x 4 2x 2

2x 2 ?

1) x 3 9x2

2) x 4 9x2

3) x 3 9x 2 1`

4) x 4 9x 2 1

3 Which expression represents 2x 2 12x

x 6 in simplest

form?1) 02) 2x3) 4x4) 2x 2

4 Which expression represents 25x 125

x 2 25 in simplest

form?

1)5x

2)5x

3)25

x 5

4)25

x 5

5 Which expression represents x 2 3x 10

x 2 25 in

simplest form?

1)25

2)x 2x 5

3)x 2x 5

4)3x 1025


x 2 3x in

simplest form?1) 5

2)x 5

x

3)2x 5

x

4)2x 15

3x

7 Which expression represents x 2 x 6

x 2 5x 6 in

simplest form?

1)x 2x 2

2)x 65x 6

3)15

4) 1

8 Express in simplest form: x 2 1

x 2 3x 2

9 The area of a rectangle is represented by

x 2 5x 24. If the width of the rectangle is represented by x 8, express the length of the rectangle as a binomial.

ID: A

1

A.A.16: Rational Expressions 1: Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest termsAnswer Section

1 ANS: 2

9x 4 27x 6

3x3

9x4 (1 3x 2 )

3x 3 3x(1 3x 2 )

REF: fall0718ia 2 ANS: 4

2x 2 (x4 9x 2 1)

2x2

REF: 081222ia 3 ANS: 2

2x 2 12xx 6

2x(x 6)

x 6 2x

REF: 060824ia 4 ANS: 4

25x 125

x 2 25

25(x 5)(x 5)(x 5)

25x 5

REF: 080821ia 5 ANS: 2

x 2 3x 10

x 2 25

(x 5)(x 2)(x 5)(x 5)

x 2x 5

REF: 061216ia 6 ANS: 2

x 2 2x 15

x 2 3x

(x 5)(x 3)x(x 3)

x 5x

REF: 060921ia 7 ANS: 1

x 2 x 6

x 2 5x 6

(x 3)(x 2)(x 3)(x 2)

x 2x 2

REF: 011130ia 8 ANS:

x 1x 2

. x 2 1

x 2 3x 2

(x 1)(x 1)(x 2)(x 1)

REF: 011233ia

ID: A

2

9 ANS:

x 2 5x 24x 8

(x 8)(x 3)

x 8 x 3

REF: 061131ia


1


1 The fraction 3 x2x 6

, x 3, is equivalent to

1)12

2) 12

3)14

4) 14

2 Written in simplest form, the expression x2 9x

45x 5x2

is equivalent to

1)15

2) 15

3) 54) 5

3 Which expression is equivalent to y x

x2 y2 ?

1)1

x y

2)1

x y

3)1

x y

4)1

x y

4 Written in simplest form, the expression x2y2 93 xy

is equivalent to1) 1

2)1

3 xy3) (3 xy)4) 3 xy

5 Written in simplest form, the expression x2y 4

4 x2y is

1) 12) 0

3)x2y 4

4 x2y4) 1

6 The expression 3y2 12y

4y2 y3 is equivalent to

1)3y

2) 3y

3) 94

4)34 12

y2

ID: A

1


1 ANS: 2 PTS: 2 REF: 060118siii 2 ANS: 2

PTS: 2 REF: 060504b 3 ANS: 4 PTS: 2 REF: 011013b 4 ANS: 3

PTS: 2 REF: 080305b 5 ANS: 4 PTS: 2 REF: fall9911b 6 ANS: 2

PTS: 2 REF: 080619b


1


1 Which expression is in simplest form?

1)x

x 2

2)9

x 2 9

3)x 2 4x 2

4)x 2 6x 9

x 2 x 6

2 For all values of x for which the expression is

defined, 2x x 2

x 2 5x 6 is equivalent to

1)1

x 3

2)x

x 3

3)1

x 2

4)x

x 2

3 Express in simplest form: x 2 5x 24

x 2 8x

4 Express x 2 3x 10

x 2 5x as a fraction in simplest form.

5 Simplify: x 2 6x 5

x 2 25

6 Simplify: 9x 2 15xy

9x 2 25y 2

ID: A

1


1 ANS: 2

. .

REF: 060712b 2 ANS: 2

REF: 060202b 3 ANS:

x 3x

. x 2 5x 24

x 2 8x

(x 8)(x 3)x(x 8)

x 3x

REF: 060837a 4 ANS:

x 2x

REF: 088704siii 5 ANS:

x 1x 5

.

REF: 010631a 6 ANS:

3x3x 5y

REF: 069924a


1


1 The expression 9x 4 27x 6

3x3 is equivalent to

2 Which expression is equivalent to

2x 6 18x 4 2x 2

2x 2 ?

3 Which expression represents 2x 2 12x

x 6 in simplest

form?

4 Which expression represents 25x 125

x 2 25 in simplest

form?


x 2 25 in

simplest form?


x 2 3x in

simplest form?

7 Which expression represents x 2 x 6

x 2 5x 6 in

simplest form?

8 Express in simplest form: x 2 1

x 2 3x 2

9 The area of a rectangle is represented by

x 2 5x 24. If the width of the rectangle is represented by x 8, express the length of the rectangle as a binomial.

ID: A

1


1 ANS:

3x(1 3x 2 )

9x 4 27x 6

3x3

9x4 (1 3x 2 )

3x 3 3x(1 3x 2 )

REF: fall0718ia 2 ANS:

x 4 9x 2 12x 2 (x4 9x 2 1)

2x2


2x2x 2 12x

x 6

2x(x 6)x 6

2x


25x 525x 125

x 2 25

25(x 5)(x 5)(x 5)

25x 5


3x 1025

x 2 3x 10

x 2 25

(x 5)(x 2)(x 5)(x 5)

x 2x 5


x 5x

x 2 2x 15

x 2 3x

(x 5)(x 3)x(x 3)

x 5x

REF: 060921ia

ID: A

2

7 ANS: x 2x 2

x 2 x 6

x 2 5x 6

(x 3)(x 2)(x 3)(x 2)

x 2x 2


x 1x 2

. x 2 1

x 2 3x 2

(x 1)(x 1)(x 2)(x 1)


x 2 5x 24x 8

(x 8)(x 3)

x 8 x 3

REF: 061131ia

Regents Exam Questions Name: ________________________ A.A.17: Addition and Subtraction of Rationals 1www.jmap.org

1

A.A.17: Addition and Subtraction of Rationals 1: Add or subtract fractional expressions with monomial or like binomial denominators

1 What is the sum of d2

and 2d3

expressed in

simplest form?

1) 3d5

2) 3d6

3) 7d5

4) 7d6

2 What is the sum of 32x

and 43x

expressed in

simplest form?

1) 12

6x 2 2) 176x

3) 75x

4) 1712x


and 74x

?

1) 21

8x 2 2) 134x

3) 106x

4) 138x

4 What is 65x

23x

in simplest form?

1) 8

15x 2 2) 8

15x 3)

415x

4) 42x

5 What is 6

4a 2

3a expressed in simplest form?

1) 4a

2) 5

6a 3)

87a

4) 10

12a

6 What is 2 x5x

x 25x

expressed in simplest form?

1) 0 2) 25

3) 45x

4) 2x 4

5x

7 What is 7

12x

y

6x 2 expressed in simplest form?

1) 7 y6x

2) 7 y

12x 6x 2 3) 7y

12x 2 4) 7x 2y

12x 2

8 What is the sum of 3x 2

x 2 and

x 2

x 2?

1) 3x 4

(x 2)2 2) 3x 4

x 2 3)

4x 2

(x 2)2 4) 4x 2

x 2

9 What is the sum of x 72x 4

and 2x 52x 4

?

1) x 122x 4

2) 3x 122x 4

3) x 124x 8

4) 3x 124x 8

10 The expression 2x 132x 6

3x 62x 6

is equivalent to

1) x 192(x 3)

2) x 7

2(x 3) 3)

5x 192(x 3)

4) 5x 74x 12

11 What is the sum of 2y

y 5 and

10y 5

expressed in

simplest form?

1) 1 2) 2 3) 12yy 5

4) 2y 10y 5

ID: A

1

A.A.17: Addition and Subtraction of Rationals 1: Add or subtract fractional expressions with monomial or like binomial denominatorsAnswer Section

1 ANS: 4(d 3) (2 2d)

2 3 3d 4d

6 7d

6


23x

43x

9x 8x

6x 2 17x

6x 2 17

6x

REF: 080917ia 3 ANS: 2

32x

74x

12x 14x

8x2 26x

8x 2 13

4x

REF: 011120ia 4 ANS: 2

65x

23x

18x 10x

15x2 8x

15x 2 8

15x

REF: 010921ia 5 ANS: 2

64a

23a

18a 8a

12a 2 10a

12a 2 5

6a

REF: 060929ia 6 ANS: 3

2 x5x

x 25x

2 x x 25x

45x

REF: 081027ia 7 ANS: 4

712x

y

6x 2

42x 2 12xy

72x 3

6x(7x 2y)

72x 3

7x 2y

12x 2

REF: 061129ia 8 ANS: 4 REF: 011025ia 9 ANS: 1 REF: 061024ia 10 ANS: 1 REF: 061220ia

ID: A

2

11 ANS: 22y

y 5 10

y 5

2y 10y 5

2(y 5)

y 5 2

REF: 011230ia


1


1 What is the sum of d2

and 2d3

expressed in

simplest form?


and 43x

expressed in

simplest form?


and 74x

?

4 What is 65x

23x

in simplest form?

5 What is 6

4a 2

3a expressed in simplest form?

6 What is 2 x5x

x 25x

expressed in simplest form?

7 What is 7

12x

y

6x 2 expressed in simplest form?

8 What is the sum of 3x 2

x 2 and

x 2

x 2?

9 What is the sum of x 72x 4

and 2x 52x 4

?

10 The expression 2x 132x 6

3x 62x 6

is equivalent to

11 What is the sum of 2y

y 5 and

10y 5

expressed in

simplest form?

ID: A

1


1 ANS: 7d6

(d 3) (2 2d)2 3

3d 4d6

7d6


176x32x

43x

9x 8x

6x 2 17x

6x 2 17

6x


134x32x

74x

12x 14x

8x2 26x

8x 2 13

4x


815x65x

23x

18x 10x

15x2 8x

15x 2 8

15x


56a6

4a 2

3a 18a 8a

12a 2 10a

12a 2 5

6a


45x2 x5x

x 25x

2 x x 25x

45x

REF: 081027ia

ID: A

2

7 ANS: 7x 2y

12x 2

712x

y

6x 2

42x 2 12xy

72x 3

6x(7x 2y)

72x 3

7x 2y

12x 2


4x 2

x 2


x 122x 4

REF: 061024ia 10 ANS:

x 192(x 3)

REF: 061220ia 11 ANS:

22y

y 5 10

y 5

2y 10y 5

2(y 5)

y 5 2

REF: 011230ia


1


1 The expression 5x6 x

4 is equivalent to

1)3x5

2)5x 2

10

3)13x12

4)5x24

2 The sum of 3x 2

5, x 0, is

1)1x

2)2x 15

5x

3)5

x 5

4)2x 15x 5


and x2

?

1) 1

2)2 x2x

3)4 x2x

4)4 x 2

2x

4 Which expression is equivalent to ax b

2x?

1)2a b

2x

2)2a b

x

3)a b

3x

4)a b

2x

5 What is the sum of 3

7n and

73n

?

1)1n

2)10

21n

3)42

21n

4)58

21n

6 The reciprocal of the expression 2x 3

1 is

1)2 3x

x

2)x

2 3x3) 2x 34) 2 3x


2

7 The expression yx 1

2 is equivalent to

1)2y x

2x

2)x 2y

2x

3)1 y2x

4)y 1x 2

8 Expressed as a single fraction, 34x

25x

is equal to

1) 1x

2)19x

3)1

20x

4)7

20x

9 Expressed in simplest form, x 7

6 3x 2

12 is

equivalent to

1)2x 5

6

2)2x 9

6

3)x 12

12

4)x 16

12

10 Express 12x

314x

as a single fraction in lowest

terms.

11 Expressed in simplest form, 5x 3

x x 1

2x is

1)4x 4

3x

2)2x 2

x

3)9x 7

2x

4)9x 5

2x

12 Which expression is equivalent to x 3

x 3 9x

x 3?

1)9xx 3

2)x

x 3

3)x 2

x 34) x(x 3)

ID: A

1


1 ANS: 3

REF: 060625a 2 ANS: 2

REF: 080207a 3 ANS: 4

REF: 010423a 4 ANS: 1

REF: 089911a 5 ANS: 4

REF: 060727a 6 ANS: 2 REF: 060327siii 7 ANS: 1

REF: 010016a 8 ANS: 4

REF: 010921a 9 ANS: 3 REF: 068927siii

ID: A

2

10 ANS: 27x

REF: 068708siii 11 ANS: 3 REF: 010118siii 12 ANS: 4 REF: 010218siii


1


1 The expression 5x6 x

4 is equivalent to

2 The sum of 3x 2

5, x 0, is


and x2

?

4 Which expression is equivalent to ax b

2x?

5 What is the sum of 3

7n and

73n

?

6 The reciprocal of the expression 2x 3

1 is

7 The expression yx 1

2 is equivalent to

8 Expressed as a single fraction, 34x

25x

is equal to

9 Expressed in simplest form, x 7

6 3x 2

12 is

equivalent to

10 Express 12x

314x

as a single fraction in lowest

terms.

11 Expressed in simplest form, 5x 3

x x 1

2x is

12 Which expression is equivalent to x 3

x 3 9x

x 3?

ID: A

1


1 ANS: 13x12

REF: 060625a 2 ANS:

2x 155x

REF: 080207a 3 ANS:

4 x 2

2x

REF: 010423a 4 ANS:

2a b2x

REF: 089911a 5 ANS:

5821n

REF: 060727a 6 ANS:

x2 3x

REF: 060327siii

ID: A

2

7 ANS: 2y x

2x

REF: 010016a 8 ANS:

720x

REF: 010921a 9 ANS:

x 1212


27x


9x 72x


x(x 3)

REF: 010218siii

Regents Exam Questions Name: ________________________ A.A.18: Multiplication and Division of Rationals 1www.jmap.org

1

A.A.18: Multiplication and Division of Rationals 1: Multiply and divide algebraic fractions and express the product or quotient in simplest form

1 What is the product of x 2 1x 1

and x 33x 3

expressed

in simplest form?1) x

2)x3

3) x 3

4)x 3

3

2 What is the product of 4x

x 1 and

x 2 13x 3

expressed

in simplest form?

1)4x3

2)4x 2

3

3)4x 2

3(x 1)

4)4(x 1)

3

3 Express the product of x 2

2 and

4x 20

x 2 6x 8 in

simplest form.

4 Perform the indicated operation and express in

simplest form: x 2 x

3 6

x 2 1


simplest form: x 2 16

x 2 x 20 x 4

x 4

6 Express the product in simplest form:

a

a 2 25

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a 2 2a 15a 3

Ê

Ë

ÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃

7 Perform the indicated operations and express in

simplest form: a 8

7a 2 3a 2 24a

a 2 64

8 Express the product in simplest form:

a 2 9

a 2 3a a 2 a

a 3

9 If the length of a rectangular garden is represented

by x 2 2x

x 2 2x 15 and its width is represented by

2x 62x 4

, which expression represents the area of the

garden?1) x2) x 5

3)x 2 2x2(x 5)

4)x

x 5

ID: A

1

A.A.18: Multiplication and Division of Rationals 1: Multiply and divide algebraic fractions and express the product or quotient in simplest formAnswer Section

1 ANS: 4

x 2 1x 1

x 33x 3

(x 1)(x 1)

x 1 x 3

3(x 1) x 3

3

REF: 060815ia 2 ANS: 1

4xx 1

x 2 13x 3

4xx 1

(x 1)(x 1)

3(x 1) 4x

3


x 22

4(x 5)

(x 4)(x 2)

2(x 5)x 4


2xx 1


x 4x 5


aa 5


37a


a 1

REF: 089602siii

ID: A

2

9 ANS: 4

REF: 080117b

Regents Exam Questions Name: ________________________ A.A.18: Multiplication and Division of Rationals 2www.jmap.org

1

A.A.18: Multiplication and Division of Rationals 2:Multiply and divide algebraic fractions and express the product or quotient in simplest form

1 What is the quotient of x

x 4 divided by

2x

x 2 16?

1)2

x 4

2)2x 2

x 4

3)2x2

x 2 16

4)x 4

2

2 Perform the indicated operation and simplify:

3x 64x 12

x 2 4x 3

3 Express in simplest form:

x 2 9x 14

x 2 49 3x 6

x2 x 56

4 Perform the indicated operation and express the

result in simplest terms: x

x 3 3x

x 2 9

5 Express in simplest form: 8x

x 2 16 2x

x 4


simplest form: b 2 42b 6

2 bb 3

7 Express in simplest form: 81 x 2

6x 54 x 2 9x

3x

8 Express in simplest form: x 2 92x 8

3 xx 4

9 Express in simplest form: 2x 2 8x 42

6x 2 x 2 9

x 2 3x

10 Perform the indicated operations and express in

simplest form: 3x 2 12x 15

x 2 2x 15 3x2 3x

3x x 2

ID: A

1

A.A.18: Multiplication and Division of Rationals 2:Multiply and divide algebraic fractions and express the product or quotient in simplest formAnswer Section

1 ANS: 4

xx 4

2x

x 2 16 x

x 4 x 2 16

2x 1

x 4

(x 4)(x 4)2

x 42


34x 8

. 3x 64x 12

x 2 4x 3

3(x 2)4(x 3)

x 3(x 2)(x 2)

34(x 2)


x 2 9x 14

x 2 49 3x 6

x 2 x 56

(x 7)(x 2)(x 7)(x 7)

(x 8)(x 7)

3(x 2) x 8

3


x 33

.

REF: 080022a 5 ANS:

4x 4

.

REF: 010935a 6 ANS:

b 22


12


(x 3)2

REF: 010141siii

ID: A

2

9 ANS:

x 73x

. 2x 2 8x 42

6x 2 x2 9

x 2 3x

2(x2 4x 21)

6x 2

x(x 3)(x 3)(x 3)

(x 7)(x 3)

3x 1

x 3 x 7

3x

REF: 080937ia 10 ANS:

1.

REF: 010928b

Regents Exam Questions Name: ________________________ A.A.19: Factoring the Difference of Perfect Squares 1www.jmap.org

1

A.A.19: Factoring the Difference of Perfect Squares 1: Identify and factor the difference of two perfect squares

1 The expression x 2 16 is equivalent to1) (x 2)(x 8)2) (x 2)(x 8)3) (x 4)(x 4)4) (x 8)(x 8)

2 Which expression is equivalent to 64 x 2?1) (8 x)(8 x)2) (8 x)(8 x)3) (x 8)(x 8)4) (x 8)(x 8)

3 Which expression is equivalent to 121 x 2 ?1) (x 11)(x 11)2) (x 11)(x 11)3) (11 x)(11 x)4) (11 x)(11 x)

4 Which expression is equivalent to 9x 2 16?1) (3x 4)(3x 4)2) (3x 4)(3x 4)3) (3x 8)(3x 8)4) (3x 8)(3x 8)

5 The expression 9x 2 100 is equivalent to1) (9x 10)(x 10)2) (3x 10)(3x 10)3) (3x 100)(3x 1)4) (9x 100)(x 1)

6 The expression x 2 36y 2 is equivalent to1) (x 6y)(x 6y)2) (x 18y)(x 18y)3) (x 6y)(x 6y)4) (x 18y)(x 18y)

7 Factored, the expression 16x 2 25y 2 is equivalent to1) (4x 5y)(4x 5y)2) (4x 5y)(4x 5y)3) (8x 5y)(8x 5y)4) (8x 5y)(8x 5y)

8 The expression 9a 2 64b 2 is equivalent to1) (9a 8b)(a 8b)2) (9a 8b)(a 8b)3) (3a 8b)(3a 8b)4) (3a 8b)(3a 8b)

9 When a 3 4a is factored completely, the result is1) (a 2)(a 2)2) a(a 2)(a 2)

3) a 2 (a 4)

4) a(a 2)2

10 Which expression represents 36x 2 100y 6 factored completely?

1) 2(9x 25y 3 )(9x 25y 3 )

2) 4(3x 5y 3 )(3x 5y 3 )

3) (6x 10y 3 )(6x 10y 3 )

4) (18x 50y 3 )(18x 50y 3 )

11 Factor completely: 4x 3 36x

12 If Ann correctly factors an expression that is the difference of two perfect squares, her factors could be1) (2x y)(x 2y)2) (2x 3y)(2x 3y)3) (x 4)(x 4)4) (2y 5)(y 5)

ID: A

1

A.A.19: Factoring the Difference of Perfect Squares 1: Identify and factor the difference of two perfect squaresAnswer Section

1 ANS: 3 REF: fall0706ia 2 ANS: 2 REF: 011201ia 3 ANS: 3 REF: 081008ia 4 ANS: 1 REF: 080902ia 5 ANS: 2 REF: 010909ia 6 ANS: 3 REF: 061101ia 7 ANS: 1 REF: 060804ia 8 ANS: 3 REF: 081207ia 9 ANS: 2

a 3 4a a(a 2 4) a(a 2)(a 2)

REF: 011108ia 10 ANS: 2

36x 2 100y6 4(9x 2 25y6 ) 4(3x 5y 3 )(3x 5y 3 )

REF: 081129ia 11 ANS:

4x(x 3)(x 3). 4x 3 36x 4x(x 2 9) 4x(x 3)(x 3)

REF: 060932ia 12 ANS: 2 REF: 011022ia


1


1 Factor completely: 3x 2 271) 3(x 3)2

2) 3(x 2 27)3) 3(x 3)(x 3)4) (3x 3)(x 9)

2 Written in simplest factored form, the binomial

2x 2 50 can be expressed as1) 2(x 5)(x 5)2) 2(x 5)(x 5)3) (x 5)(x 5)4) 2x(x 50)

3 Expressed in factored form, the binomial 4a 2 9b 2 is equivalent to1) (2a 3b)(2a 3b)2) (2a 3b)(2a 3b)3) (4a 3b)(a 3b)4) (2a 9b)(2a b)

4 One of the factors of 4x 2 9 is1) (x 3)2) (2x 3)3) (4x 3)4) (x 3)

5 One factor of the expression x 2y 2 16 is1) xy 42) xy 8

3) x 2 44) x 2 8

6 What is a common factor of x 2 9 and x 2 5x 6?1) x 32) x 33) x 24) x 2

7 Factor completely: 5n 2 80


9 Factor completely: 9x 3 x


11 Factor completely: 3ax 2 27a

12 Factor completely: 5x 2y 3 180y

ID: A

1


1 ANS: 3

PTS: 2 REF: 060109a 2 ANS: 2

PTS: 2 REF: 080103a 3 ANS: 2 PTS: 2 REF: 010201a 4 ANS: 2 PTS: 2 REF: 010105a 5 ANS: 1 PTS: 2 REF: 080711a 6 ANS: 2 PTS: 2 REF: 010414a 7 ANS:

5(n 4)(n 4).

PTS: 2 REF: 080533a 8 ANS:

2x(x 7)(x 7)

PTS: 2 REF: 019503siii 9 ANS:

x(3x 1)(3x 1)


3x(x 8)(x 8)


3a(x 3)(x 3).

PTS: 2 REF: 080434a 12 ANS:

5y(xy 6)(xy 6)

PTS: 2 REF: 069813siii


1


1 Factor: x2 36

2 Factor: 9 x2

3 Factor: 16x2 9

4 Factor: 3a2 3

5 Factor: 4x3 9x

6 Factor: 12a2 27b2

7 Factor: 9x2 y2

8 Factor: 28a2 7b2

9 Factor: 6a2 6b2

10 Factor: 8a3 32ab2

ID: A

1


1 ANS: (x 6)(x 6)

PTS: 2 REF: 019604al 2 ANS:

(x 3)(x 3)


(4x 3)(4x 3)


3(a 1)(a 1)


x(2x 3)(2x 3)


3(2a 3b)(2a 3b)


(3x y)(3x y)


7(2a b)(2a b)


6(a b)(a b)

PTS: 2 REF: 099607al 10 ANS:

8a(a 2b)(a 2b)

PTS: 4 REF: 069503al


1


1 The expression x 2 16 is equivalent to

2 Which expression is equivalent to 64 x 2?

3 Which expression is equivalent to 121 x 2 ?

4 Which expression is equivalent to 9x 2 16?

5 The expression 9x 2 100 is equivalent to

6 The expression x 2 36y 2 is equivalent to

7 Factored, the expression 16x 2 25y 2 is equivalent to

8 The expression 9a 2 64b 2 is equivalent to

9 When a 3 4a is factored completely, the result is

10 Which expression represents 36x 2 100y 6 factored completely?


12 If Ann correctly factors an expression that is the difference of two perfect squares, her factors could be1) (2x y)(x 2y)2) (2x 3y)(2x 3y)3) (x 4)(x 4)4) (2y 5)(y 5)

ID: A

1


1 ANS: (x 4)(x 4)


(8 x)(8 x)


(11 x)(11 x)


(3x 4)(3x 4)


(3x 10)(3x 10)


(x 6y)(x 6y)


(4x 5y)(4x 5y)


(3a 8b)(3a 8b)


a(a 2)(a 2)

a 3 4a a(a 2 4) a(a 2)(a 2)

REF: 011108ia 10 ANS:

4(3x 5y 3 )(3x 5y 3 )

36x 2 100y6 4(9x 2 25y6 ) 4(3x 5y 3 )(3x 5y 3 )

REF: 081129ia

ID: A

2

11 ANS:

4x(x 3)(x 3). 4x 3 36x 4x(x 2 9) 4x(x 3)(x 3)

REF: 060932ia 12 ANS: 2 REF: 011022ia

Regents Exam Questions A.A.20: Factoring Polynomials 1 Name: ________________________ www.jmap.org

1

A.A.20: Factoring Polynomials 1: Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)

1 What are the factors of x 2 10x 24?1) (x 4)(x 6)2) (x 4)(x 6)3) (x 12)(x 2)4) (x 12)(x 2)

2 What are the factors of x 2 5x 6?1) (x 2) and (x 3)2) (x 2) and (x 3)3) (x 6) and (x 1)4) (x 6) and (x 1)

3 What are the factors of the expression x 2 x 20?1) (x 5) and (x 4)2) (x 5) and (x 4)3) (x 5) and (x 4)4) (x 5) and (x 4)

4 Factored completely, the expression 2x 2 10x 12 is equivalent to1) 2(x 6)(x 1)2) 2(x 6)(x 1)3) 2(x 2)(x 3)4) 2(x 2)(x 3)

5 Factored completely, the expression 2y 2 12y 54 is equivalent to1) 2(y 9)(y 3)2) 2(y 3)(y 9)3) (y 6)(2y 9)4) (2y 6)(y 9)

6 Factored completely, the expression 3x 2 3x 18 is equivalent to

1) 3(x 2 x 6)2) 3(x 3)(x 2)3) (3x 9)(x 2)4) (3x 6)(x 3)

7 Factored completely, the expression

3x 3 33x2 90x is equivalent to

1) 3x(x 2 33x 90)

2) 3x(x 2 11x 30)3) 3x(x 5)(x 6)4) 3x(x 5)(x 6)

8 Factor completely: 3x 2 15x 42

9 Factor completely: x 3 x2 6x

10 If x 2 is a factor of x 2 bx 10, what is the value of b?


2

11 Which expression is a factor of x 2 2x 15?1) (x 3)2) (x 3)3) (x 15)4) (x 5)

12 Which expression is a factor of n 2 3n 54?1) n 62) n 2 93) n 94) n 9

13 Which is a factor of x 2 5x 24?1) (x 4)2) (x 4)3) (x 3)4) (x 3)

14 If 3x is one factor of 3x 2 9x, what is the other factor?1) 3x2) x 2 6x3) x 34) x 3

15 If one factor of 56x 4y 3 42x2y 6 is 14x 2y 3 , what is the other factor?

1) 4x 2 3y 3

2) 4x 2 3y 2

3) 4x 2y 3xy 3

4) 4x 2y 3xy 2

ID: A

1

A.A.20: Factoring Polynomials 1: Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)Answer Section

1 ANS: 3

REF: 010318a 2 ANS: 2

REF: 010814a 3 ANS: 2 REF: 061105ia 4 ANS: 2

2x 2 10x 12 2(x 2 5x 6) 2(x 6)(x 1)

REF: 080806ia 5 ANS: 1

REF: 060623a 6 ANS: 2 REF: 061027ia 7 ANS: 4

3x 3 33x 2 90x 3x(x 2 11x 30) 3x(x 5)(x 6)


3(x 7)(x 2).

REF: 060535a 9 ANS:

x(x 3)(x 2)


7

REF: 010007siii 11 ANS: 1

REF: 010004a 12 ANS: 4

REF: 060206a

ID: A

2

13 ANS: 4

x 2 5x 24 (x 8)(x 3)

REF: spring9806a 14 ANS: 3

REF: 060421a 15 ANS: 1

REF: 060318a


1


1 What are the factors of x 2 10x 24?

2 What are the factors of x 2 5x 6?

3 What are the factors of the expression x 2 x 20?


5 Factored completely, the expression 2y 2 12y 54 is equivalent to


7 Factored completely, the expression

3x 3 33x2 90x is equivalent to

8 Factor completely: 3x 2 15x 42

9 Factor completely: x 3 x2 6x

10 If x 2 is a factor of x 2 bx 10, what is the value of b?

11 Which expression is a factor of x 2 2x 15?1) (x 3)2) (x 3)3) (x 15)4) (x 5)

12 Which expression is a factor of n 2 3n 54?1) n 62) n 2 93) n 94) n 9

13 Which is a factor of x 2 5x 24?1) (x 4)2) (x 4)3) (x 3)4) (x 3)

14 If 3x is one factor of 3x 2 9x, what is the other factor?

15 If one factor of 56x 4y 3 42x2y 6 is 14x 2y 3 , what is the other factor?

ID: A

1


1 ANS: (x 12)(x 2)

REF: 010318a 2 ANS:

(x 2) and (x 3)

REF: 010814a 3 ANS:

(x 5) and (x 4)


2(x 6)(x 1)

2x 2 10x 12 2(x 2 5x 6) 2(x 6)(x 1)


2(y 9)(y 3)

REF: 060623a 6 ANS:

3(x 3)(x 2)


3x(x 5)(x 6)

3x 3 33x 2 90x 3x(x 2 11x 30) 3x(x 5)(x 6)


3(x 7)(x 2).

REF: 060535a 9 ANS:

x(x 3)(x 2)

REF: 018912siii

ID: A

2

10 ANS: 7

REF: 010007siii 11 ANS: 1

REF: 010004a 12 ANS: 4

REF: 060206a 13 ANS: 4

x 2 5x 24 (x 8)(x 3)

REF: spring9806a 14 ANS:

x 3

REF: 060421a 15 ANS:

4x 2 3y 3

REF: 060318a


1


1 Factor: ab2 ab

2 Factor: x2 10x 21

3 Factor: a2 2a 1

4 Factor: a2 a 2

5 Factor: a2 a 6

6 Factor: x2 x 12

7 Factor: a2 4a 21

8 Factor: x2 x 30

9 Factor: 214c c2

10 Factor: 6 x x2

11 Factor: 2a2 10a 28

12 Factor: 3x2 6x 105

13 Factor: a3 3a2 10a

14 Factor: x3 8x2 7x

15 Factor: 2x8 16x7 32x6

ID: A

1


1 ANS: ab(b 1)


(x 3)(x 7)


(a 1)2


(a 2)(a 1)


(a 3)(a 2)


(x 4)(x 3)


(a 7)(a 3)


(x 6)(x 5)


(c 7)(c 3)

PTS: 2 REF: 030003al 10 ANS:

(x 3)(x 2)

PTS: 2 REF: 089304al 11 ANS:

2(a 7)(a 2)


ID: A

2

12 ANS: 3(x 7)(x 5)

PTS: 2 REF: 099806al 13 ANS:

a(a 5)(a 2)

PTS: 2 REF: 069903al 14 ANS:

x(x 7)(x 1)

PTS: 2 REF: 019105al 15 ANS:

2x6(x 4)(x 4)


Regents Exam Questions A.A.21: Interpreting Solutions Name: ________________________ www.jmap.org

1

A.A.21: Interpreting Solutions: Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable

1 Which value of x is in the solution set of the inequality 2x 5 17?1) 82) 63) 44) 12

2 Which value of x is in the solution set of the inequality 4x 2 10?1) 22) 23) 34) 4

3 Which value of x is in the solution set of 43

x 5 17?

1) 82) 93) 124) 16

4 Which value of x is in the solution set of the inequality 2(x 5) 4?1) 02) 23) 34) 5

5 Which number is in the solution set of the inequality 5x 3 38?1) 52) 63) 74) 8

6 In the set of positive integers, what is the solution set of the inequality 2x 3 5?1) {0,1,2,3}2) {1,2,3}3) {0,1,2,3,4}4) {1,2,3,4}

7 Find all the negative odd integers that satisfy the following inequality: 3x 1 17

8 Given: A {18,6,3,12}Determine all elements of set A that are in the

solution of the inequality 23

x 3 2x 7.

ID: A

1

A.A.21: Interpreting Solutions: Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variableAnswer Section

1 ANS: 12x 5 17

2x 12

x 6

PTS: 2 REF: fall0724ia 2 ANS: 4

4x 2 10

4x 8

x 2

PTS: 2 REF: 080805ia 3 ANS: 1

43

x 5 17

43

x 12

4x 36

x 9

PTS: 2 REF: 060914ia 4 ANS: 4

2(x 5) 4

2x 10 4

2x 6

x 3

PTS: 2 REF: 080913ia 5 ANS: 4

PTS: 2 REF: 060311a

ID: A

2

6 ANS: 2

PTS: 2 REF: 060118a 7 ANS:

5, 3, 1.

PTS: 3 REF: 010536a 8 ANS:

12. 323

x 3 2x 7Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

x 9 6x 21

7x 30

x 307

PTS: 3 REF: 061034ia

Regents Exam Questions A.A.22: Solving Equations 1 Name: ________________________ www.jmap.org

1

A.A.22: Solving Equations 1: Solve all types of linear equations in one variable

1 Which value of p is the solution of 5p − 1 = 2p + 20?

1) 197

2) 193

3) 34) 7

2 What is the value of x in the equation 2(x − 4) = 4(2x + 1)?1) −22) 2

3) −12

4) 12

3 If 12x = 4(x + 5), then x equals

1) 112

2) 58

3) 1.254) 2.5

4 Solve for x: 15x − 3(3x + 4) = 61) 1

2) −12

3) 3

4) 13

5 What is the solution of the equation 3y − 5y + 10 = 361) −132) 23) 4.54) 13

6 If 2x + 5 = −25 and −3m− 6 = 48, what is the product of x and m?1) −2702) −333) 34) 270

7 If 2(x + 3) = x + 10, then x equals1) 142) 73) 54) 4

8 If 3(x − 2) = 2x + 6, the value of x is1) 02) 53) 124) 20

9 What is the value of x in the equation 2(x − 3) + 1 = 19?1) 62) 93) 10.54) 12

10 What is the solution for the equation x + 1 = x + 2?1) −1

2) 12

3) all real numbers4) There is no solution.

11 If −2x + 3 = 7 and 3x + 1 = 5+ y, the value of y is1) 12) 03) −104) 10

12 What is the value of x in the equation 5(2x − 7) = 15x − 10?1) 12) 0.63) −54) −9


2

13 What is the value of x in the equation 13x − 2(x + 4) = 8x + 1?1) 12) 23) 34) 4

14 What is the value of p in the equation 2(3p − 4) = 10?1) 1

2) 2 13

3) 3

4) 13

15 What is the value of n in the equation 3n − 8 = 32 − n?1) −102) −63) 64) 10

16 What is the value of x in the equation 6(x − 2) = 36− 10x?1) −62) 1.53) 34) 6

17 What is the value of p in the equation 8p + 2 = 4p − 10?1) 12) −13) 34) −3

18 What is the value of x in the equation 5 − 3x = −7?

1) −23

2) 23

3) −44) 4

19 If 3(x + 2) − 2(x + 1) = 8, the value of x is1) 1

2) 15

3) 54) 4

20 What is the value of m in the equation 2m− (m+ 1) = 01) 12) −1

3) 13

4) 0

21 Debbie solved the linear equation 3(x + 4) − 2 = 16 as follows:

She made an error between lines 1) 1 and 22) 2 and 33) 3 and 44) 4 and 5

22 Solve for x: 5(x − 2) = 2(10 + x)

23 Solve for g: 3+ 2g = 5g − 9

24 Solve algebraically for x: 3(x + 1) − 5x = 12− (6x − 7)

ID: A

1

A.A.22: Solving Equations 1: Solve all types of linear equations in one variableAnswer Section

1 ANS: 4

5p − 1 = 2p + 20

3p = 21

p = 7

REF: 080801ia 2 ANS: 1

2(x − 4) = 4(2x + 1)

2x − 8 = 8x + 4

−12 = 6x

−2 = x

REF: 011106ia 3 ANS: 4

12x = 4(x + 5)

12x = 4x + 20

8x = 20

x = 208 = 2.5

REF: spring9802a 4 ANS: 3

REF: 080015a 5 ANS: 1

REF: 060214a

ID: A

2

6 ANS: 4

. . The product of x and m is 270.

REF: 080219a 7 ANS: 4

REF: 010401a 8 ANS: 3

REF: 060404a 9 ANS: 4

REF: 010904a 10 ANS: 4

REF: 010908a 11 ANS: 3

. .

REF: 060519a

ID: A

3

12 ANS: 3

REF: 010601a 13 ANS: 3

REF: 060602a 14 ANS: 3

REF: 080602a 15 ANS: 4

REF: 010705a 16 ANS: 3

REF: 060702a 17 ANS: 4

REF: 010807a

ID: A

4

18 ANS: 4

REF: 060810a 19 ANS: 4

REF: 060813a 20 ANS: 1

REF: 080812a 21 ANS: 2

Debbie failed to distribute the 3 properly.

REF: 011009ia 22 ANS:

10. .

REF: 080731a 23 ANS:

4. 3+ 2g = 5g − 9

12 = 3g

g = 4

REF: fall0732ia

ID: A

5

24 ANS: 4. 3(x + 1) − 5x = 12− (6x − 7)

3x + 3 − 5x = 12− 6x + 7

−2x + 3 = −6x + 19

4x = 16

x = 4

REF: 061238ia


1

A.A.22: Solving Equations 2: Solve all types of linear equations in one variable

1 Which value of p is the solution of 5p − 1 = 2p + 20?

2 What is the value of x in the equation 2(x − 4) = 4(2x + 1)?

3 If 12x = 4(x + 5), then x equals

4 Solve for x: 15x − 3(3x + 4) = 6

5 What is the solution of the equation 3y − 5y + 10 = 36

6 If 2x + 5 = −25 and −3m− 6 = 48, what is the product of x and m?

7 If 2(x + 3) = x + 10, then x equals

8 If 3(x − 2) = 2x + 6, the value of x is

9 What is the value of x in the equation 2(x − 3) + 1 = 19?

10 What is the solution for the equation x + 1 = x + 2?

11 If −2x + 3 = 7 and 3x + 1 = 5+ y, the value of y is

12 What is the value of x in the equation 5(2x − 7) = 15x − 10?

13 What is the value of x in the equation 13x − 2(x + 4) = 8x + 1?

14 What is the value of p in the equation 2(3p − 4) = 10?


2

15 What is the value of n in the equation 3n − 8 = 32 − n?

16 What is the value of x in the equation 6(x − 2) = 36− 10x?

17 What is the value of p in the equation 8p + 2 = 4p − 10?

18 What is the value of x in the equation 5 − 3x = −7?

19 If 3(x + 2) − 2(x + 1) = 8, the value of x is

20 What is the value of m in the equation 2m− (m+ 1) = 0

21 Debbie solved the linear equation 3(x + 4) − 2 = 16 as follows:

She made an error between lines

22 Solve for x: 5(x − 2) = 2(10 + x)

23 Solve for g: 3+ 2g = 5g − 9

24 Solve algebraically for x: 3(x + 1) − 5x = 12− (6x − 7)

ID: A

1

A.A.22: Solving Equations 2: Solve all types of linear equations in one variableAnswer Section

1 ANS: 7

5p − 1 = 2p + 20

3p = 21

p = 7


−22(x − 4) = 4(2x + 1)

2x − 8 = 8x + 4

−12 = 6x

−2 = x


2.512x = 4(x + 5)

12x = 4x + 20

8x = 20

x = 208 = 2.5


3

REF: 080015a

ID: A

2

5 ANS: −13

REF: 060214a 6 ANS:

270

. . The product of x and m is 270.

REF: 080219a 7 ANS:

4

REF: 010401a 8 ANS:

12

REF: 060404a 9 ANS:

12

REF: 010904a 10 ANS:

There is no solution.

REF: 010908a

ID: A

3

11 ANS: −10

. .

REF: 060519a 12 ANS:

−5

REF: 010601a 13 ANS:

3

REF: 060602a 14 ANS:

3

REF: 080602a 15 ANS:

10

REF: 010705a

ID: A

4

16 ANS: 3

REF: 060702a 17 ANS:

−3

REF: 010807a 18 ANS:

4

REF: 060810a 19 ANS:

4

REF: 060813a 20 ANS:

1

REF: 080812a 21 ANS:

2 and 3Debbie failed to distribute the 3 properly.

REF: 011009ia

ID: A

5

22 ANS:

10. .

REF: 080731a 23 ANS:

4. 3+ 2g = 5g − 9

12 = 3g

g = 4


4. 3(x + 1) − 5x = 12− (6x − 7)

3x + 3 − 5x = 12− 6x + 7

−2x + 3 = −6x + 19

4x = 16

x = 4

REF: 061238ia

Regents Exam Questions A.A.23: Transforming Formulas 1 Name: ________________________ www.jmap.org

1

A.A.23: Transforming Formulas 1: Solve literal equations for a given variable

1 If 3ax b c, then x equals1) c b 3a2) c b 3a

3)c b3a

4)b c3a

2 If the formula for the perimeter of a rectangle is P 2l 2w, then w can be expressed as

1) w 2l P2

2) w P 2l2

3) w P l2

4) w P 2w2l

3 The members of the senior class are planning a dance. They use the equation r pn to determine the total receipts. What is n expressed in terms of r and p ?1) n r p2) n r p

3) n pr

4) n rp

4 The formula for the volume of a pyramid is

V 13

Bh. What is h expressed in terms of B and

V?

1) h 13

VB

2) h V3B

3) h 3VB

4) h 3VB

5 A formula used for calculating velocity is

v 12

at2 . What is a expressed in terms of v and t?

1) a 2vt

2) a 2v

t2

3) a vt

4) a v

2t2

6 If s 2x tr

, then x equals

1)rs t

2

2)rs 1

23) 2rs t4) rs 2t


2

7 If eyn k t, what is y in terms of e, n, k, and t?

1) y tn ke

2) y tn ke

3) y n(t k)

e

4) y n(t k)

e

8 If a ar b r, the value of a in terms of b and r can be expressed as

1)br 1

2)1 b

r

3)b r1 r

4)1 br b

9 If k am 3mx, the value of m in terms of a, k, and x can be expressed as

1)k

a 3x

2)k 3mx

a

3)k am

3x

4)k a

3x

10 Solve for c in terms of a and b: bc ac ab

ID: A

1

A.A.23: Transforming Formulas 1: Solve literal equations for a given variableAnswer Section

1 ANS: 33ax b c

3ax c b

x c b3a

REF: 080808ia 2 ANS: 2

P 2l 2w

P 2l 2w

P 2l2

w

REF: 010911ia 3 ANS: 4 REF: 011016ia 4 ANS: 3 REF: 081230ia 5 ANS: 2 REF: 061023ia 6 ANS: 1

s 2x tr

rs 2x t

rs t 2x

rs t2

x

REF: 011228ia 7 ANS: 4

eyn k t

eyn

t k

y n(t k)

e

REF: 011125ia

ID: A

2

8 ANS: 3a ar b r

a(1 r) b r

a b r1 r

REF: 060913ia 9 ANS: 1

k am 3mx

k m(a 3x)

ka 3x

m

REF: 061215ia 10 ANS:

bc ac ab

c(b a) ab

c abb a

REF: 081131ia


1


1 If 3ax b c, then x equals

2 If the formula for the perimeter of a rectangle is P 2l 2w, then w can be expressed as

3 The members of the senior class are planning a dance. They use the equation r pn to determine the total receipts. What is n expressed in terms of r and p ?

4 The formula for the volume of a pyramid is

V 13

Bh. What is h expressed in terms of B and

V?

5 A formula used for calculating velocity is

v 12

at2 . What is a expressed in terms of v and t?

6 If s 2x tr

, then x equals

7 If eyn k t, what is y in terms of e, n, k, and t?

8 If a ar b r, the value of a in terms of b and r can be expressed as

9 If k am 3mx, the value of m in terms of a, k, and x can be expressed as

10 Solve for c in terms of a and b: bc ac ab

ID: A

1


1 ANS: c b3a

3ax b c

3ax c b

x c b3a


w P 2l2

P 2l 2w

P 2l 2w

P 2l2

w


n rp


h 3VB


a 2v

t2

REF: 061023ia

ID: A

2

6 ANS: rs t

2

s 2x tr

rs 2x t

rs t 2x

rs t2

x


y n(t k)

eeyn k t

eyn

t k

y n(t k)

e


b r1 ra ar b r

a(1 r) b r

a b r1 r


ka 3x

k am 3mx

k m(a 3x)

ka 3x

m

REF: 061215ia

ID: A

3

10 ANS: bc ac ab

c(b a) ab

c abb a

REF: 081131ia


1


1 If bx 2 K, then x equals

1)Kb 2

2)K 2

b

3)2 K

b

4)K 2

b

2 If x 2a b 2 , then a equals

1)x b 2

2

2)x b 2

2

3)b 2 x

2

4) x b 2

3 If 2m 2p 16, p equals1) 8 m2) 16 m3) 16 2m4) 9m

4 In the equation A p prt, t is equivalent to

1)A pr

p

2)A p

pr

3)Apr

p

4)Ap pr

5 If c 2m d , then m is equal to

1)c d

2

2)c2 d

3) c d2

4) d 2c

6 Sean knows the length of the base, b, and the area, A, of a triangular window in his bedroom. Which formula could he use to find the height, h, of this window?1) h 2A b

2) h A2b

3) h (2A)(b)

4) h 2Ab

7 The formula for the volume of a right circular

cylinder is V r2h. The value of h can be expressed as

1)V r2

2)V

r2

3) r2

V

4) V r2

8 The formula for potential energy is P mgh , where P is potential energy, m is mass, g is gravity, and h is height. Which expression can be used to represent g?1) P m h2) P mh

3)Pm h

4)Pmh


2

9 If 9x 2a 3a 4x, then x equals1) a2) a

3)5a12

4)a13

10 If x y 9x y , then x is equal to1) y

2)15

y

3) 04) 8

11 If 7x 2a 3x 5a, then x is equivalent to

1)7a10

2)7a4

3)3a10

4)3a4

12 If 2ax 5x 2, then x is equivalent to

1)2 5a

2a

2)1

a 5

3)2

2a 54) 7 2a

13 If x4 a

b 0, b 0, then x is equal to

1) a4b

2)a4b

3) 4ab

4)4ab

14 The equation P 2L 2W is equivalent to

1) L P 2W2

2) L P 2W2

3) 2L P2W

4) L P W

15 Which equation is equivalent to 3x 4y 15?

1) y 15 3x4

2) y 3x 154

3) y 15 3x4) y 3x 15

16 Solve: (a x)(b x) x 2

17 Shoe sizes and foot length are related by the formula S 3F 24, where S represents the shoe size and F represents the length of the foot, in inches.a Solve the formula for F.b To the nearest tenth of an inch, how long is the

foot of a person who wears a size 1012

shoe?

ID: A

1


1 ANS: 4

REF: 010116a 2 ANS: 2

REF: 060219a 3 ANS: 1

REF: 080218a 4 ANS: 2

REF: 010620a 5 ANS: 1

REF: 060719a

ID: A

2

6 ANS: 4

REF: 010517a 7 ANS: 2

REF: 060617a 8 ANS: 4

P mgh

g Pmh

REF: 010710a 9 ANS: 4

REF: 010011a 10 ANS: 3

REF: 060310a 11 ANS: 4

REF: 060513a

ID: A

3

12 ANS: 3

REF: 010421a 13 ANS: 4

REF: 080530a 14 ANS: 1

REF: 010310a 15 ANS: 1

REF: 080722a 16 ANS:

a 2

a b

REF: 039008al 17 ANS:

S 243

, 11.5. .

REF: 069922a


1


1 If bx 2 K, then x equals

2 If x 2a b 2 , then a equals

3 If 2m 2p 16, p equals

4 In the equation A p prt, t is equivalent to

5 If c 2m d , then m is equal to

6 Sean knows the length of the base, b, and the area, A, of a triangular window in his bedroom. Which formula could he use to find the height, h, of this window?

7 The formula for the volume of a right circular

cylinder is V r2h. The value of h can be expressed as

8 The formula for potential energy is P mgh , where P is potential energy, m is mass, g is gravity, and h is height. Which expression can be used to represent g?

9 If 9x 2a 3a 4x, then x equals

10 If x y 9x y , then x is equal to

11 If 7x 2a 3x 5a, then x is equivalent to

12 If 2ax 5x 2, then x is equivalent to

13 If x4 a

b 0, b 0, then x is equal to

14 The equation P 2L 2W is equivalent to

1) L P 2W2

2) L P 2W2

3) 2L P2W

4) L P W

15 Which equation is equivalent to 3x 4y 15?

1) y 15 3x4

2) y 3x 154

3) y 15 3x4) y 3x 15

16 Solve: (a x)(b x) x 2

17 Shoe sizes and foot length are related by the formula S 3F 24, where S represents the shoe size and F represents the length of the foot, in inches.a Solve the formula for F.b To the nearest tenth of an inch, how long is the

foot of a person who wears a size 1012

shoe?

ID: A

1


1 ANS: K 2

b

REF: 010116a 2 ANS:

x b 2

2

REF: 060219a 3 ANS:

8 m

REF: 080218a 4 ANS:

A ppr

REF: 010620a

ID: A

2

5 ANS: c d

2

REF: 060719a 6 ANS:

h 2Ab

REF: 010517a 7 ANS:

V

r2

REF: 060617a 8 ANS:

PmhP mgh

g Pmh

REF: 010710a

ID: A

3

9 ANS: a13

REF: 010011a 10 ANS:

0

REF: 060310a 11 ANS:

3a4

REF: 060513a 12 ANS:

22a 5

REF: 010421a

ID: A

4

13 ANS: 4ab

REF: 080530a 14 ANS: 1

REF: 010310a 15 ANS: 1

REF: 080722a 16 ANS:

a 2

a b

REF: 039008al 17 ANS:

S 243

, 11.5. .

REF: 069922a

Regents Exam Questions A.A.24: Solving Inequalities Name: ________________________ www.jmap.org

1

A.A.24: Solving Inequalities: Solve linear inequalities in one variable

1 The inequality 12 x + 3 < 2x − 6 is equivalent to

1) x < −56 3) x < 6

2) x > −56 4) x > 6

2 What is the solution of the inequality −6x − 17 ≥ 8x + 25?1) x ≥ 3 3) x ≥ −3

2) x ≤ 3 4) x ≤ −3

3 What is the solution of 3(2m− 1) ≤ 4m+ 7?1) m ≤ 5 3) m ≤ 4

2) m ≥ 5 4) m ≥ 4

4 Solve algebraically for x: 2(x − 4) ≥ 12 (5 − 3x)

5 Which inequality is shown on the accompanying graph?

1) x < −1 3) x > −1

2) x ≤ −1 4) x ≥ −1


2

6 Which inequality is represented in the graph below?

1) −4 < x < 2 3) −4 < x ≤ 2

2) −4 ≤ x < 2 4) −4 ≤ x ≤ 2

7 Which inequality is represented in the accompanying graph?

1) −3 ≤ x < 4 3) −3 < x < 4

2) −3 ≤ x ≤ 4 4) −3 < x ≤ 4

8 Which graph best represents the solution set for the inequality x > 2 ?

1) 3)

2) 4)

9 In order to be admitted for a certain ride at an amusement park, a child must be greater than or equal to 36 inches tall and less than 48 inches tall. Which graph represents these conditions?

1) 3)

2) 4)


3

10 Which graph represents the solution set for 2x − 4 ≤ 8 and x + 5 ≥ 7?

1) 3)

2) 4)

11 The manufacturer of Ron's car recommends that the tire pressure be at least 26 pounds per square inch and less than 35 pounds per square inch. On the accompanying number line, graph the inequality that represents the recommended tire pressure.

ID: A

1

A.A.24: Solving Inequalities: Solve linear inequalities in one variableAnswer Section

1 ANS: 4

REF: 010425a 2 ANS: 4

−6x − 17 ≥ 8x + 25

−42 ≥ 14x

−3 ≥ x

REF: 081121ia 3 ANS: 1

3(2m− 1) ≤ 4m+ 7

6m− 3 ≤ 4m+ 7

2m ≤ 10

m ≤ 5


2(x − 4) ≥ 12 (5 − 3x)

4(x − 4) ≥ 5 − 3x

4x − 16 ≥ 5 − 3x

7x ≥ 21

x ≥ 3

REF: 011234 5 ANS: 4

10× 8+ 12 π × 42 = 80+ 8π

REF: 080815a 6 ANS: 2 REF: 060001a 7 ANS: 4 REF: 080411a 8 ANS: 2 REF: 060616a 9 ANS: 1 REF: 010610a

ID: A

2

10 ANS: 2

.

REF: 010312a 11 ANS:

REF: 060532a

Regents Exam Questions Name: ________________________ A.A.25: Solving Equations with Decimalswww.jmap.org

1

A.A.25: Solving Equations with Decimals: Solve equations involving fractional expressions. Note: Expressions which result in linear equations in one variable.

1 If 0.02x 0.7 0.8, then x is equal to1) 0.52) 23) 54) 50

2 What is the value of w in the equation 0.04w 0.6 2.4?1) 0.0452) 0.453) 4.54) 45

3 What is the value of n in the equation 0.6(n 10) 3.6?1) 0.42) 53) 44) 4

4 The value of y in the equation 0.06y 200 0.03y 350 is1) 500

2) 1,666. 63) 5,000

4) 18,333. 3

5 Solve for m: 0.6m 3 2m 0.2

6 Solve for x: 0.35x 0.6 0.1x 1

7 Solve for x: 2(x 3) 1.2 x

8 Solve for x: 3.3 x 3(x 1.7)

9 A candy store sells 8-pound bags of mixed hazelnuts and cashews. If c pounds of cashews are in a bag, the price p of the bag can be found using the formula p 2.59c 1.72(8 c). If one bag is priced at $18.11, how many pounds of cashews does it contain?

ID: A

1

A.A.25: Solving Equations with Decimals: Solve equations involving fractional expressions. Note: Expressions which result in linear equations in one variable.Answer Section

1 ANS: 3

REF: 010906a 2 ANS: 4

REF: 060804a 3 ANS: 3

REF: 080406a 4 ANS: 3

0.06y 200 0.03y 350

0.03y 150

y 5,000


2.

REF: 060323a 6 ANS:

1.6.

REF: 080831a

ID: A

2

7 ANS:

2.4.

REF: 089921a 8 ANS:

2.1.

REF: 060634a 9 ANS:

5.

REF: 010635a

Regents Exam Questions Name: ________________________ A.A.25: Solving Equations with Fractional Expressions 1www.jmap.org

1

A.A.25: Solving Equations with Fractional Expressions 1: Solve equations involving fractional expressions. Note: Expressions which result in linear equations in one variable.

1 What is the solution set of the equation x5 x

2 14?

1) {4}2) {10}3) {20}4) {49}

2 What is the value of x in the equation x2 x

6 2?

1) 122) 83) 3

4)14

3 Which value of x is the solution of the equation 2x3 x

6 5?

1) 62) 103) 154) 30

4 Which value of x is the solution of the equation 23

x 12 5

6?

1)12

2) 2

3)23

4)32

5 In the equation 14

n 5 512

, n is equal to

1) 82) 2

3)12

4)18

6 What is the value of x in the equation 34

x 2 54

x 6?

1) 162) 163) 44) 4


2

7 What is the value of w in the equation 34

w 8 13

w 7?

1) 2.42) 0.23) 13.8464) 36


w 7 2w 2?

1) 62) 2

3) 313

4) 3.6

9 Solve for x: 35

(x 2) x 4

1) 82) 133) 154) 23

10 Which value of x is the solution of 2x5 1

3 7x 2

15?

1)35

2)3126

3) 34) 7

11 Which value of x is the solution of x3 x 1

2 x?

1) 12) 13) 34) 3

12 The number of people on the school board is represented by x. Two subcommittees with an equal number of members are formed, one with 23

x 5 members and the other x4

with members.

How many people are on the school board?1) 202) 123) 84) 4

13 Solve for x: 116

x 14 1

2

14 Solve for x: x 3

2 2x

7 7

15 Solve for x: x 3

5 4x

3 4

16 Solve for m: m5

3(m 1)2

2(m 3)

ID: A

1

A.A.25: Solving Equations with Fractional Expressions 1: Solve equations involving fractional expressions. Note: Expressions which result in linear equations in one variable.Answer Section

1 ANS: 3

REF: 010507a 2 ANS: 3

REF: 010719a 3 ANS: 1

(2x 6) (3 x)3 6

5

12x 3x18

5

15x 90

x 6

REF: 060907ia 4 ANS: 1

2x3 1

2 5

6

2x3

13

6x 3

x 12

REF: 011112ia

ID: A

2

5 ANS: 2

REF: 080708a 6 ANS: 2

REF: 010204a 7 ANS: 4

REF: 080620a 8 ANS: 1

REF: 060704a 9 ANS: 2

35

(x 2) x 4

3(x 2) 5(x 4)

3x 6 5x 20

26 2x

x 13

REF: 080909ia

ID: A

3

10 ANS: 4

2x5 1

3 7x 2

15

(2x 3) (5 1)5 3

7x 215

6x 515

7x 215

6x 5 7x 2

x 7

REF: 080820ia 11 ANS: 3

x3 x 1

2 x

2x 3(x 1)6

x

5x 3 6x

3 x

REF: 061019ia 12 ANS: 2

REF: 060418a 13 ANS:

4. . .

REF: 010636a

ID: A

4

14 ANS: 7


3


m5

3(m 1)2

2(m 3)

2m10

15(m 1)

10 2m 6

17m 1510

2m 6

17m 15 20m 60

45 3m

15 m

REF: 081139ia


1


1 What is the solution set of the equation x5 x

2 14?

2 What is the value of x in the equation x2 x

6 2?

3 Which value of x is the solution of the equation 2x3 x

6 5?

4 Which value of x is the solution of the equation 23

x 12 5

6?

1)12

2) 2

3)23

4)32

5 In the equation 14

n 5 512

, n is equal to

6 What is the value of x in the equation 34

x 2 54

x 6?


w 8 13

w 7?


w 7 2w 2?

9 Solve for x: 35

(x 2) x 4

10 Which value of x is the solution of 2x5 1

3 7x 2

15?

11 Which value of x is the solution of x3 x 1

2 x?

12 The number of people on the school board is represented by x. Two subcommittees with an equal number of members are formed, one with 23

x 5 members and the other x4

with members.

How many people are on the school board?

13 Solve for x: 116

x 14 1

2

14 Solve for x: x 3

2 2x

7 7

15 Solve for x: x 3

5 4x

3 4

16 Solve for m: m5

3(m 1)2

2(m 3)

ID: A

1


1 ANS: {20}

REF: 010507a 2 ANS:

3

REF: 010719a 3 ANS:

6

(2x 6) (3 x)3 6

5

12x 3x18

5

15x 90

x 6

REF: 060907ia

ID: A

2

4 ANS: 12x3 1

2 5

6

2x3

13

6x 3

x 12


2

REF: 080708a 6 ANS:

16

REF: 010204a 7 ANS:

36

REF: 080620a

ID: A

3

8 ANS: 6

REF: 060704a 9 ANS:

1335

(x 2) x 4

3(x 2) 5(x 4)

3x 6 5x 20

26 2x

x 13

REF: 080909ia 10 ANS:

7

2x5 1

3 7x 2

15

(2x 3) (5 1)5 3

7x 215

6x 515

7x 215

6x 5 7x 2

x 7

REF: 080820ia

ID: A

4

11 ANS: 3

x3 x 1

2 x

2x 3(x 1)6

x

5x 3 6x

3 x

REF: 061019ia 12 ANS:

12

REF: 060418a 13 ANS:

4. . .

REF: 010636a 14 ANS:

7


3

REF: 069803siii

ID: A

5

16 ANS: m5

3(m 1)2

2(m 3)

2m10

15(m 1)

10 2m 6

17m 1510

2m 6

17m 15 20m 60

45 3m

15 m

REF: 081139ia


1


1 Solve: 3x 1

3 4x 5

4 8 x

6 2x 5

8

2 Solve: x 3

2 x 3

3 x 4x 2

6 x

3 5

3 Solve: 2x 1 2x 22

3x 15

x 14

ID: A

1


1 ANS:

52

REF: 019104al 2 ANS:

5


52

REF: 069805al

Regents Exam Questions A.A.26: Solving Rationals 1 Name: ________________________ www.jmap.org

1

A.A.26: Solving Rationals 1: Solve algebraic proportions in one variable which result in linear or quadratic equations

1 What is the solution of k 4

2 k 9

3?

1) 12) 53) 64) 14

2 Which value of x is the solution of 2x 3x 4

23

?

1) 14

2)14

3) 44) 4

3 What is the value of x in the equation 2x 3 26

x?

1) 8

2) 18

3)18

4) 8

4 Which value of x is a solution of 5x x 13

6?

1) 22) 33) 104) 15

5 What is the solution set of x 2x 2

3x

?

1) {2,3}2) {3,2}3) {1,6}4) {6,1}

6 What is the solution of 2

x 1 x 1

2?

1) 1 and 32) 1 and 33) 1 and 34) 1 and 3

7 Solve algebraically for x: x 2

6 3

x 1

8 Solve for x: x 1

x 7

x 12

9 Solve algebraically for x: 34(x 11)

4x 1

2x

ID: A

1

A.A.26: Solving Rationals 1: Solve algebraic proportions in one variable which result in linear or quadratic equationsAnswer Section

1 ANS: 3

k 42

k 93

3(k 4) 2(k 9)

3k 12 2k 18

k 6

REF: 010906ia 2 ANS: 2

2x 3x 4

23

3(2x 3) 2(x 4)

6x 9 2x 8

4x 1

x 14

REF: 081012ia 3 ANS: 1

2x 3 26

x

3 24x

x 8

REF: 010918ia

ID: A

2

4 ANS: 4

5x x 13

6

x 2 13x 30

x 2 13x 30 0

(x 15)(x 2) 0

x 15 or 2

REF: 060826ia 5 ANS: 4

x 2x 2

3x

x(x 2) 3(x 2)

x 2 2x 3x 6

x 2 5x 6 0

(x 6)(x 1) 0

x 6 or 1

REF: 011028ia 6 ANS: 3

2x 1

x 12

x 2 2x 1 4

x 2 2x 3 0

(x 3)(x 1) 3

x 3,1

REF: 081226ia

ID: A

3

7 ANS:

4,5. x 2

6 3

x 1

(x 2)(x 1) 18

x 2 x 2x 2 18

x 2 x 20 0

(x 5)(x 4) 0

x 5or 4


6,2. x 1

x 7

x 12

(x 1)(x 12) 7x

x 2 11x 12 7x

x 2 4x 12 0

(x 6)(x 2) 0

x 6 or 2


94

. 34(x 11)

4x 1

2x

34 x 11

4x 2

4x

34 x 9

4x

12x 4x 36

16x 36

x 94

REF: 061137ia

Regents Exam Questions A.A.26: Solving Rationals 2 Name: ________________________ www.jmap.org

1

A.A.26: Solving Rationals 2: Solve algebraic proportions in one variable which result in linear or quadratic equations

1 What is the value of x in the equation x

2x 1 4

3?

1) 15

2) 45

3) 54

4) 5

2 If 5n 1

2 3

6n, what is the value of n?

1) 22) 23) 9

4)27

3 Solve for r: 1r 1

2 1

3

4 Solve for x: 115

110

1x

5 Solve: 2x 1 1

4

6 Solve for y: 53y

64y

16

7 Solve for x: 54x

63x

112

8 Solve for y: 4

5y 3 2

3y 4

9 Solve algebraically for x: 1x x 1

6

10 Solve for all values of x that satisfy the equation x

x 3 5

x 7.

11 Solve for all values of x: 2

x 1 x

12 Solve for the positive value of x: x3 4

x 4

3

ID: A

1

A.A.26: Solving Rationals 2: Solve algebraic proportions in one variable which result in linear or quadratic equationsAnswer Section

1 ANS: 2

REF: 060612a 2 ANS: 3

REF: 010825a 3 ANS:

65


6


83


1


9

REF: 010204siii

ID: A

2

8 ANS: 11


2, 3.

REF: 010131a 10 ANS:

3, 5.

REF: 080439a 11 ANS:

1, 2.

REF: 080722b 12 ANS:

6

REF: 089809siii

Regents Exam Questions A.A.27: Solving Quadratics by Factoring Name: ________________________ www.jmap.org

1

A.A.27: Solving Quadratics by Factoring: Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots

1 What is the solution set of the equation 3x2 48?1) {2,8}2) {2,8}3) {4,4}4) {4,4}

2 What is the solution set of the equation x2 5x 0?1) {0,5}2) {0,5}3) {0}4) {5}

3 The solution to the equation x2 6x 0 is1) 0, only2) 6, only3) 0 and 6

4) 6

4 The solution set for the equation x2 2x 15 0 is1) {5,3}2) {5,3}3) {5,3}4) {5,3}

5 What is the solution set of m2 3m10 0?1) {5,2}2) {2,5}3) {3,10}4) {3,10}

6 What is the solution set of the equation

x2 5x 24 0?1) {3,8}2) {3,8}3) {3,8}4) {3,8}

7 What is the solution set for the equation

x2 5x 6 0?1) {6,1}2) {6,1}3) {2,3}4) {2,3}

8 What is the solution set of the equation

x2 11x 28 0?1) {7,4}2) {7,4}3) {3,4}4) {3,4}

9 The solution set of the equation x2 4x 12 0 is 1) {6,2}2) {4,3}3) {2,6}4) {3,4}

10 The solution set for the equation x2 5x 6 is1) {1,6}2) {2,3}3) {1,6}4) {2,3}

11 What is the positive solution of the equation

4x2 36 0?

12 Solve for x: x2 2x 24 0



15 Solve: (x 3)(x 3) 6x 14

ID: A

1

A.A.27: Solving Quadratics by Factoring: Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral rootsAnswer Section

1 ANS: 3

PTS: 2 REF: 010215a 2 ANS: 2

PTS: 2 REF: 010727a 3 ANS: 3

x2 6x 0

x(x 6) 0

x 0 x 6

PTS: 2 REF: 080921ia 4 ANS: 2

PTS: 2 REF: 080012a 5 ANS: 1

PTS: 2 REF: 080118a

ID: A

2

6 ANS: 1

PTS: 2 REF: 060313a 7 ANS: 4

PTS: 2 REF: 010520a 8 ANS: 2

PTS: 2 REF: 060514a 9 ANS: 3

PTS: 2 REF: 060725a 10 ANS: 3

PTS: 2 REF: 080525a 11 ANS:

3.

PTS: 2 REF: 080733a

ID: A

3

12 ANS:

6,4.

PTS: 3 REF: 010637a 13 ANS:

8 and 5.

PTS: 3 REF: 089926a 14 ANS:

7 and 4.

PTS: 3 REF: 060229a 15 ANS:

1, 5


Regents Exam Questions A.A.28: Roots of Quadratics Name: ________________________ www.jmap.org

1

A.A.28: Roots of Quadratics: Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression

1 What are the roots of the equation

x 2 10x 21 0?1) 1 and 212) 5 and 53) 3 and 74) 3 and 7

2 What are the roots of the equation x 2 5x 6 0?1) 1 and 62) 2 and 33) 1 and 64) 2 and 3

3 What are the roots of the equation x 2 7x 6 0?1) 1 and 72) 1 and 73) 1 and 64) 1 and 6

4 The roots of the equation 3x 2 27x 0 are1) 0 and 92) 0 and 93) 0 and 34) 0 and 3

5 One of the roots of the equation x 2 3x 18 0 is 3. What is the other root?1) 152) 63) 64) 21

6 The larger root of the equation (x 4)(x 3) 0 is1) 42) 33) 34) 4

7 Find the roots of the equation x 2 x 6 algebraically.

8 Find the roots of the equation x 2 30 13x algebraically.

9 Which equation has roots of 3 and 5?

1) x 2 2x 15 02) x 2 2x 15 03) x 2 2x 15 04) x 2 2x 15 0

10 Which equation has the solution set {1,3}?

1) x 2 4x 3 02) x 2 4x 3 03) x 2 4x 3 04) x 2 4x 3 0

11 For which equation is the solution set {5,2}?

1) x 2 3x 10 02) x 2 3x 103) x 2 3x 104) x 2 3x 10 0

12 Form the quadratic equation whose roots are 5 and 7.

13 The two roots of an equation are 4 and 3. Form the equation.

ID: A

1

A.A.28: Roots of Quadratics: Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expressionAnswer Section

1 ANS: 3

x 2 10x 21 0

(x 7)(x 3) 0

x 7 x 3

REF: 010914ia 2 ANS: 2

x 2 5x 6 0

(x 3)(x 2) 0

x 3 x 2

REF: 081120ia 3 ANS: 4

x 2 7x 6 0

(x 6)(x 1) 0

x 6 x 1

REF: 060902ia 4 ANS: 1

3x 2 27x 0

3x(x 9) 0

x 0,9

REF: 011223ia 5 ANS: 3

REF: 080622a 6 ANS: 3

The two roots are 4 and 3. The larger root is 3.

REF: 069909a

ID: A

2

7 ANS:

2, 3. x2 x 6

x 2 x 6 0

(x 3)(x 2) 0

x 3 or 2


15,2 x 2 13x 30 0

(x 15)(x 2) 0

x 15,2

REF: 081036ia 9 ANS: 2

x 2 2x 15 0

(x 5)(x 3) 0

x 5 x 3

REF: 011128ia 10 ANS: 1

x 2 4x 3 0

(x 3)(x 1) 0

x 3 x 1

REF: 010913a 11 ANS: 1

REF: 080825a 12 ANS:

x 2 2x 35 0

REF: 019012al 13 ANS:

x 2 x 12 0

REF: 119207al

Regents Exam Questions A.A.29: Set Theory 1 Name: ________________________ www.jmap.org

1

A.A.29: Set Theory 1: Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form

1 Which interval notation represents the set of all numbers from 2 through 7, inclusive?1) (2,7]2) (2,7)3) [2,7)4) [2,7]

2 Which interval notation represents the set of all numbers greater than or equal to 5 and less than 12?1) [5,12)2) (5,12]3) (5,12)4) [5,12]

3 In interval notation, the set of all real numbers greater than 6 and less than or equal to 14 is represented by1) (6,14)2) [6,14)3) (6,14]4) [6,14]

4 Which interval notation represents the set of all real numbers greater than 2 and less than or equal to 20?1) (2,20)2) (2,20]3) [2,20)4) [2,20]

5 Which interval notation describes the set S {x | 1 x 10}?1) [1,10]2) (1,10]3) [1,10)4) (1,10)

6 Which set-builder notation describes {3,2,1,0,1,2}?1) {x | 3 x 2, where x is an integer}2) {x | 3 x 2, where x is an integer}3) {x | 3 x 2, where x is an integer}4) {x | 3 x 2, where x is an integer}

7 Which set builder notation describes {2,1,0,1,2,3}?1) {x | 3 x 3, where x is an integer}2) {x | 3 x 4, where x is an integer}3) {x | 2 x 3, where x is an integer}4) {x | 2 x 4, where x is an integer}

8 The set {1,2,3,4} is equivalent to1) {x | 1 x 4, where x is a whole number}2) {x | 0 x 4, where x is a whole number}3) {x | 0 x 4, where x is a whole number}4) {x | 1 x 4, where x is a whole number}

9 The set {11,12} is equivalent to1) {x | 11 x 12, where x is an integer}2) {x | 11 x 12, where x is an integer}3) {x | 10 x 12, where x is an integer}4) {x | 10 x 12, where x is an integer}

10 Which notation describes {1,2,3}?1) {x | 1 x 3, where x is an integer}2) {x | 0 x 3, where x is an integer}3) {x | 1 x 3, where x is an integer}4) {x | 0 x 3, where x is an integer}

ID: A

1

A.A.29: Set Theory 1: Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster formAnswer Section

1 ANS: 4 REF: fall0704ia 2 ANS: 1 REF: 061021ia 3 ANS: 3 REF: 081117ia 4 ANS: 2 REF: 011119ia 5 ANS: 3 REF: 061217ia 6 ANS: 4 REF: 081022ia 7 ANS: 4 REF: 011222ia 8 ANS: 3 REF: 010917ia 9 ANS: 4 REF: 060930ia 10 ANS: 2 REF: 061128ia


1

A.A.29: Set Theory 2: Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form

1 Which interval notation represents the set of all numbers from 2 through 7, inclusive?

2 Which interval notation represents the set of all numbers greater than or equal to 5 and less than 12?

3 In interval notation, the set of all real numbers greater than 6 and less than or equal to 14 is represented by

4 Which interval notation represents the set of all real numbers greater than 2 and less than or equal to 20?

5 Which interval notation describes the set S {x | 1 x 10}?

6 Which set-builder notation describes {3,2,1,0,1,2}?

7 Which set builder notation describes {2,1,0,1,2,3}?

8 The set {1,2,3,4} is equivalent to1) {x | 1 x 4, where x is a whole number}2) {x | 0 x 4, where x is a whole number}3) {x | 0 x 4, where x is a whole number}4) {x | 1 x 4, where x is a whole number}

9 The set {11,12} is equivalent to1) {x | 11 x 12, where x is an integer}2) {x | 11 x 12, where x is an integer}3) {x | 10 x 12, where x is an integer}4) {x | 10 x 12, where x is an integer}

10 Which notation describes {1,2,3}?1) {x | 1 x 3, where x is an integer}2) {x | 0 x 3, where x is an integer}3) {x | 1 x 3, where x is an integer}4) {x | 0 x 3, where x is an integer}

ID: A

1

A.A.29: Set Theory 2: Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster formAnswer Section

1 ANS: [2,7]


[5,12)


(6,14]


(2,20]


[1,10)


{x | 3 x 2, where x is an integer}


{x | 2 x 4, where x is an integer}

REF: 011222ia 8 ANS: 3 REF: 010917ia 9 ANS: 4 REF: 060930ia 10 ANS: 2 REF: 061128ia

Regents Exam Questions A.A.30: Set Theory Name: ________________________ www.jmap.org

1

A.A.30: Set Theory: Find the complement of a subset of a given set, within a given universe

1 If the universal set is {pennies, nickels, dimes, quarters}, what is the complement of the set {nickels}?1) { }2) {pennies, quarters}3) {pennies, dimes, quarters}4) {pennies, nickels, dimes, quarters}

2 Given: Set U {S,O,P,H,I,A}

Set B {A,I,O}If set B is a subset of set U, what is the complement of set B?1) {O,P,S}2) {I,P,S}3) {A,H,P}4) {H,P,S}

3 Given: U {1,2,3,4,5,6,7,8}

B {2,3,5,6}Set B is a subset of set U. What is the complement of set B?1) { }2) {2,3,5,6}3) {1,4,7,8}4) {1,2,3,4,5,6,7,8}

4 Given:A {All even integers from 2 to 20, inclusive}

B {10,12,14,16,18}What is the complement of set B within the universe of set A?1) {4,6,8}2) {2,4,6,8}3) {4,6,8,20}4) {2,4,6,8,20}

5 Consider the set of integers greater than 2 and less than 6. A subset of this set is the positive factors of 5. What is the complement of this subset?1) {0,2,3,4}2) {1,0,2,3,4}3) {2,1,0,2,3,4,6}4) {2,1,0,1,2,3,4,5,6}

6 Twelve players make up a high school basketball team. The team jerseys are numbered 1 through 12. The players wearing the jerseys numbered 3, 6, 7, 8, and 11 are the only players who start a game. Using set notation, list the complement of this subset.

ID: A

1

A.A.30: Set Theory: Find the complement of a subset of a given set, within a given universeAnswer Section

1 ANS: 3 REF: 081103ia 2 ANS: 4 REF: 061001ia 3 ANS: 3 REF: 081009ia 4 ANS: 4

A {2,4,6,8,10,12,14,16,18,20}

REF: 080912ia 5 ANS: 2

The set of integers greater than -2 and less than 6 is {1,0,1,2,3,4,5}. The subset of this set that is the positive factors of 5 is {1,5}. The complement of this subset is {1,0,2,3,4}.


{1,2,4,5,9,10,12}

REF: 080833ia


1

A.A.31: Set Theory 1: Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)

1 Given: A = {2,4,5,7,8}

B = {3,5,8,9}What is A∪B?1) {5}2) {5,8}3) {2,3,4,7,9}4) {2,3,4,5,7,8,9}

2 Given: A = {3,6,9,12,15}

B = {2,4,6,8,10,12}What is the union of sets A and B?1) {6}2) {6,12}3) {2,3,4,8,9,10,15}4) {2,3,4,6,8,9,10,12,15}

3 Given:Set A = {(−2,−1),(−1,0),(1,8)}

Set B = {(−3,−4),(−2,−1),(−1,2),(1,8)}.What is the intersection of sets A and B?1) {(1,8)}2) {(−2,−1)}3) {(−2,−1),(1,8)}4) {(−3,−4),(−2,−1),(−1,2),(−1,0),(1,8)}

4 Given: Q = {0,2,4,6}

W = {0,1,2,3}

Z = {1,2,3,4}What is the intersection of sets Q, W, and Z?1) {2}2) {0,2}3) {1,2,3}4) {0,1,2,3,4,6}

5 Given: X = {1,2,3,4}

Y = {2,3,4,5}

Z = {3,4,5,6}What is the intersection of sets X, Y, and Z?1) {3,4}2) {2,3,4}3) {3,4,5}4) {1,2,3,4,5,6}

6 If A = {0,1,3,4,6,7), B = {0,2,3,5,6), and C = {0,1,4,6,7), then A∩B∩C is1) {0,1,2,3,4,5,6,7}2) {0,3,6}3) {0,6}4) {0}


2

7 Which set represents the intersection of sets A, B, and C shown in the diagram below?

1) {3,4,5,6,7}2) {2}3) {2,3,4,5,6,7}4) {1,2,3,4,5,6,7,8,9}

8 Given: A = {1,3,5,7,9}

B = {2,4,6,8,10}

C = {2,3,5,7}

D = {1,2,3,4,5,6,7,8,9,10}What statement is false?1) A∪B∪C = D2) A∩B∩C = {}3) A∪C = {1,2,3,5,7}4) A∩C = {3,5,7}

9 Maureen tracks the range of outdoor temperatures over three days. She records the following information.

Express the intersection of the three sets as an inequality in terms of temperature, t.

ID: A

1

A.A.31: Set Theory 1: Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)Answer Section

1 ANS: 4 REF: 011225ia 2 ANS: 4 REF: 061123ia 3 ANS: 3 REF: fall0710ia 4 ANS: 1 REF: 011004ia 5 ANS: 1 REF: 011101ia 6 ANS: 3 REF: 061208ia 7 ANS: 2 REF: 081003ia 8 ANS: 3

A∪C = {1,2,3,5,7,9}

REF: 081221IA 9 ANS:

0 ≤ t ≤ 40

REF: 060833ia


1

A.A.31: Set Theory 2: Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)

1 Given: A = {2,4,5,7,8}

B = {3,5,8,9}What is A∪B?

2 Given: A = {3,6,9,12,15}

B = {2,4,6,8,10,12}What is the union of sets A and B?

3 Given:Set A = {(−2,−1),(−1,0),(1,8)}

Set B = {(−3,−4),(−2,−1),(−1,2),(1,8)}.What is the intersection of sets A and B?

4 Given: Q = {0,2,4,6}

W = {0,1,2,3}

Z = {1,2,3,4}What is the intersection of sets Q, W, and Z?

5 Given: X = {1,2,3,4}

Y = {2,3,4,5}

Z = {3,4,5,6}What is the intersection of sets X, Y, and Z?

6 If A = {0,1,3,4,6,7), B = {0,2,3,5,6), and C = {0,1,4,6,7), then A∩B∩C is

7 Which set represents the intersection of sets A, B, and C shown in the diagram below?

8 Given: A = {1,3,5,7,9}

B = {2,4,6,8,10}

C = {2,3,5,7}

D = {1,2,3,4,5,6,7,8,9,10}What statement is false?1) A∪B∪C = D2) A∩B∩C = {}3) A∪C = {1,2,3,5,7}4) A∩C = {3,5,7}

9 Maureen tracks the range of outdoor temperatures over three days. She records the following information.

Express the intersection of the three sets as an inequality in terms of temperature, t.

ID: A

1

A.A.31: Set Theory 2: Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)Answer Section

1 ANS: {2,3,4,5,7,8,9}


{2,3,4,6,8,9,10,12,15}


{(−2,−1),(1,8)}


{2}


{3,4}


{0,6}


{2}

REF: 081003ia 8 ANS: 3

A∪C = {1,2,3,5,7,9}

REF: 081221IA 9 ANS:

0 ≤ t ≤ 40

REF: 060833ia

Regents Exam Questions A.A.32: Slope Name: ________________________ www.jmap.org

1

A.A.32: Slope: Explain slope as a rate of change between dependent and independent variables

1 In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate. The slope of this line is1) zero2) negative3) positive4) undefined

2 In a given linear equation, the value of the independent variable decreases at a constant rate while the value of the dependent variable increases at a constant rate. The slope of this line is1) positive2) negative3) zero4) undefined

3 If the value of dependent variable y increases as the value of independent variable x increases, the graph of this relationship could be a1) horizontal line2) vertical line3) line with a negative slope4) line with a positive slope

4 The data in the table below are graphed, and the slope is examined.

The rate of change represented in this table can be described as1) negative2) positive3) undefined4) zero

ID: A

1

A.A.32: Slope: Explain slope as a rate of change between dependent and independent variablesAnswer Section

1 ANS: 2 REF: 080823ia 2 ANS: 2 REF: 081223ia 3 ANS: 4 REF: 080417a 4 ANS: 1 REF: 081115ia

Regents Exam Questions A.A.33: Slope 1 Name: ________________________ www.jmap.org

1

A.A.33: Slope 1: Determine the slope of a line, given the coordinates of two points on the line

1 What is the slope of the line containing the points (3,4) and (−6,10)?

1) 12

2) 2

3) −23

4) −32

2 What is the slope of the line that passes through the points (−6,1) and (4,−4)?1) −22) 2

3) −12

4) 12

3 What is the slope of the line that passes through the points (2,5) and (7,3)?

1) −52

2) −25

3) 89

4) 98

4 What is the slope of the line passing through the points (−2,4) and (3,6)?

1) −52

2) −25

3) 25

4) 52

5 What is the slope of the line that passes through the points (3,5) and (−2,2)?

1) 15

2) 35

3) 53

4) 5

6 What is the slope of the line that passes through the points (2,−3) and (5,1)?

1) −23

2) 23

3) −43

4) 43

7 What is the slope of the line that passes through the points (−5,4) and (15,−4)?

1) −25

2) 0

3) −52

4) undefined


2

8 What is the slope of the line passing through the points A and B, as shown on the graph below?

1) −3

2) −13

3) 3

4) 13

9 What is the slope of line shown in the accompanying diagram?

1) 43

2) 34

3) −34

4) −43

10 What is the slope of line in the accompanying diagram?

1) −32

2) −23

3) 23

4) 32

11 In the diagram below, what is the slope of the line passing through points A and B?

1) −22) 2

3) −12

4) 12

ID: A

1

A.A.33: Slope 1: Determine the slope of a line, given the coordinates of two points on the lineAnswer Section

1 ANS: 3

m = 4 − 103− (−6) = −

23


m =1− (−4)−6 − 4 = −1

2

REF: 060820ia 3 ANS: 2

m = 5− 32− 7 = −2

5

REF: 010913ia 4 ANS: 3

m = 6 − 43− (−2) =

25

REF: 061110ia 5 ANS: 2

m = 5 − 23− (−2) =

35

REF: 061004ia 6 ANS: 4

m = −3− 12− 5 = −4

−3 = 43

REF: 011215ia 7 ANS: 1

m =4− (−4)−5 − 15 = −2

5

REF: 080915ia 8 ANS: 2

A(−3,8) and B(3,6). m = 8− 6−3− 3 = 2

−6 = −13

REF: 081005ia

ID: A

2

9 ANS: 1

m = −4− 00− 3 = 4

3

REF: 069918a 10 ANS: 2

m = 2− 00− 3 = −2

3

REF: 010115a 11 ANS: 4

A(−3,4) and B(5,8). m = 4− 8−3− 5 = −4

−8 = 12

REF: 011007ia


1


1 What is the slope of the line containing the points (3,4) and (−6,10)?


3 What is the slope of the line that passes through the points (2,5) and (7,3)?

4 What is the slope of the line passing through the points (−2,4) and (3,6)?

5 What is the slope of the line that passes through the points (3,5) and (−2,2)?

6 What is the slope of the line that passes through the points (2,−3) and (5,1)?


8 What is the slope of the line passing through the points A and B, as shown on the graph below?

9 What is the slope of line shown in the accompanying diagram?

10 What is the slope of line in the accompanying diagram?

11 In the diagram below, what is the slope of the line passing through points A and B?

ID: A

1


Answer Section

1 ANS:

−23

m = 4 − 103− (−6) = −

23


−12

m =1− (−4)−6 − 4 = −1

2


−25

m = 5− 32− 7 = −2

5


25

m = 6 − 43− (−2) =

25


35

m = 5 − 23− (−2) =

35


43

m = −3− 12− 5 = −4

−3 = 43

REF: 011215ia

ID: A

2

7 ANS:

−25

m =4− (−4)−5 − 15 = −2

5


−13

A(−3,8) and B(3,6). m = 8− 6−3− 3 = 2

−6 = −13


43

m = −4− 00− 3 = 4

3

REF: 069918a 10 ANS:

−23

m = 2− 00− 3 = −2

3

REF: 010115a 11 ANS:

12

A(−3,4) and B(5,8). m = 4− 8−3− 5 = −4

−8 = 12

REF: 011007ia

Regents Exam Questions A.A.34: Writing Linear Equations Name: ________________________ www.jmap.org

1

A.A.34: Writing Linear Equations: Write the equation of a line, given its slope and the coordinates of a point on the line

1 What is an equation of the line that passes through the point (4,6) and has a slope of 3?1) y 3x 62) y 3x 63) y 3x 104) y 3x 14

2 What is an equation of the line that passes through the point (3,1) and has a slope of 2?1) y 2x 52) y 2x 13) y 2x 44) y 2x 7

3 Which equation represents the line that passes through the point (1,5) and has a slope of 2?1) y 2x 72) y 2x 113) y 2x 94) y 2x 3

4 An equation of the line that has a slope of 3 and a y-intercept of 2 is1) x 3y 22) y 3x 2

3) y 23

x

4) y 2x 3

5 Which equation represents the line whose slope is 2 and whose y-intercept is 6?1) y 2x 62) y 6x 23) 2y 6x 04) y 2x 6

6 Which equation represents a line that has a slope of 34

and passes through the point (2,1)?

1) 3y 4x 52) 3y 4x 23) 4y 3x 24) 4y 3x 5

7 If point (1,0) is on the line whose equation is y 2x b , what is the value of b?1) 12) 23) 34) 0

8 A line having a slope of 34

passes through the point

(8,4). Write the equation of this line in slope-intercept form.

ID: A

1

A.A.34: Writing Linear Equations: Write the equation of a line, given its slope and the coordinates of a point on the lineAnswer Section

1 ANS: 1y mx b

6 (3)(4) b

b 6

REF: 060922ia 2 ANS: 4

y mx b

1 (2)(3) b

b 7

REF: 080927ia 3 ANS: 1

y mx b

5 (2)(1) b

b 7

REF: 081108ia 4 ANS: 2 REF: 010408a 5 ANS: 1 REF: 010905a 6 ANS: 3

y mx b

1 34

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃(2) b

1 32 b

b 12

y 34

x 12

4y 3x 2

REF: 081219ia 7 ANS: 2

REF: 060521a

ID: A

2

8 ANS:

y 34

x 10. y mx b

4 34

(8) b

4 6 b

10 b

REF: 011134ia

Regents Exam Questions A.A.35: Writing Linear Equations Name: ________________________ www.jmap.org

1

A.A.35: Writing Linear Equations: Write the equation of a line, given the coordinates of two points on the line

1 What is an equation for the line that passes through the coordinates (2,0) and (0,3)?

1) y 32

x 3

2) y 32

x 3

3) y 23

x 2

4) y 23

x 2

2 Which equation represents the line that passes through the points (3,7) and (3,3)?

1) y 23

x 1

2) y 23

x 9

3) y 23

x 5

4) y 23

x 9

3 What is an equation of the line that passes through the points (1,3) and (8,5)?

1) y 1 27

(x 3)

2) y 5 27

(x 8)

3) y 1 27

(x 3)

4) y 5 27

(x 8)

4 What is an equation of the line that passes through the points (3,3) and (3,3)?1) y 32) x 33) y 34) x y

5 Write an equation that represents the line that passes through the points (5,4) and (5,0).

ID: A

1

A.A.35: Writing Linear Equations: Write the equation of a line, given the coordinates of two points on the lineAnswer Section

1 ANS: 1

m 3002

32

. Using the given y-intercept (0,3) to write the equation of the line y 32

x 3.

PTS: 2 REF: fall0713ia 2 ANS: 3

m 7333

46

23

y mx b

3 23

(3) b

3 2b

5 b

PTS: 2 REF: 011013ia 3 ANS: 2

m 5381

27

y y1 m(x xi)

y 5 27

(x 8)

PTS: 2 REF: 081029ia 4 ANS: 3 PTS: 2 REF: 010910ia 5 ANS:

y 25

x 2. m 405 (5)

25

. y mx b

4 25

(5) b

b 2

.


Regents Exam Questions A.A.36: Parallel and Perpendicular Lines Name: ________________________ www.jmap.org

1

A.A.36: Parallel and Perpendicular Lines: Write the equation of a line parallel to the x- or y-axis

1 Which equation represents a line parallel to the x-axis?1) x 52) y 10

3) x 13

y

4) y 5x 17

2 Which equation represents a line parallel to the x-axis?1) y 52) y 5x3) x 34) x 3y

3 Which equation represents a line parallel to the y-axis?1) x y2) x 43) y 44) y x 4

4 Which equation represents a line parallel to the y-axis?1) y x2) y 33) x y4) x 4

ID: A

1

A.A.36: Parallel and Perpendicular Lines: Write the equation of a line parallel to the x- or y-axisAnswer Section

1 ANS: 2 REF: 080810ia 2 ANS: 1 REF: 080911ia 3 ANS: 2 REF: 081014ia 4 ANS: 4 REF: 061112ia


1

A.A.37: Slope 1: Determine the slope of a line, given its equation in any form

1 What is the slope of the line whose equation is 2y = 5x + 4?1) 52) 2

3) 52

4) 25

2 What is the slope of the line whose equation is 3x − 7y = 9?

1) −37

2) 37

3) −73

4) 73

3 What is the slope of the line whose equation is 3x − 4y − 16 = 0?

1) 34

2) 43

3) 34) −4

4 What is the slope of the linear equation 5y − 10x = −15?1) 102) 23) −104) −15

5 The line represented by the equation 2y − 3x = 4 has a slope of

1) −32

2) 23) 3

4) 32

6 The accompanying figure shows the graph of the equation x = 5.

What is the slope of the line x = 5?1) 52) −53) 04) undefined

ID: A

1

A.A.37: Slope 1: Determine the slope of a line, given its equation in any formAnswer Section

1 ANS: 3

To solve for y, divide the equation by 2.

REF: 010203a 2 ANS: 2

m = −AB = −3

−7 = 37

REF: 011122ia 3 ANS: 1

REF: 089919a 4 ANS: 2

REF: 060205a 5 ANS: 4

m = −AB =

−(−3)2 = 3

2

REF: 061212ia 6 ANS: 4 REF: 060012a


1

A.A.37: Slope 2: Determine the slope of a line, given its equation in any form

1 What is the slope of the line whose equation is 2y = 5x + 4?

2 What is the slope of the line whose equation is 3x − 7y = 9?

3 What is the slope of the line whose equation is 3x − 4y − 16 = 0?

4 What is the slope of the linear equation 5y − 10x = −15?

5 The line represented by the equation 2y − 3x = 4 has a slope of

6 The accompanying figure shows the graph of the equation x = 5.

What is the slope of the line x = 5?

ID: A

1

A.A.37: Slope 2: Determine the slope of a line, given its equation in any formAnswer Section

1 ANS: 52

To solve for y, divide the equation by 2.

REF: 010203a 2 ANS:

37

m = −AB = −3

−7 = 37


34

REF: 089919a 4 ANS:

2

REF: 060205a 5 ANS:

32

m = −AB =

−(−3)2 = 3

2


undefined

REF: 060012a

Regents Exam Questions A.A.38: Parallel and Perpendicular Lines Name: ________________________ www.jmap.org

1

A.A.38: Parallel and Perpendicular Lines: Determine if two lines are parallel, given their equations in any form

1 Which equation represents a line that is parallel to the line y 4x 5?1) y 4x 3

2) y 14

x 5

3) y 14

x 3

4) y 4x 5

2 Which equation represents a line parallel to the line y 2x 5?1) y 2x 5

2) y 12

x 5

3) y 5x 24) y 2x 5

3 Which equation represents a line that is parallel to the line y 3 2x?1) 4x 2y 52) 2x 4y 13) y 3 4x4) y 4x 2

4 Which equation represents a line parallel to the graph of 2x 4y 16?

1) y 12

x 5

2) y 12

x 4

3) y 2x 64) y 2x 8

5 Which equation represents a line that is parallel to the line whose equation is 2x 3y 12?1) 6y 4x 22) 6y 4x 23) 4x 6y 24) 6x 4y 2

6 The graphs of the equations y 2x 7 and y kx 7 are parallel when k equals1) 22) 23) 74) 7

ID: A

1

A.A.38: Parallel and Perpendicular Lines: Determine if two lines are parallel, given their equations in any formAnswer Section

1 ANS: 1The slope of both is 4.

PTS: 2 REF: 060814ia 2 ANS: 1

The slope of both is 2.

PTS: 2 REF: 080009a 3 ANS: 1

The slope of y 3 2x is 2. Using m AB

, the slope of 4x 2y 5 is 42 2.

PTS: 2 REF: 010926ia 4 ANS: 1

The slope of 2x 4y 16 is AB

24

12

PTS: 2 REF: 011026ia 5 ANS: 2

Using m AB

, the slope of both 2x 3y 12 and 6y 4x 2 is 23

.

PTS: 2 REF: 010522a 6 ANS: 2

y kx 7 may be rewritten as y kx 7


Regents Exam Questions A.A.39: Identifying Points on a Line Name: ________________________ www.jmap.org

1

A.A.39: Identifying Points on a Line: Determine whether a given point is on a line, given the equation of the line

1 Which linear equation represents a line containing the point (1,3)?1) x 2y 52) x 2y 53) 2x y 54) 2x y 5

2 Which point lies on the line whose equation is 2x 3y 9?1) (1,3)2) (1,3)3) (0,3)4) (0,3)

3 Which point is on the line 4y 2x 0?1) (2,1)2) (2,1)3) (1,2)4) (1,2)

4 Which point lies on the graph represented by the equation 3y 2x 8?1) (2,7)2) (0,4)3) (2,4)4) (7,2)

5 Which set of coordinates is a solution of the equation 2x y 11?1) (6,1)2) (1,9)3) (0,11)4) (2,7)

6 The graph of the equation x 3y 6 intersects the y-axis at the point whose coordinates are1) (0,2)2) (0,6)3) (0,18)4) (6,0)

7 Point (k ,3) lies on the line whose equation is x 2y 2. What is the value of k?1) 82) 63) 64) 8

8 The graph of the equation 2x 6y 4 passes through point (x,2). What is the value of x?1) 42) 83) 164) 4

ID: A

1

A.A.39: Identifying Points on a Line: Determine whether a given point is on a line, given the equation of the lineAnswer Section

1 ANS: 32(1)+3=5

REF: 061007ia 2 ANS: 4

2x 3y 9

2(0) 3(3) 9

0 9 9

REF: 081016ia 3 ANS: 1

4y 2x 0

4(1) 2(2) 0

4 4 0

REF: 011021ia 4 ANS: 4

3y 2x 8

3(2) 2(7) 8

6 14 8

REF: 011218ia 5 ANS: 4

2(2) (7) 11

REF: 081217ia 6 ANS: 1

REF: 080619a 7 ANS: 1

REF: 080628a

ID: A

2

8 ANS: 2

REF: 060721a

Regents Exam Questions A.A.40: Systems of Linear Inequalities Name: ________________________ www.jmap.org

1

A.A.40: Systems of Linear Inequalities: Determine whether a given point is in the solution set of a system of linear inequalities

1 Which ordered pair is in the solution set of the following system of inequalities?

y < 12 x + 4

y ≥ −x + 11) (−5,3)2) (0,4)3) (3,−5)4) (4,0)

2 Which ordered pair is in the solution set of the following system of linear inequalities?

y < 2x + 2

y ≥ −x − 11) (0,3)2) (2,0)3) (−1,0)4) (−1,−4)

3 Which coordinates represent a point in the solution set of the system of inequalities shown below?

y ≤ 12 x + 13

4x + 2y > 31) (−4,1)2) (−2,2)3) (1,−4)4) (2,−2)

4 Which ordered pair is in the solution set of the system of linear inequalities graphed below?

1) (1,−4)2) (−5,7)3) (5,3)4) (−7,−2)


2

5 Which point is a solution for the system of inequalities shown on the accompanying graph?

1) (−4,−1)2) (2,3)3) (1,1)4) (−2,2)

6 Which point is in the solution set of the system of inequalities shown in the accompanying graph?

1) (0,4)2) (2,4)3) (−4,1)4) (4,−1)

7 Which coordinate point is in the solution set for the system of inequalities shown in the accompanying graph?

1) (3,1)2) (2,2)3) (1,−1)4) (0,1)


3

8 Which ordered pair is in the solution set of the system of inequalities shown in the accompanying graph?

1) (0,0)2) (0,1)3) (1,5)4) (3,2)

9 Which point is in the solution set of the system of inequalities shown on the accompanying graph?

1) (0,0)2) (3,3)3) (5,2)4) (2,3)

10 Which ordered pair is in the solution set of the system of inequalities shown in the graph below?

1) (−2,−1)2) (−2,2)3) (−2,−4)4) (2,−2)

ID: A

1

A.A.40: Systems of Linear Inequalities: Determine whether a given point is in the solution set of a system of linear inequalitiesAnswer Section

1 ANS: 4 REF: 080825ia 2 ANS: 2 REF: 011023ia 3 ANS: 4 REF: 061222ia 4 ANS: 1 REF: 061010ia 5 ANS: 1 REF: 010922a 6 ANS: 3 REF: 010528a 7 ANS: 1 REF: 060620a 8 ANS: 4 REF: 080615a 9 ANS: 3 REF: 080822a 10 ANS: 2 REF: 081127ia

Regents Exam Questions Name: ________________________ A.A.41: Identifying the Vertex of a Quadratic Given Equation 1www.jmap.org

1

A.A.41: Identifying the Vertex of a Quadratic Given Equation 1: Determine the vertex and axis of symmetry of a parabola, given its equation

1 What are the vertex and axis of symmetry of the

parabola y x 2 16x 63?1) vertex: (8,1); axis of symmetry: x 82) vertex: (8,1); axis of symmetry: x 83) vertex: (8,1); axis of symmetry: x 84) vertex: (8,1); axis of symmetry: x 8

2 What is an equation of the axis of symmetry of the

parabola represented by y x2 6x 4?1) x 32) y 33) x 64) y 6

3 The equation of the axis of symmetry of the graph

of y 2x 2 3x 7 is

1) x 34

2) y 34

3) x 32

4) y 32

4 What is the vertex of the parabola represented by

the equation y 2x 2 24x 100?1) x 62) x 63) (6,28)4) (6,316)

5 The height, y, of a ball tossed into the air can be

represented by the equation y x 2 10x 3, where x is the elapsed time. What is the equation of the axis of symmetry of this parabola?1) y 52) y 53) x 54) x 5

6 Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the

parabola whose equation is y 2x 2 8x 3.

ID: A

1

A.A.41: Identifying the Vertex of a Quadratic Given Equation 1: Determine the vertex and axis of symmetry of a parabola, given its equationAnswer Section

1 ANS: 1

x b2a

(16)

2(1) 8. y (8)2 16(8) 63 1

REF: 060918ia 2 ANS: 1

x b2a

62(1)

3.

REF: 011127ia 3 ANS: 1

x b2a

(3)2(2)

34

.

REF: 011219ia 4 ANS: 3

x b2a

242(2)

6. y 2(6)2 24(6) 100 28

REF: 061214ia 5 ANS: 3

x b2a

102(1)

5.


(2,11).

REF: 080934ia


1


1 What is the turning point, or vertex, of the parabola whose equation is y = 3x 2 + 6x − 1?1) (1,8)2) (−1,−4)3) (−3,8)4) (3,44)

2 What are the coordinates of the turning point of the parabola whose equation is y = −x 2 + 4x + 1?1) (−2,−11)2) (−2,−3)3) (2,5)4) (2,13)

3 What is the minimum point of the graph of the equation y = 2x 2 + 8x + 9?1) (2,33)2) (2,17)3) (−2,−15)4) (−2,1)

4 The height of a swimmer’s dive off a 10-foot platform into a diving pool is modeled by the equation y = 2x2 − 12x + 10, where x represents the number of seconds since the swimmer left the diving board and y represents the number of feet above or below the water’s surface. What is the farthest depth below the water’s surface that the swimmer will reach?1) 6 feet2) 8 feet3) 10 feet4) 12 feet

5 A model rocket is launched from ground level. Its height, h meters above the ground, is a function of time t seconds after launch and is given by the equation h = −4.9t2 + 68.6t. What would be the maximum height, to the nearest meter, attained by the model?1) 2432) 2423) 2414) 240

6 When a current, I, flows through a given electrical circuit, the power, W, of the circuit can be determined by the formula W = 120I − 12I2 . What amount of current, I, supplies the maximum power, W?


2

7 The equation W = 120I − 12I2 represents the power (W), in watts, of a 120-volt circuit having a resistance of 12 ohms when a current (I) is flowing through the circuit. What is the maximum power, in watts, that can be delivered in this circuit?

8 For which quadratic equation is the axis of symmetry x = 3?1) y = −x 2 + 3x + 52) y = −x 2 + 6x + 23) y = x 2 + 6x + 34) y = x 2 + x + 3

9 An equation of a parabola that has x = −2 as its axis of symmetry is1) y = x 2 − 4x + 12) y = x 2 − 2x + 33) y = 2x 2 + 8x − 34) y = 2x 2 + 4x − 7

10 A laundry owner's estimate of her weekly profits, p, in dollars, is given by the equation p = −4w2 + 160w, where w represents the number of workers she hires. What is the number of workers she should hire in order to earn the greatest profit? [The use of the accompanying grid is optional.]

ID: A

1


Answer Section

1 ANS: 2

.

REF: 080501b 2 ANS: 3

REF: 080902b 3 ANS: 4

REF: 080603b 4 ANS: 2

REF: 010907b 5 ANS: 4

REF: fall9915b

ID: A

2

6 ANS:

5.

REF: 010424b 7 ANS:

300.

REF: 060225b 8 ANS: 2

REF: 060514b 9 ANS: 3 REF: 011004b 10 ANS:

20. .

REF: 060822b

Regents Exam Questions A.A.42: Trigonometric Ratios 1 Name: ________________________ www.jmap.org

1

A.A.42: Trigonometric Ratios 1: Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides

1 The diagram below shows right triangle UPC.

Which ratio represents the sine of ∠U ?

1) 158 2) 15

17 3) 815 4) 8

17

2 Which ratio represents sinx in the right triangle shown below?

1) 2853 2) 28

45 3) 4553 4) 53

28

3 Which ratio represents cos A in the accompanying diagram of ABC?

1) 513 2) 12

13 3) 125 4) 13

5

4 In the accompanying diagram of right triangle ABC, AB = 8, BC = 15, AC = 17, and m∠ABC = 90.

What is tan∠C?

1) 815 2) 17

15 3) 817 4) 15

17


2

5 The diagram below shows right triangle ABC.

Which ratio represents the tangent of ∠ABC?

1) 513 2) 5

12 3) 1213 4) 12

5

6 The diagram below shows right triangle LMP.

Which ratio represents the tangent of ∠PLM ?

1) 34 2) 3

5 3) 43 4) 5

4

7 Right triangle ABC has legs of 8 and 15 and a hypotenuse of 17, as shown in the diagram below.

The value of the tangent of ∠B is1) 0.4706 2) 0.5333 3) 0.8824 4) 1.8750

8 In triangle MCT, the measure of ∠T = 90°, MC = 85 cm, CT = 84 cm, and TM = 13cm. Which ratio represents the sine of ∠C?

1) 1385 2) 84

85 3) 1384 4) 84

13

9 In ABC, the measure of ∠B = 90°, AC = 50, AB = 48, and BC = 14. Which ratio represents the tangent of ∠A?

1) 1450 2) 14

48 3) 4850 4) 48

14

10 Which equation shows a correct trigonometric ratio for angle A in the right triangle below?

1) sinA = 1517 2) tanA = 8

17 3) cos A = 1517

4) tanA = 58

11 In ABC, m∠C = 90. If AB = 5 and AC = 4, which statement is not true?

1) cos A = 45 2) tanA = 3

4 3) sinB = 45

4) tanB = 53

ID: A

1

A.A.42: Trigonometric Ratios 1: Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sidesAnswer Section

1 ANS: 2

sinU =opposite

hypotenuse = 1517

REF: 010919ia 2 ANS: 1

sinx =opposite

hypotenuse = 2853

REF: 011008ia 3 ANS: 1

cos A =adjacent

hypotenuse = 513

REF: 080414a 4 ANS: 1

tanC =oppositeadjacent =

815

REF: 010316a 5 ANS: 2

tanABC =oppositeadjacent =

512

REF: 081112ia 6 ANS: 3

tanPLM =oppositeadjacent =

43

REF: 011226ia 7 ANS: 2

tanB =oppositeadjacent =

815 = 0.53

REF: 081026ia 8 ANS: 1

sinC =opposite

hypotenuse = 1385

REF: fall0721ia

ID: A

2

9 ANS: 2

tanA =oppositeadjacent =

1448

REF: 061009ia 10 ANS: 3

cos A =adjacent

hypotenuse = 1517

REF: 011008ia 11 ANS: 4

If m∠C = 90, then AB is the hypotenuse, and the triangle is a 3-4-5 triangle.

REF: 061224ia


1

A.A.42: Trigonometric Ratios 2: Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides

1 The diagram below shows right triangle UPC.

Which ratio represents the sine of ∠U ?

2 Which ratio represents sinx in the right triangle shown below?

3 Which ratio represents cos A in the accompanying diagram of ABC?

4 In the accompanying diagram of right triangle ABC, AB = 8, BC = 15, AC = 17, and m∠ABC = 90.

What is tan∠C?

5 The diagram below shows right triangle ABC.

Which ratio represents the tangent of ∠ABC?


2

6 The diagram below shows right triangle LMP.

Which ratio represents the tangent of ∠PLM ?

7 Right triangle ABC has legs of 8 and 15 and a hypotenuse of 17, as shown in the diagram below.

The value of the tangent of ∠B is

8 In triangle MCT, the measure of ∠T = 90°, MC = 85 cm, CT = 84 cm, and TM = 13cm. Which ratio represents the sine of ∠C?

9 In ABC, the measure of ∠B = 90°, AC = 50, AB = 48, and BC = 14. Which ratio represents the tangent of ∠A?

10 Which equation shows a correct trigonometric ratio for angle A in the right triangle below?

1) sinA = 1517

2) tanA = 817

3) cos A = 1517

4) tanA = 58

11 In ABC, m∠C = 90. If AB = 5 and AC = 4, which statement is not true?

1) cos A = 45

2) tanA = 34

3) sinB = 45

4) tanB = 53

ID: A

1

A.A.42: Trigonometric Ratios 2: Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sidesAnswer Section

1 ANS: 1517

sinU =opposite

hypotenuse = 1517


2853

sinx =opposite

hypotenuse = 2853


513

cos A =adjacent

hypotenuse = 513

REF: 080414a 4 ANS:

815

tanC =oppositeadjacent =

815

REF: 010316a 5 ANS:

512

tanABC =oppositeadjacent =

512

REF: 081112ia

ID: A

2

6 ANS: 43

tanPLM =oppositeadjacent =

43


0.5333

tanB =oppositeadjacent =

815 = 0.53


1385

sinC =opposite

hypotenuse = 1385


1448

tanA =oppositeadjacent =

1448

REF: 061009ia 10 ANS: 3

cos A =adjacent

hypotenuse = 1517

REF: 011008ia 11 ANS: 4

If m∠C = 90, then AB is the hypotenuse, and the triangle is a 3-4-5 triangle.

REF: 061224ia

Regents Exam Questions Name: _____________________________A.A.43: Using Trigonometry to Find an Angle 1www.jmap.org

1

A.A.43: Using Trigonometry to Find an Angle 1: Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle

1 Which equation could be used to find the measure of one acute angle in the right triangle shown below?

1) sinA = 45

2) tanA = 54

3) cos B = 54

4) tanB = 45

2 In the diagram of ABC shown below, BC = 10 and AB = 16.

To the nearest tenth of a degree, what is the measure of the largest acute angle in the triangle?1) 32.02) 38.73) 51.34) 90.0

3 In right triangle ABC shown below, AB = 18.3 and BC = 11.2.

What is the measure of ∠A, to the nearest tenth of a degree?1) 31.52) 37.73) 52.34) 58.5


2

4 The center pole of a tent is 8 feet long, and a side of the tent is 12 feet long as shown in the diagram below.

If a right angle is formed where the center pole meets the ground, what is the measure of angle A to the nearest degree?1) 342) 423) 484) 56

5 A communications company is building a 30-foot antenna to carry cell phone transmissions. As shown in the diagram below, a 50-foot wire from the top of the antenna to the ground is used to stabilize the antenna.

Find, to the nearest degree, the measure of the angle that the wire makes with the ground.

6 In right triangle ABC, AB = 20, AC = 12, BC = 16, and m∠C = 90. Find, to the nearest degree, the measure of ∠A.

7 A 28-foot ladder is leaning against a house. The bottom of the ladder is 6 feet from the base of the house. Find the measure of the angle formed by the ladder and the ground, to the nearest degree.

8 A trapezoid is shown below.

Calculate the measure of angle x, to the nearest tenth of a degree.

9 In right triangle ABC shown below, AC = 29 inches, AB = 17 inches, and m∠ABC = 90. Find the number of degrees in the measure of angle BAC, to the nearest degree.

Find the length of BC to the nearest inch.

ID: A

1

A.A.43: Using Trigonometry to Find an Angle 1: Determine the measure of an angle of a right triangle, given the length of any two sides of the triangleAnswer Section

1 ANS: 1 REF: 080824ia 2 ANS: 3

sinA = 1016

A ≈ 38.7

B = 180− (90 = 38.7) = 51.3. A 90º angle is not acute.

REF: 080829ia 3 ANS: 1 REF: 061114ia 4 ANS: 2

sinA = 812

A ≈ 42


sinx = 3050

x = sin−1 35

x ≈ 37


53. sinA = 1620

A ≈ 53


78. cos x = 628

x ≈ 78


41.8. sinx = 812

A ≈ 41.8

REF: 081135ia

ID: A

2

9 ANS:

54, 23. cos A = 1729

x ≈ 54

. 292 − 172 ≈ 23

REF: 081238ia


1


1 Cassandra is calculating the measure of angle A in right triangle ABC, as shown in the accompanying diagram. She knows the lengths of AB and BC ,

If she finds the measure of angle A by solving only one equation, which concept will be used in her calculations?1) Pythagorean theorem2) sinA3) cos A4) tanA

2 Ron and Francine are building a ramp for performing skateboard stunts, as shown in the accompanying diagram. The ramp is 7 feet long and 3 feet high. What is the measure of the angle, x, that the ramp makes with the ground, to the nearest tenth of a degree?

3 A person standing on level ground is 2,000 feet away from the foot of a 420-foot-tall building, as shown in the accompanying diagram. To the nearest degree, what is the value of x?

4 If a tree 28 meters tall casts a shadow 32 meters long, what is the angle of elevation of the Sun to the nearest degree?1) 292) 413) 504) 61


2

5 As seen in the accompanying diagram, a person can travel from New York City to Buffalo by going north 170 miles to Albany and then west 280 miles to Buffalo.

If an engineer wants to design a highway to connect New York City directly to Buffalo, at what angle, x, would she need to build the highway? Find the angle to the nearest degree. To the nearest mile, how many miles would be saved by traveling directly from New York City to Buffalo rather than by traveling first to Albany and then to Buffalo?

6 In the accompanying diagram, the base of a 15-foot ladder rests on the ground 4 feet from a 6-foot fence.

a If the ladder touches the top of the fence and the side of a building, what angle, to the nearest degree, does the ladder make with the ground?

b Using the angle found in part a, determine how far the top of the ladder reaches up the side of the building, to the nearest foot.

7 The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s, are attached to the pole at a point 16 feet above the ground. The combined length of the two cables is 50 feet. If cable r is attached to the ground 12 feet from the base of the pole, what is the measure of the angle, x, to the nearest degree, that cable s makes with the ground?

ID: A

1


Answer Section

1 ANS: 4 PTS: 2 REF: 060820a 2 ANS:

25.4.

PTS: 2 REF: 060735a 3 ANS:

12. tanx = 4202000

x ≈ 12

PTS: 3 REF: 089927a 4 ANS: 2 PTS: 2 REF: 068533siii 5 ANS:

59, 122. . . The trip from New York City to Buffalo via Albany is 450 (280 +

170) miles. Therefore traveling directly to Buffalo would save (450 – 328) 122 miles.

PTS: 4 REF: 060231a 6 ANS:

56, 12. .

PTS: 4 REF: 010438a 7 ANS:

32. . If the combined length of the two cables is 50 feet, then s is 30 (50 – 20) feet.

PTS: 4 REF: 060539a

Regents Exam Questions Name: _____________________________A.A.44: Using Trigonometry to Find a Side 1www.jmap.org

1

A.A.44: Using Trigonometry to Find a Side 1: Find the measure of a side of a right triangle, given an acute angle and the length of another side

1 In the right triangle shown in the diagram below, what is the value of x to the nearest whole number?

1) 122) 143) 214) 28

2 A tree casts a 25-foot shadow on a sunny day, as shown in the diagram below.

If the angle of elevation from the tip of the shadow to the top of the tree is 32°, what is the height of the tree to the nearest tenth of a foot?1) 13.22) 15.63) 21.24) 40.0

3 An 8-foot rope is tied from the top of a pole to a stake in the ground, as shown in the diagram below.

If the rope forms a 57° angle with the ground, what is the height of the pole, to the nearest tenth of a foot?1) 4.42) 6.73) 9.54) 12.3

4 A right triangle contains a 38° angle whose adjacent side measures 10 centimeters. What is the length of the hypotenuse, to the nearest hundredth of a centimeter?1) 7.882) 12.693) 12.804) 16.24


2

5 As shown in the diagram below, a ladder 5 feet long leans against a wall and makes an angle of 65° with the ground. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.

6 A stake is to be driven into the ground away from the base of a 50-foot pole, as shown in the diagram below. A wire from the stake on the ground to the top of the pole is to be installed at an angle of elevation of 52°.

How far away from the base of the pole should the stake be driven in, to the nearest foot? What will be the length of the wire from the stake to the top of the pole, to the nearest foot?

7 A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the diagram below. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground.

Determine the height, to the nearest foot, of the balloon directly above the ground. Determine the distance, to the nearest foot, on the ground between the two ropes.

ID: A

1

A.A.44: Using Trigonometry to Find a Side 1: Find the measure of a side of a right triangle, given an acute angle and the length of another sideAnswer Section

1 ANS: 3

cos 30 = x24

x ≈ 21

REF: 010912ia 2 ANS: 2

tan32 = x25

x ≈ 15.6

REF: 080914ia 3 ANS: 2

sin57 = x8

x ≈ 6.7

REF: 061108ia 4 ANS: 2

cos 38 = 10x

x = 10cos 38 ≈ 12.69


2.1. cos 65 = x5

x ≈ 2.1


39, 63. tan52 = 50x

x ≈ 39

. sin52 = 50x

x ≈ 63

REF: 060937ia

ID: A

2

7 ANS:

84, 71 sin50 = x110

x ≈ 84

cos 50 =y

110

y ≈ 71

REF: 081039ia


1


1 In the accompanying diagram of right triangle ABC, BC = 12 and m∠C = 40.

Which single function could be used to find AB?1) tan502) sin503) cos404) sin40

2 In right triangle ABC, m∠C = 90. Which equation is true for this triangle?

1) a = b sinA2) a = c tanA3) a = ccosA4) a = c sinA

3 The accompanying diagram shows a ramp 30 feet long leaning against a wall at a construction site.

If the ramp forms an angle of 32° with the ground, how high above the ground, to the nearest tenth, is the top of the ramp?1) 15.9 ft2) 18.7 ft3) 25.4 ft4) 56.6 ft

4 The tailgate of a truck is 2 feet above the ground. The incline of a ramp used for loading the truck is 11°, as shown below.

Find, to the nearest tenth of a foot, the length of the ramp.


2

5 Joe is holding his kite string 3 feet above the ground, as shown in the accompanying diagram. The distance between his hand and a point directly under the kite is 95 feet. If the angle of elevation to the kite is 50°, find the height, h, of his kite, to the nearest foot.

6 A surveyor needs to determine the distance across the pond shown in the accompanying diagram. She determines that the distance from her position to point P on the south shore of the pond is 175 meters and the angle from her position to point X on the north shore is 32°. Determine the distance, PX, across the pond, rounded to the nearest meter.

7 Find, to the nearest tenth of a foot, the height of the tree represented in the accompanying diagram.

8 In the accompanying diagram, x represents the length of a ladder that is leaning against a wall of a building, and y represents the distance from the foot of the ladder to the base of the wall. The ladder makes a 60° angle with the ground and reaches a point on the wall 17 feet above the ground. Find the number of feet in x and y.


3

9 In the accompanying diagram, a ladder leaning against a building makes an angle of 58º with level ground. If the distance from the foot of the ladder to the building is 6 feet, find, to the nearest foot, how far up the building the ladder will reach.

10 As shown in the accompanying diagram, a ladder is leaning against a vertical wall, making an angle of 70° with the ground and reaching a height of 10.39 feet on the wall. Find, to the nearest foot, the length of the ladder. Find, to the nearest foot, the distance from the base of the ladder to the wall.

11 From a point on level ground 25 feet from the base of a tower, the angle of elevation to the top of the tower is 78°, as shown in the accompanying diagram. Find the height of the tower, to the nearest tenth of a foot.

12 A lighthouse is built on the edge of a cliff near the ocean, as shown in the accompanying diagram. From a boat located 200 feet from the base of the cliff, the angle of elevation to the top of the cliff is 18° and the angle of elevation to the top of the lighthouse is 28°. What is the height of the lighthouse, x, to the nearest tenth of a foot?

ID: A

1


Answer Section

1 ANS: 1 PTS: 2 REF: 010926a 2 ANS: 4 PTS: 2 REF: 018933siii 3 ANS: 1

PTS: 2 REF: 080724a 4 ANS:

10.5.

PTS: 2 REF: spring9825a 5 ANS:

116.

PTS: 4 REF: 069934a 6 ANS:

109.

PTS: 3 REF: 060030a 7 ANS:

28.2.

PTS: 4 REF: 010135a 8 ANS:

x = 19.6 and y = 9.8.

PTS: 4 REF: 080231a

ID: A

2

9 ANS:

10.

PTS: 2 REF: 010531a 10 ANS:

Length of ladder = 11 and distance from the base of the ladder to the wall = 4. .

PTS: 4 REF: 010638a 11 ANS:

117.6.

PTS: 2 REF: 010735a 12 ANS:

41.4.

PTS: 4 REF: 010837a


1


1 The angle of elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is 30°. Which equation can be used to find the height of the tree?

1) tan30 x25

2) sin30 x25

3) cos 30 x25

4) 302 252 x 2

2 In right triangle ABC, mC 90, a 4, and

sinA 12

. What is the length of the hypotenuse?

1) 4 3

2)8 3

33) 8

4) 8 2

3 A 10-foot ladder is to be placed against the side of a building. The base of the ladder must be placed at an angle of 72° with the level ground for a secure footing. Find, to the nearest inch, how far the base of the ladder should be from the side of the building and how far up the side of the building the ladder will reach.

4 Draw and label a diagram of the path of an airplane climbing at an angle of 11° with the ground. Find, to the nearest foot, the ground distance the airplane has traveled when it has attained an altitude of 400 feet.

5 A tree casts a shadow that is 20 feet long. The angle of elevation from the end of the shadow to the top of the tree is 66°. Determine the height of the tree, to the nearest foot.

6 A person measures the angle of depression from the top of a wall to a point on the ground. The point is located on level ground 62 feet from the base of the wall and the angle of depression is 52°. How high is the wall, to the nearest tenth of a foot?

7 A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 50°. The distance between the ship on the surface and the sunken ship on the ocean floor is 200 meters. If the ocean floor is level in this area, how far above the ocean floor, to the nearest meter, is the ship on the surface?

8 At Mogul’s Ski Resort, the beginner’s slope is inclined at an angle of 12.3°, while the advanced slope is inclined at an angle of 26.4°. If Rudy skis 1,000 meters down the advanced slope while Valerie skis the same distance on the beginner’s slope, how much longer was the horizontal distance that Valerie covered?1) 81.3 m2) 231.6 m3) 895.7 m4) 977.0 m

ID: A

1

A.A.44: Using Trigonometry to Find a Side 3: Find the measure of a side of a right triangle, given an acute angle and the length of another sideAnswer Section

1 ANS: 1 REF: 060419a 2 ANS: 3 REF: 088725siii 3 ANS:

114” and 37”. .

REF: 080033a 4 ANS:

2,058.

REF: 010235a 5 ANS:

45.

REF: 080536a 6 ANS:

79.4.

REF: 060639a 7 ANS:

153.

REF: 080133a 8 ANS: 1

REF: 080108b


1


1 Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards, as shown in the diagram below.

What is the length of the diagonal, in yards, that Tanya runs?1) 502) 603) 704) 80

2 Nancy’s rectangular garden is represented in the diagram below.

If a diagonal walkway crosses her garden, what is its length, in feet?1) 172) 223) 1614) 529

3 What is the value of x, in inches, in the right triangle below?

1) 152) 83) 344) 4

4 The end of a dog's leash is attached to the top of a 5-foot-tall fence post, as shown in the diagram below. The dog is 7 feet away from the base of the fence post.

How long is the leash, to the nearest tenth of a foot?1) 4.92) 8.63) 9.04) 12.0

5 The legs of an isosceles right triangle each measure 10 inches. What is the length of the hypotenuse of this triangle, to the nearest tenth of an inch?1) 6.32) 7.13) 14.14) 17.1


2

6 The length of one side of a square is 13 feet. What is the length, to the nearest foot, of a diagonal of the square?1) 132) 183) 194) 26

7 The rectangle shown below has a diagonal of 18.4 cm and a width of 7 cm.

To the nearest centimeter, what is the length, x, of the rectangle?1) 112) 173) 204) 25

8 Campsite A and campsite B are located directly opposite each other on the shores of Lake Omega, as shown in the diagram below. The two campsites form a right triangle with Sam’s position, S. The distance from campsite B to Sam’s position is 1,300 yards, and campsite A is 1,700 yards from his position.

What is the distance from campsite A to campsite B, to the nearest yard?1) 1,0952) 1,0963) 2,1404) 2,141

9 Don placed a ladder against the side of his house as shown in the diagram below.

Which equation could be used to find the distance, x, from the foot of the ladder to the base of the house?1) x = 20 − 19.52) x = 202 − 19.52

3) x = 202 − 19.52

4) x = 202 + 19.52

10 The length of the hypotenuse of a right triangle is 34 inches and the length of one of its legs is 16 inches. What is the length, in inches, of the other leg of this right triangle?1) 162) 183) 254) 30

ID: A

1


1 ANS: 1302 + 402 = c 2

2500 = c 2

50 = c

. 30, 40, 50 is a multiple of 3, 4, 5.


82 + 152 = c 2

c 2 = 289

c = 17

REF: 080906ia 3 ANS: 3

32 + 52 = x 2

34 = x 2

34 = x

REF: 060909ia 4 ANS: 2

52 + 72 ≈ 8.6

REF: 081004ia 5 ANS: 3

102 + 102 = c 2

c 2 = 200

c ≈ 14.1

REF: 061102ia 6 ANS: 2

132 + 132 = x 2

338 = x 2

338 = x

18 ≈ x

REF: 061223ia

ID: A

2

7 ANS: 2

18.42 − 72 ≈ 17

REF: 011107ia 8 ANS: 1

17002 − 13002 ≈ 1095


162 + b 2 = 342

b 2 = 900

b = 30

REF: 080809ia


1


1 Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards, as shown in the diagram below.

What is the length of the diagonal, in yards, that Tanya runs?

2 Nancy’s rectangular garden is represented in the diagram below.

If a diagonal walkway crosses her garden, what is its length, in feet?

3 What is the value of x, in inches, in the right triangle below?

4 The end of a dog's leash is attached to the top of a 5-foot-tall fence post, as shown in the diagram below. The dog is 7 feet away from the base of the fence post.

How long is the leash, to the nearest tenth of a foot?

5 The legs of an isosceles right triangle each measure 10 inches. What is the length of the hypotenuse of this triangle, to the nearest tenth of an inch?

6 The length of one side of a square is 13 feet. What is the length, to the nearest foot, of a diagonal of the square?


2

7 The rectangle shown below has a diagonal of 18.4 cm and a width of 7 cm.

To the nearest centimeter, what is the length, x, of the rectangle?

8 Campsite A and campsite B are located directly opposite each other on the shores of Lake Omega, as shown in the diagram below. The two campsites form a right triangle with Sam’s position, S. The distance from campsite B to Sam’s position is 1,300 yards, and campsite A is 1,700 yards from his position.

What is the distance from campsite A to campsite B, to the nearest yard?

9 Don placed a ladder against the side of his house as shown in the diagram below.

Which equation could be used to find the distance, x, from the foot of the ladder to the base of the house?

10 The length of the hypotenuse of a right triangle is 34 inches and the length of one of its legs is 16 inches. What is the length, in inches, of the other leg of this right triangle?

ID: A

1


1 ANS: 50302 + 402 = c 2

2500 = c 2

50 = c

. 30, 40, 50 is a multiple of 3, 4, 5.


1782 + 152 = c 2

c 2 = 289

c = 17


3432 + 52 = x 2

34 = x 2

34 = x


8.6

52 + 72 ≈ 8.6


14.1102 + 102 = c 2

c 2 = 200

c ≈ 14.1

REF: 061102ia

ID: A

2

6 ANS: 18132 + 132 = x 2

338 = x 2

338 = x

18 ≈ x


17

18.42 − 72 ≈ 17


1,095

17002 − 13002 ≈ 1095


x = 202 − 19.52

REF: 060825ia 10 ANS:

30162 + b 2 = 342

b 2 = 900

b = 30

REF: 080809ia


1


1 A wall is supported by a brace 10 feet long, as shown in the diagram below. If one end of the brace is placed 6 feet from the base of the wall, how many feet up the wall does the brace reach?

2 The NuFone Communications Company must run a telephone line between two poles at opposite ends of a lake, as shown in the accompanying diagram. The length and width of the lake are 75 feet and 30 feet, respectively.

What is the distance between the two poles, to the nearest foot?1) 1052) 813) 694) 45

3 A 10-foot ladder is placed against the side of a building as shown in figure 1 below. The bottom of the ladder is 8 feet from the base of the building. In order to increase the reach of the ladder against the building, it is moved 4 feet closer to the base of the building as shown in figure 2.

To the nearest foot, how much further up the building does the ladder now reach? Show how you arrived at your answer.

4 The accompanying diagram shows a kite that has been secured to a stake in the ground with a 20-foot string. The kite is located 12 feet from the ground, directly over point X. What is the distance, in feet, between the stake and point X?

5 In the accompanying diagram of right triangles ABD and DBC, AB = 5, AD = 4, and CD = 1. Find the length of BC, to the nearest tenth.

ID: A

1


Answer Section

1 ANS:

8. 6, 8, 10 is a multiple of the 3, 4, 5 triangle.

PTS: 2 REF: 010023a 2 ANS: 2

PTS: 2 REF: 010508a 3 ANS:

3. Figure 1: . Figure 2: . 9−6 = 3


16. . 12, 16, 20 is a multiple of the 3, 4, 5 triangle.

PTS: 2 REF: 080531a 5 ANS:

2.8.

PTS: 2 REF: 080633a

Regents Exam Questions A.A.1: Expressions 1 Name: ________________________ www.jmap.org

1

A.A.1: Expressions 1: Translate a quantitative verbal phrase into an algebraic expression

1 Which algebraic expression represents 15 less than x divided by 9?

1) x9 15

2) 9x 15

3) 15 x9

4) 15 9x

2 A correct translation of “six less than twice the value of x” is1) 2x 62) 2x 63) 6 2x4) 6 2x

3 Marcy determined that her father's age is four less than three times her age. If x represents Marcy's age, which expression represents her father's age?1) 3x 42) 3(x 4)3) 4x 34) 4 3x

4 Marie currently has a collection of 58 stamps. If she buys s stamps each week for w weeks, which expression represents the total number of stamps she will have?1) 58sw2) 58 sw3) 58s w4) 58 s w

5 Timmy bought a skateboard and two helmets for a total of d dollars. If each helmet cost h dollars, the cost of the skateboard could be represented by1) 2dh

2) dh2

3) d 2h

4) d h2

6 Tim ate four more cookies than Alice. Bob ate twice as many cookies as Tim. If x represents the number of cookies Alice ate, which expression represents the number of cookies Bob ate?1) 2 (x 4)2) 2x 43) 2(x 4)4) 4(x 2)

7 Mr. Turner bought x boxes of pencils. Each box holds 25 pencils. He left 3 boxes of pencils at home and took the rest to school. Which expression represents the total number of pencils he took to school?1) 22x2) 25x 33) 25 3x4) 25x 75

8 What is the perimeter of a regular pentagon with a side whose length is x 4?

1) x2 162) 4x 163) 5x 44) 5x 20

9 The length of a rectangular room is 7 less than three times the width, w, of the room. Which expression represents the area of the room?1) 3w 42) 3w 7

3) 3w2 4w

4) 3w2 7w

ID: A

1

A.A.1: Expressions 1: Translate a quantitative verbal phrase into an algebraic expressionAnswer Section

1 ANS: 1 REF: 081110ia 2 ANS: 2 REF: 081215ia 3 ANS: 1 REF: 061204ia 4 ANS: 2 REF: 060904ia 5 ANS: 3 REF: 011205ia 6 ANS: 3 REF: 011104ia 7 ANS: 4

25(x 3) 25x 75

REF: 060823ia 8 ANS: 4

5(x 4) 5x 20

REF: 081013ia 9 ANS: 4

A lw (3w 7)(w) 3w2 7w

REF: 010924ia


1


1 Which algebraic expression represents 15 less than x divided by 9?

2 A correct translation of “six less than twice the value of x” is

3 Marcy determined that her father's age is four less than three times her age. If x represents Marcy's age, which expression represents her father's age?

4 Marie currently has a collection of 58 stamps. If she buys s stamps each week for w weeks, which expression represents the total number of stamps she will have?

5 Timmy bought a skateboard and two helmets for a total of d dollars. If each helmet cost h dollars, the cost of the skateboard could be represented by

6 Tim ate four more cookies than Alice. Bob ate twice as many cookies as Tim. If x represents the number of cookies Alice ate, which expression represents the number of cookies Bob ate?

7 Mr. Turner bought x boxes of pencils. Each box holds 25 pencils. He left 3 boxes of pencils at home and took the rest to school. Which expression represents the total number of pencils he took to school?

8 What is the perimeter of a regular pentagon with a side whose length is x 4?

9 The length of a rectangular room is 7 less than three times the width, w, of the room. Which expression represents the area of the room?

ID: A

1


1 ANS: x9 15


2x 6


3x 4


58 sw


d 2h


2(x 4)


25x 7525(x 3) 25x 75


5x 205(x 4) 5x 20


3w2 7w

A lw (3w 7)(w) 3w2 7w

REF: 010924ia


1


1 If x represents a given number, the expression "5 less than twice the given number" is written as1) 5 2x2) 5 2 x3) 2x 54) 5 2x

2 Which expression represents "5 less than the product of 7 and x"?1) 7(x 5)2) 7x 53) 7 x 54) 5 7x

3 If rain is falling at the rate of 2 inches per hour, how many inches of rain will fall in x minutes?1) 2x

2)30x

3)60x

4)x30

4 Which expression represents the number of yards in x feet?

1)x12

2)x3

3) 3x4) 12x

5 Tara buys two items that cost d dollars each. She gives the cashier $20. Which expression represents the change she should receive?1) 20 2d2) 20 d3) 20 2d4) 2d 20

6 A hockey team played n games, losing four of them and winning the rest. The ratio of games won to games lost is

1)n 4

4

2)4

n 4

3)4n

4)n4

7 A ship sailed t miles on Tuesday and w miles on Wednesday. Which expression represents the average distance per day traveled by the ship?1) 2(t w)

2) t w2

3)t w

24) t w

8 The sum of Scott's age and Greg's age is 33 years. If Greg's age is represented by g, Scott's age is represented by1) 33 g2) g 333) g 334) 33g

9 In the Ambrose family, the ages of the three children are three consecutive even integers. If the age of the youngest child is represented by x 3, which expression represents the age of the oldest child?1) x 52) x 63) x 74) x 8


2

10 The width, w, of a rectangular rug is 4 less than its length, ™. Which expression represents the area of the rug?1) ™(4 ™)2) ™(™ 4)3) 2(™ 4) 2™4) 2w 2™

11 If 2n 1 represents an odd integer, the next larger odd integer is represented by1) 2n 32) 2n 23) 2n4) 2n 1

12 If n 3 is an even integer, what is the next larger consecutive even integer?1) n 52) n 13) n 14) n 2

13 If the number represented by n 3 is an odd integer, which expression represents the next greater odd integer?1) n 52) n 23) n 14) n 1

14 If n 4 represents an odd integer, the next larger odd integer is represented by1) n 22) n 33) n 54) n 6

15 The larger of two consecutive integers is represented by x 4. Which expression represents the smaller integer?1) x 22) x 33) x 54) x 6

16 Which expression represents the product of two consecutive odd integers, where n is an odd integer?1) n(n 1)2) n(n 2)3) n(n 3)4) 2n 1

17 A store advertises that during its Labor Day sale $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars, x 100, at 8 a.m., what, in terms of x, is the cost of Hakeem’s purchase?1) 0.20x 152) 0.20x 33) 0.85x 204) 0.80x 12

18 Mr. Cash bought d dollars worth of stock. During the first year, the value of the stock tripled. The next year, the value of the stock decreased by $1200.(a) Write an expression in terms of d to represent the value of the stock after two years.(b) If an initial investment is $1,000, determine its value at the end of 2 years.

19 Ashanti and Maria went to the store to buy snacks for their back-to-school party. They bought bags of chips, pretzels, and nachos. They bought three times as many bags of pretzels as bags of chips, and two fewer bags of nachos than bags of pretzels. If x represents the number of bags of chips they bought, express, in terms of x, how many bags of snacks they bought in all.

ID: A

1


1 ANS: 3 REF: 010820a TOP: Expressions 2 ANS: 2 REF: 010604a TOP: Expressions 3 ANS: 4

.

REF: 060014a TOP: Expressions 4 ANS: 2

x feet =

REF: 010427a TOP: Expressions 5 ANS: 1 REF: 060408a TOP: Expressions 6 ANS: 1 REF: 080002a TOP: Expressions 7 ANS: 3 REF: 010903a TOP: Expressions 8 ANS: 1 REF: 080509a TOP: Expressions 9 ANS: 3

The distance between two consecutive even integers is 2. (x 3) 4 x 7

REF: 080716a TOP: Expressions 10 ANS: 2 REF: 080811a TOP: Expressions 11 ANS: 1

The distance between consecutive odd integers is 2. (2n 1) 2 2n 3


The distance between consecutive odd integers is 2. (n 3) 2 n 1

REF: spring9804a TOP: Expressions 13 ANS: 3





The distance between consecutive integers is 1. (x 4) 1 x 3

REF: 010824a TOP: Expressions

ID: A

2

16 ANS: 2The distance between consecutive odd integers is 2.


REF: 060113b TOP: Expressions 18 ANS:

3d 1200, 1800. 3(1000) 1200 1800.

REF: spring9824a TOP: Expressions 19 ANS:

7x 2. Let chips = x, then pretzels = 3x and nachos = 3x – 2. .



1


1 If x represents a given number, the expression "5 less than twice the given number" is written as

2 Which expression represents "5 less than the product of 7 and x"?

3 If rain is falling at the rate of 2 inches per hour, how many inches of rain will fall in x minutes?

4 Which expression represents the number of yards in x feet?

5 Tara buys two items that cost d dollars each. She gives the cashier $20. Which expression represents the change she should receive?

6 A hockey team played n games, losing four of them and winning the rest. The ratio of games won to games lost is

7 A ship sailed t miles on Tuesday and w miles on Wednesday. Which expression represents the average distance per day traveled by the ship?

8 The sum of Scott's age and Greg's age is 33 years. If Greg's age is represented by g, Scott's age is represented by

9 In the Ambrose family, the ages of the three children are three consecutive even integers. If the age of the youngest child is represented by x 3, which expression represents the age of the oldest child?

10 The width, w, of a rectangular rug is 4 less than its length, ™. Which expression represents the area of the rug?

11 If 2n 1 represents an odd integer, the next larger odd integer is represented by

12 If n 3 is an even integer, what is the next larger consecutive even integer?

13 If the number represented by n 3 is an odd integer, which expression represents the next greater odd integer?

14 If n 4 represents an odd integer, the next larger odd integer is represented by

15 The larger of two consecutive integers is represented by x 4. Which expression represents the smaller integer?

16 Which expression represents the product of two consecutive odd integers, where n is an odd integer?

17 A store advertises that during its Labor Day sale $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars, x 100, at 8 a.m., what, in terms of x, is the cost of Hakeem’s purchase?

18 Mr. Cash bought d dollars worth of stock. During the first year, the value of the stock tripled. The next year, the value of the stock decreased by $1200.(a) Write an expression in terms of d to represent the value of the stock after two years.(b) If an initial investment is $1,000, determine its value at the end of 2 years.

19 Ashanti and Maria went to the store to buy snacks for their back-to-school party. They bought bags of chips, pretzels, and nachos. They bought three times as many bags of pretzels as bags of chips, and two fewer bags of nachos than bags of pretzels. If x represents the number of bags of chips they bought, express, in terms of x, how many bags of snacks they bought in all.

ID: A

1


1 ANS: 2x 5

REF: 010820a TOP: Expressions 2 ANS:

7x 5


x30

.


x3

x feet =


20 2d


n 44


t w2


33 g


x 7The distance between two consecutive even integers is 2. (x 3) 4 x 7


ID: A

2

10 ANS: ™(™ 4)


2n 3The distance between consecutive odd integers is 2. (2n 1) 2 2n 3


n 1The distance between consecutive odd integers is 2. (n 3) 2 n 1






x 3The distance between consecutive integers is 1. (x 4) 1 x 3


n(n 2)The distance between consecutive odd integers is 2.


0.80x 12

REF: 060113b TOP: Expressions 18 ANS:

3d 1200, 1800. 3(1000) 1200 1800.


7x 2. Let chips = x, then pretzels = 3x and nachos = 3x – 2. .


Regents Exam Questions A.A.2: Expressions Name: ________________________ www.jmap.org

1

A.A.2: Expressions: Write a verbal expression that matches a given mathematical expression

1 Which verbal expression represents 2(n 6)?1) two times n minus six2) two times six minus n3) two times the quantity n less than six4) two times the quantity six less than n

2 Which verbal expression can be represented by 2(x 5)?1) 5 less than 2 times x2) 2 multiplied by x less than 53) twice the difference of x and 54) the product of 2 and x, decreased by 5

3 Which verbal expression is represented by 12

(n 3)?

1) one-half n decreased by 32) one-half n subtracted from 33) the difference of one-half n and 34) one-half the difference of n and 3

ID: A

1

A.A.2: Expressions: Write a verbal expression that matches a given mathematical expressionAnswer Section

1 ANS: 4 REF: fall0729ia 2 ANS: 3 REF: 061119ia 3 ANS: 4 REF: 061016ia

Regents Exam Questions A.A.3: Expressions Name: ________________________ www.jmap.org

1

A.A.3: Expressions: Distinguish the difference between an algebraic expression and an algebraic equation

1 An example of an algebraic expression is

1) 2x + 37 = 13

x2) (2x + 1)(x − 7)3) 4x − 1 = 44) x = 2

2 An example of an algebraic expression is1) x + 22) y = x + 23) y < x + 24) y = x 2 + 2x

3 An example of an algebraic expression is1) y = mx + b2) 3x + 4y − 73) 2x + 3y ≤ 184) (x + y)(x − y) = 25

4 Mr. Stanton asked his students to write an algebraic expression on a piece of paper. He chose four students to go to the board and write their expression.

Robert wrote: 4(2x + 5) ≥ 17Meredith wrote: 3y − 7+ 11zSteven wrote: 9w + 2 = 20Cynthia wrote: 8 + 10 − 4 = 14

Which student wrote an algebraic expression?1) Robert2) Meredith3) Steven4) Cynthia

5 Chad complained to his friend that he had five equations to solve for homework. Are all of the homework problems equations? Justify your answer.

ID: A

1

A.A.3: Expressions: Distinguish the difference between an algebraic expression and an algebraic equation

Answer Section

1 ANS: 2 REF: 011027ia 2 ANS: 1 REF: 081030ia 3 ANS: 2 REF: 061121ia 4 ANS: 2 REF: 011227ia 5 ANS:

Not all of the homework problems are equations. The first problem is an expression.

REF: 080931ia

Regents Exam Questions A.A.4: Modeling Equations Name: ________________________ www.jmap.org

1

A.A.4: Modeling Equations: Translate verbal sentences into mathematical equations or inequalities

1 If h represents a number, which equation is a correct translation of "Sixty more than 9 times a number is 375"?1) 9h 375 3) 9h 60 3752) 9h 60 375 4) 60h 9 375

ID: A

1

A.A.4: Modeling Equations: Translate verbal sentences into mathematical equations or inequalitiesAnswer Section

1 ANS: 2 PTS: 2 REF: 080901ia

Regents Exam Questions A.A.4: Modeling Inequalities Name: ________________________ www.jmap.org

1

A.A.4: Modeling Inequalities: Translate verbal sentences into mathematical equations or inequalities

1 Mrs. Smith wrote "Eight less than three times a number is greater than fifteen" on the board. If x represents the number, which inequality is a correct translation of this statement?1) 3x −8 > 152) 3x −8 < 153) 8−3x > 154) 8−3x < 15

2 The sign shown below is posted in front of a roller coaster ride at the Wadsworth County Fairgrounds.

If h represents the height of a rider in inches, what is a correct translation of the statement on this sign?1) h < 482) h > 483) h ≤ 484) h ≥ 48

ID: A

1

A.A.4: Modeling Inequalities: Translate verbal sentences into mathematical equations or inequalitiesAnswer Section

1 ANS: 1 PTS: 2 REF: 080803ia 2 ANS: 4 PTS: 2 REF: 060906ia

Regents Exam Questions A.A.5: Modeling Equations Name: ________________________ www.jmap.org

1

A.A.5: Modeling Equations: Write algebraic equations or inequalities that represent a situation

1 When Albert flips open his mathematics textbook, he notices that the product of the page numbers of the two facing pages that he sees is 156. Which equation could be used to find the page numbers that Albert is looking at?1) x (x 1) 1562) (x 1) (x 2) 1563) (x 1)(x 3) 1564) x(x 1) 156

2 If n is an odd integer, which equation can be used to find three consecutive odd integers whose sum is 3?1) n (n 1) (n 3) 32) n (n 1) (n 2) 33) n (n 2) (n 4) 34) n (n 2) (n 3) 3

3 Rhonda has $1.35 in nickels and dimes in her pocket. If she has six more dimes than nickels, which equation can be used to determine x, the number of nickels she has?1) 0.05(x 6) 0.10x 1.352) 0.05x 0.10(x 6) 1.353) 0.05 0.10(6x) 1.354) 0.15(x 6) 1.35

4 The length of a rectangular window is 5 feet more than its width, w. The area of the window is 36 square feet. Which equation could be used to find the dimensions of the window?

1) w2 5w 36 02) w2 5w 36 03) w2 5w 36 04) w2 5w 36 0

5 The width of a rectangle is 3 less than twice the length, x. If the area of the rectangle is 43 square feet, which equation can be used to find the length, in feet?1) 2x(x 3) 432) x(3 2x) 433) 2x 2(2x 3) 434) x(2x 3) 43

6 A farmer has a rectangular field that measures 100 feet by 150 feet. He plans to increase the area of the field by 20%. He will do this by increasing the length and width by the same amount, x. Which equation represents the area of the new field?1) (100 2x)(150 x) 18,0002) 2(100 x) 2(150 x) 15,0003) (100 x)(150 x) 18,0004) (100 x)(150 x) 15,000

ID: A

1

A.A.5: Modeling Equations: Write algebraic equations or inequalities that represent a situationAnswer Section

1 ANS: 4 REF: 080627a 2 ANS: 3 REF: 061225ia 3 ANS: 2 REF: 010915ia 4 ANS: 4

w(w 5) 36

w2 5w 36 0

REF: fall0726ia 5 ANS: 4 REF: 081011ia 6 ANS: 3

REF: 060425a

Regents Exam Questions A.A.5: Modeling Equations from a Table Name: ________________________ www.jmap.org

1

A.A.5: Modeling Equations from a Table: Write algebraic equations or inequalities that represent a situation

1 Which equation could represent the relationship between the x and y values shown in the accompanying table?

1) y = x +22) y = x2 +23) y = x2

4) y = 2x

2 If x and y are defined as indicated by the accompanying table, which equation correctly represents the relationship between x and y?

1) y = x +22) y = 2x +23) y = 2x +34) y = 2x −3

3 Which equation expresses the relationship between x and y, as shown in the accompanying table?

1) y = x +32) y = 2x +33) y = 3x +24) y = x +2

4 Which linear equation represents the data in the accompanying table?

1) d = 1.50c2) d = 1.50c +20.003) d = 20.00c +1.504) d = 21.50c

5 Which equation models the data in the accompanying table?

1) y = 2x +52) y = 2x

3) y = 2x4) y = 5(2x)

6 The accompanying diagram represents the biological process of cell division.

If this process continues, which expression best represents the number of cells at any time, t?1) t +22) 2t3) t2

4) 2t

ID: A

1

A.A.5: Modeling Equations from a Table: Write algebraic equations or inequalities that represent a situationAnswer Section

1 ANS: 2 PTS: 2 REF: 010113a 2 ANS: 4 PTS: 2 REF: 010211a 3 ANS: 3 PTS: 2 REF: 010813a 4 ANS: 2 PTS: 2 REF: 080420a 5 ANS: 4 PTS: 2 REF: 060411b 6 ANS: 4 PTS: 2 REF: 060909b


1

A.A.5: Modeling Inequalities: Write algebraic equations or inequalities that represent a situation

1 Roger is having a picnic for 78 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine how many packages of hot dogs Roger will need to buy?1) p 782) 8p 783) 8 p 784) 78 p 8

2 An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store wants to make a profit of at least $255.00 from its sales of DVD players and cordless phones. Which inequality describes this situation?1) 75d 30c 2552) 75d 30c 2553) 75d 30c 2554) 75d 30c 255

3 Students in a ninth grade class measured their heights, h, in centimeters. The height of the shortest student was 155 cm, and the height of the tallest student was 190 cm. Which inequality represents the range of heights?1) 155 h 1902) 155 h 1903) h 155 or h 1904) h 155 or h 190

4 The ninth grade class at a local high school needs to purchase a park permit for $250.00 for their upcoming class picnic. Each ninth grader attending the picnic pays $0.75. Each guest pays $1.25. If 200 ninth graders attend the picnic, which inequality can be used to determine the number of guests, x, needed to cover the cost of the permit?1) 0.75x (1.25)(200) 250.002) 0.75x (1.25)(200) 250.003) (0.75)(200) 1.25x 250.004) (0.75)(200) 1.25x 250.00

5 The length of a rectangle is 15 and its width is w. The perimeter of the rectangle is, at most, 50. Which inequality can be used to find the longest possible width?1) 30 2w 502) 30 2w 503) 30 2w 504) 30 2w 50

ID: A

1

A.A.5: Modeling Inequalities: Write algebraic equations or inequalities that represent a situationAnswer Section

1 ANS: 2 REF: 011005ia 2 ANS: 4 REF: fall0715ia 3 ANS: 2 REF: 060821ia 4 ANS: 4 REF: 081107ia 5 ANS: 2 REF: 081212ia


1

A.A.5: Modeling Inequalities: Write algebraic equations or inequalities that represent a situation

1 Roger is having a picnic for 78 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine how many packages of hot dogs Roger will need to buy?1) p 782) 8p 783) 8 p 784) 78 p 8

2 An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store wants to make a profit of at least $255.00 from its sales of DVD players and cordless phones. Which inequality describes this situation?1) 75d 30c 2552) 75d 30c 2553) 75d 30c 2554) 75d 30c 255

3 Students in a ninth grade class measured their heights, h, in centimeters. The height of the shortest student was 155 cm, and the height of the tallest student was 190 cm. Which inequality represents the range of heights?1) 155 h 1902) 155 h 1903) h 155 or h 1904) h 155 or h 190

4 The ninth grade class at a local high school needs to purchase a park permit for $250.00 for their upcoming class picnic. Each ninth grader attending the picnic pays $0.75. Each guest pays $1.25. If 200 ninth graders attend the picnic, which inequality can be used to determine the number of guests, x, needed to cover the cost of the permit?1) 0.75x (1.25)(200) 250.002) 0.75x (1.25)(200) 250.003) (0.75)(200) 1.25x 250.004) (0.75)(200) 1.25x 250.00

5 The length of a rectangle is 15 and its width is w. The perimeter of the rectangle is, at most, 50. Which inequality can be used to find the longest possible width?1) 30 2w 502) 30 2w 503) 30 2w 504) 30 2w 50

ID: A

1

A.A.5: Modeling Inequalities: Write algebraic equations or inequalities that represent a situationAnswer Section

1 ANS: 2 REF: 011005ia 2 ANS: 4 REF: fall0715ia 3 ANS: 2 REF: 060821ia 4 ANS: 4 REF: 081107ia 5 ANS: 2 REF: 081212ia

Regents Exam Questions A.A.6: Modeling Equations 1 Name: ________________________ www.jmap.org

1

A.A.6: Modeling Equations 1: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

1 The ages of three brothers are consecutive even integers. Three times the age of the youngest brother exceeds the oldest brother's age by 48 years. What is the age of the youngest brother?1) 14 2) 18 3) 22 4) 26

2 If one-half of a number is 8 less than two-thirds of the number, what is the number?1) 24 2) 32 3) 48 4) 54

3 At the beginning of her mathematics class, Mrs. Reno gives a warm-up problem. She says, “I am thinking of a number such that 6 less than the product of 7 and this number is 85.” Which number is she thinking of? 1) 11 2) 13 3) 84 4) 637

4 If five times the measure of an angle is decreased by 30°, the result is the same as when two times the measure of the angle is increased by 18°. What is the measure of the angle?1) 16 2) 4 3) 16° 4) 4°

5 Robin spent $17 at an amusement park for admission and rides. If she paid $5 for admission, and rides cost $3 each, what is the total number of rides that she went on?1) 12 2) 2 3) 9 4) 4

6 Mario paid $44.25 in taxi fare from the hotel to the airport. The cab charged $2.25 for the first mile plus $3.50 for each additional mile. How many miles was it from the hotel to the airport?1) 10 2) 11 3) 12 4) 13

7 The sum of the ages of the three Romano brothers is 63. If their ages can be represented as consecutive integers, what is the age of the middle brother?

8 The sum of three consecutive odd integers is 18 less than five times the middle number. Find the three integers. [Only an algebraic solution can receive full credit.]

9 Every month, Omar buys pizzas to serve at a party for his friends. In May, he bought three more than twice the number of pizzas he bought in April. If Omar bought 15 pizzas in May, how many pizzas did he buy in April?

10 Sara’s telephone service costs $21 per month plus $0.25 for each local call, and long-distance calls are extra. Last month, Sara’s bill was $36.64, and it included $6.14 in long-distance charges. How many local calls did she make?

ID: A

1

A.A.6: Modeling Equations 1: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variableAnswer Section

1 ANS: 4Let x = youngest brother and x + 4 = oldest brother. 3x (x 4) 48

2x 4 48

x 26

.

REF: 080928ia 2 ANS: 3

REF: 060111a 3 ANS: 2

REF: 060409a 4 ANS: 3

REF: 010909a 5 ANS: 4

REF: 010801a 6 ANS: 4

REF: 010726a

ID: A

2

7 ANS:

21. Let x = youngest brother, x + 1 = middle brother, x + 2 = oldest brother. .

The age of the middle brother is x 1, or 21.

REF: 080024a 8 ANS:

7, 9, 11. x (x 2) (x 4) 5(x 2) 18

3x 6 5x 8

14 2x

7 x


6.

REF: 010733a 10 ANS:

38.

REF: 069925a

Regents Exam Questions A.A.6: Modeling Equations 2 Name: ________________________ www.jmap.org

1

A.A.6: Modeling Equations 2: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

1 Find three consecutive numbers whose sum is 9 greater than twice the largest number.

2 What number is that which being multiplied by 7 gives a product as much greater as the number itself is less than 20?

3 What number is that, the treble of which, increased by 12, shall as much exceed 54 as that treble is less than 144?

4 Find the number such that if 16 be subtracted from

it, 17

of the remainder will be equal to 19

of the

number.

5 A person expends $240 in the purchase of wheat. If he had paid 20 cents a bushel less he could have obtained 100 bushels more for the same money. How many bushels did he buy?

ID: A

1

A.A.6: Modeling Equations 2: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variableAnswer Section

1 ANS: 10, 11, 12

PTS: 12 REF: 010606al 2 ANS:

5


31


72

PTS: 12 REF: 010504al 5 ANS:

120,000

PTS: 20 REF: 019714al

Regents Exam Questions A.A.6: Modeling Inequalities 1 Name: ________________________ www.jmap.org

1

A.A.6: Modeling Inequalities 1: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

1 If five times a number is less than 55, what is the greatest possible integer value of the number?1) 122) 113) 104) 9

2 Jason’s part-time job pays him $155 a week. If he has already saved $375, what is the minimum number of weeks he needs to work in order to have enough money to buy a dirt bike for $900?1) 82) 93) 34) 4

3 An online music club has a one-time registration fee of $13.95 and charges $0.49 to buy each song. If Emma has $50.00 to join the club and buy songs, what is the maximum number of songs she can buy?1) 732) 743) 1304) 131

4 Tamara has a cell phone plan that charges $0.07 per minute plus a monthly fee of $19.00. She budgets $29.50 per month for total cell phone expenses without taxes. What is the maximum number of minutes Tamara could use her phone each month in order to stay within her budget?1) 1502) 2713) 4214) 692

5 A prom ticket at Smith High School is $120. Tom is going to save money for the ticket by walking his neighbor’s dog for $15 per week. If Tom already has saved $22, what is the minimum number of weeks Tom must walk the dog to earn enough to pay for the prom ticket?

6 Chelsea has $45 to spend at the fair. She spends $20 on admission and $15 on snacks. She wants to play a game that costs $0.65 per game. Write an inequality to find the maximum number of times, x, Chelsea can play the game. Using this inequality, determine the maximum number of times she can play the game.

7 Peter begins his kindergarten year able to spell 10 words. He is going to learn to spell 2 new words every day. Write an inequality that can be used to determine how many days, d, it takes Peter to be able to spell at least 75 words. Use this inequality to determine the minimum number of whole days it will take for him to be able to spell at least 75 words.

ID: A

1

A.A.6: Modeling Inequalities 1: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variableAnswer Section

1 ANS: 35x 55

x 11

REF: 061211ia 2 ANS: 4

375 155w 900

155w 525

w 3.4

REF: 081206ia 3 ANS: 1

13.95 0.49s 50.00

0.49s 36.05

s 73.57

REF: 080904ia 4 ANS: 1

0.07m 19 29.50

0.07m 10.50

m 150


7. 15x 22 120

x 6.53


0.65x 35 45

0.65x 10

x 15

REF: 061135ia

ID: A

2

7 ANS: 10 2d 75, 33. 10 2d 75

d 32.5

REF: 060834ia

Regents Exam Questions A.A.6: Modeling Inequalities 2 Name: ________________________ www.jmap.org

1

A.A.6: Modeling Inequalities 2: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

1 In a hockey league, 87 players play on seven different teams. Each team has at least 12 players. What is the largest possible number of players on any one team?1) 132) 143) 154) 21

2 There are 461 students and 20 teachers taking buses on a trip to a museum. Each bus can seat a maximum of 52. What is the least number of buses needed for the trip?1) 82) 93) 104) 11

3 Parking charges at Superior Parking Garage are $5.00 for the first hour and $1.50 for each additional 30 minutes. If Margo has $12.50, what is the maximum amount of time she will be able to park her car at the garage?

1) 212

hours

2) 312

hours

3) 6 hours

4) 612

hours

4 A doughnut shop charges $0.70 for each doughnut and $0.30 for a carryout box. Shirley has $5.00 to spend. At most, how many doughnuts can she buy if she also wants them in one carryout box?

5 Mr. Braun has $75.00 to spend on pizzas and soda pop for a picnic. Pizzas cost $9.00 each and the drinks cost $0.75 each. Five times as many drinks as pizzas are needed. What is the maximum number of pizzas that Mr. Braun can buy?

6 The Eye Surgery Institute just purchased a new laser machine for $500,000 to use during eye surgery. The Institute must pay the inventor $550 each time the machine is used. If the Institute charges $2,000 for each laser surgery, what is the minimum number of surgeries that must be performed in order for the Institute to make a profit?

7 Thelma and Laura start a lawn-mowing business and buy a lawnmower for $225. They plan to charge $15 to mow one lawn. What is the minimum number of lawns they need to mow if they wish to earn a profit of at least $750?

8 A swimmer plans to swim at least 100 laps during a 6-day period. During this period, the swimmer will increase the number of laps completed each day by one lap. What is the least number of laps the swimmer must complete on the first day?

ID: A

1

A.A.6: Modeling Inequalities 2: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variableAnswer Section

1 ANS: 3To find the largest possible number of players on any one team, assume the other six teams have the minimum

number of players.

REF: 089914a 2 ANS: 3

REF: 010101a 3 ANS: 2

The hourly parking rate is $3.

REF: 060406a 4 ANS:

6.

REF: 080224a 5 ANS:

5.

REF: 010938a

ID: A

2

6 ANS:

345.

REF: 010737a 7 ANS:

65.

REF: 080732a 8 ANS:

15.

REF: 069928a

Regents Exam Questions A.A.6: Speed Name: ________________________ www.jmap.org

1

A.A.6: Speed: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

1 A girl can ski down a hill five times as fast as she can climb up the same hill. If she can climb up the hill and ski down in a total of 9 minutes, how many minutes does it take her to climb up the hill?1) 1.82) 4.53) 7.24) 7.5

2 A bicyclist leaves Bay Shore traveling at an average speed of 12 miles per hour. Three hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 30 miles per hour. How many hours after the car leaves Bay Shore will the car catch up to the cyclist?1) 82) 23) 54) 4

3 A truck traveling at a constant rate of 45 miles per hour leaves Albany. One hour later a car traveling at a constant rate of 60 miles per hour also leaves Albany traveling in the same direction on the same highway. How long will it take for the car to catch up to the truck, if both vehicles continue in the same direction on the highway?

4 Two trains leave the same station at the same time and travel in opposite directions. One train travels at 80 kilometers per hour and the other at 100 kilometers per hour. In how many hours will they be 900 kilometers apart?

5 A who travels 4 miles an hour, starts from a certain place two hours in advance of B who travels 5 miles an hour in the same direction. How many hours must B travel to overtake A?

6 It took a man 12 hours to make a certain journey. Had he traveled 1 mile an hour faster he would have required 2 hours less time. What was his rate an hour and how long was the journey?

ID: A

1

A.A.6: Speed: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variableAnswer Section

1 ANS: 4

. .

PTS: 2 REF: 080019a 2 ANS: 2

PTS: 2 REF: 080518a 3 ANS:

3.

PTS: 3 REF: 010027a 4 ANS:

5. Since the trains are traveling in opposite directions, you add the distances they have traveled to find their

distance apart.

PTS: 2 REF: 010125a 5 ANS:

8

PTS: 12 REF: 090405al 6 ANS:

5 and 60 miles

PTS: 20 REF: 039512al

Regents Exam Questions A.A.7: Break Even Name: ________________________ www.jmap.org

1

A.A.7: Break Even: Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables

1 A hotel charges $20 for the use of its dining room and $2.50 a plate for each dinner. An association gives a dinner and charges $3 a plate but invites four nonpaying guests. If each person has one plate, how many paying persons must attend for the association to collect the exact amount needed to pay the hotel?1) 602) 443) 404) 20

2 A cellular telephone company has two plans. Plan A charges $11 a month and $0.21 per minute. Plan B charges $20 a month and $0.10 per minute. After how much time, to the nearest minute, will the cost of plan A be equal to the cost of plan B?1) 1 hr 22 min2) 1 hr 36 min3) 81 hr 8 min4) 81 hr 48 min

3 Juan has a cellular phone that costs $12.95 per month plus 25¢ per minute for each call. Tiffany has a cellular phone that costs $14.95 per month plus 15¢ per minute for each call. For what number of minutes do the two plans cost the same?

4 The Excel Cable Company has a monthly fee of $32.00 and an additional charge of $8.00 for each premium channel. The Best Cable Company has a monthly fee of $26.00 and an additional charge of $10.00 for each premium channel. The Horton family is deciding which of these two cable companies to subscribe to. For what number of premium channels will the total monthly subscription fee for the Excel and Best Cable companies be the same? The Horton family decides to subscribe to 2 premium channels for a period of one year. Which cable company should they subscribe to in order to spend less money? How much money will the Hortons save in one year by using the less expensive company?

5 Two video rental clubs offer two different rental fee plans: Club A charges $12 for membership and $2 for each rented video. Club B has a $4 membership fee and charges $4 for each rented video. The graph below represents the total cost of renting videos from Club A.

(a) On the same set of xy-axes, draw a line to represent the total cost of renting videos from Club B.(b) For what number of video rentals is it less expensive to belong to Club A? Explain how you arrived at your answer.


2

6 Two health clubs offer different membership plans. The graph below represents the total cost of belonging to Club A and Club B for one year.

If the yearly cost includes a membership fee plus a monthly charge, what is the membership fee for Club A? What is the number of the month when the total cost is the same for both clubs? What is the total cost for Club A when both plans are the same? What is the monthly charge for Club B?

7 Currently, Tyrone has $60 and his sister has $135. Both get an allowance of $5 each week. Tyrone decides to save his entire allowance, but his sister spends all of hers each week plus an additional $10 each week. After how many weeks will they each have the same amount of money? [The use of the grid is optional.]

8 The senior class is sponsoring a dance. The cost of a student disk jockey is $40, and tickets sell for $2 each. Write a linear equation and, on the accompanying grid, graph the equation to represent the relationship between the number of tickets sold and the profit from the dance. Then find how many tickets must be sold to break even.


3

9 Island Rent-a-Car charges a car rental fee of $40 plus $5 per hour or fraction of an hour. Wayne’s Wheels charges a car rental fee of $25 plus $7.50 per hour or fraction of an hour. Under what conditions does it cost less to rent from Island Rent-a-Car? [The use of the accompanying grid is optional.]

10 At Ron’s Rental, a person can rent a big-screen television for $10 a month plus a one-time “wear-and-tear” fee of $100. At Josie’s Rental, the charge is $20 a month and an additional charge of $20 for delivery with no “wear-and-tear” fee.a If c equals the cost, write one equation representing the cost of the rental for m months at Ron’s Rental and one equation representing the cost of the rental for m months at Josie’s Rental.b On the accompanying grid, graph and label each equation.c From your graph, determine in which month Josie’s cost will equal Ron’s cost.

ID: A

1

A.A.7: Break Even: Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables

Answer Section

1 ANS: 1

PTS: 2 REF: 060117a 2 ANS: 1

PTS: 2 REF: 080114b 3 ANS:

20.

PTS: 3 REF: 010130a 4 ANS:

3, Best; 24. Best, 26 + 10(2) = 46. Excel, 32 + 8(2) = 48. The Hortons should subscribe to Best. Since Best is $2/month cheaper, the Hortons will save $24 in one year.

PTS: 4 REF: 010035a 5 ANS:

. It is less expensive to rent 5 or more videos from Club A, as indicated from the graph above.

PTS: 4 REF: spring9831a

ID: A

2

6 ANS:

$50, 5, $125, $10. .

PTS: 4 REF: 089935a 7 ANS:

5. .

PTS: 3 REF: 010329a 8 ANS:

y = 2x −40. . 20

PTS: 4 REF: 060335a

ID: A

3

9 ANS:

h > 6. .

PTS: 2 REF: 060226b 10 ANS:

a) Ron: c = 10m+100, Josie: c = 20m+20; b) c) 8

PTS: 4 REF: 060232a

Regents Exam Questions A.A.7: Writing Linear Systems 1 Name: ________________________ www.jmap.org

1

A.A.7: Writing Linear Systems 1: Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables

1 The sum of two numbers is 47, and their difference is 15. What is the larger number?1) 162) 313) 324) 36

2 The total score in a football game was 72 points. The winning team scored 12 points more than the losing team. How many points did the winning team score?1) 302) 423) 544) 60

3 Michael is 25 years younger than his father. The sum of their ages is 53. What is Michael’s age?1) 142) 253) 284) 39

4 Ben has four more than twice as many CDs as Jake. If they have a total of 31 CDs, how many CDs does Jake have?1) 92) 133) 144) 22

5 Pam is playing with red and black marbles. The number of red marbles she has is three more than twice the number of black marbles she has. She has 42 marbles in all. How many red marbles does Pam have?1) 132) 153) 294) 33

6 Sam and Odel have been selling frozen pizzas for a class fundraiser. Sam has sold half as many pizzas as Odel. Together they have sold a total of 126 pizzas. How many pizzas did Sam sell?1) 212) 423) 634) 84

7 At Genesee High School, the sophomore class has 60 more students than the freshman class. The junior class has 50 fewer students than twice the students in the freshman class. The senior class is three times as large as the freshman class. If there are a total of 1,424 students at Genesee High School, how many students are in the freshman class?1) 2022) 2053) 2354) 236


2

8 Josh and Mae work at a concession stand. They each earn $8 per hour. Josh worked three hours more than Mae. If Josh and Mae earned a total of $120, how many hours did Josh work?1) 62) 93) 124) 15

9 Julia went to the movies and bought one jumbo popcorn and two chocolate chip cookies for $5.00. Marvin went to the same movie and bought one jumbo popcorn and four chocolate chip cookies for $6.00. How much does one chocolate chip cookie cost?1) $0.502) $0.753) $1.004) $2.00

10 Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?1) $1.502) $2.003) $3.004) $3.50

11 The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90. What is the cost of each item? Include appropriate units in your answer.

ID: A

1

A.A.7: Writing Linear Systems 1: Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variablesAnswer Section

1 ANS: 2L S 47

L S 15

2L 62

L 31

REF: 060912ia 2 ANS: 2

W L 72

W L 12

2W 84

W 42

REF: 081227ia 3 ANS: 1

f m 53

f m 25

2m 28

m 14

REF: 061126ia 4 ANS: 1

b 2j 4

b j 31

b 31 j

2j 4 31 j

3j 27

j 9

REF: 081119ia 5 ANS: 3

b 42 r

r 2b 3

r 2b 3

r 2(42 r) 3

r 84 2r 3

3r 87

r 29

REF: 060812ia

ID: A

2

6 ANS: 2s o 126

o 2s

. s 2s 126

s 42

REF: 080811ia 7 ANS: 1

so f 60 j 2f 50 se 3f . f (f 60) (2f 50) 3f 1424

7f 10 1424

f 202

REF: 060917ia 8 ANS: 2

J M 3

8J 8M 120

8J 8M 24

16J 144

J 9

REF: 011115ia 9 ANS: 1

1P 2C 5

1P 4C 6

2C 1

C 0.5

REF: 011003ia 10 ANS: 2

3c 4m 12.50

3c 2m 8.50

2m 4.00

m 2.00

REF: 060806ia 11 ANS:

m = 50¢, p = 15¢. 3m 2p 1.80

4m 6p 2.90

. 9m 6p 5.40

4m 6p 2.90

5m 2.50

m $0.50

. 4(.50) 6p 2.90

6p .90

p $0.15

REF: 080837ia


1


1 Three times as many robins as cardinals visited a bird feeder. If a total of 20 robins and cardinals visited the feeder, how many were robins?1) 5 2) 10 3) 15 4) 20

2 Jamie is 5 years older than her sister Amy. If the sum of their ages is 19, how old is Jamie?1) 5 2) 7 3) 12 4) 14

3 The ratio of Tariq’s telephone bill to Pria’s telephone bill was 7:5. Tariq’s bill was $14 more than Pria’s bill. What was Tariq’s bill?1) $21 2) $28 3) $35 4) $49

4 Two numbers are in the ratio 2:5. If 6 is subtracted from their sum, the result is 50. What is the larger number?1) 55 2) 45 3) 40 4) 35

5 Sal keeps quarters, nickels, and dimes in his change jar. He has a total of 52 coins. He has three more quarters than dimes and five fewer nickels than dimes. How many dimes does Sal have?1) 13 2) 18 3) 20 4) 21

6 At a concert, $720 was collected for hot dogs, hamburgers, and soft drinks. All three items sold for $1.00 each. Twice as many hot dogs were sold as hamburgers. Three times as many soft drinks were sold as hamburgers. The number of soft drinks sold was1) 120 2) 240 3) 360 4) 480

ID: A

1


1 ANS: 3

. r 3(20 r)

r 603r

4r 60

r 15

PTS: 2 REF: 010104a 2 ANS: 3

.

PTS: 2 REF: 060201a 3 ANS: 4

.

PTS: 2 REF: 080412a 4 ANS: 3

. .

PTS: 2 REF: 060004a 5 ANS: 2

.

PTS: 2 REF: 080606a

ID: A

2

6 ANS: 3

. .

PTS: 2 REF: 089916a


1


1 Three times as many robins as cardinals visited a bird feeder. If a total of 20 robins and cardinals visited the feeder, how many were robins?

2 Jamie is 5 years older than her sister Amy. If the sum of their ages is 19, how old is Jamie?

3 The ratio of Tariq’s telephone bill to Pria’s telephone bill was 7:5. Tariq’s bill was $14 more than Pria’s bill. What was Tariq’s bill?

4 Two numbers are in the ratio 2:5. If 6 is subtracted from their sum, the result is 50. What is the larger number?

5 Sal keeps quarters, nickels, and dimes in his change jar. He has a total of 52 coins. He has three more quarters than dimes and five fewer nickels than dimes. How many dimes does Sal have?

6 At a concert, $720 was collected for hot dogs, hamburgers, and soft drinks. All three items sold for $1.00 each. Twice as many hot dogs were sold as hamburgers. Three times as many soft drinks were sold as hamburgers. The number of soft drinks sold was

ID: A

1


1 ANS: 15

. r 3(20 r)

r 603r

4r 60

r 15

PTS: 2 REF: 010104a 2 ANS:

12

.

PTS: 2 REF: 060201a 3 ANS:

$49

.

PTS: 2 REF: 080412a 4 ANS:

40

. .

PTS: 2 REF: 060004a

ID: A

2

5 ANS: 18

.

PTS: 2 REF: 080606a 6 ANS:

360

. .

PTS: 2 REF: 089916a


1


1 A ribbon 56 centimeters long is cut into two pieces. One of the pieces is three times longer than the other. Find the lengths, in centimeters, of both pieces of ribbon.

2 Mary and Amy had a total of 20 yards of material from which to make costumes. Mary used three times more material to make her costume than Amy used, and 2 yards of material was not used. How many yards of materials did Amy use for her costumer?

3 Arielle has a collection of grasshoppers and crickets. She has 561 insects in all. The number of grasshoppers is twice the number of crickets. Find the number of each type of insect that she has.

4 Ramón rented a sprayer and a generator. On his first job, he used each piece of equipment for 6 hours at a total cost of $90. On his second job, he used the sprayer for 4 hours and the generator for 8 hours at a total cost of $100. What was the hourly cost of each piece of equipment?

5 Sharu has $2.35 in nickels and dimes. If he has a total of thirty-two coins, how many of each coin does he have?

6 Ben had twice as many nickels as dimes. Altogether, Ben had $4.20. How many nickels and how many dimes did Ben have?

7 A total of 600 tickets were sold for a concert. Twice as many tickets were sold in advance than were sold at the door. If the tickets sold in advance cost $25 each and the tickets sold at the door cost $32 each, how much money was collected for the concert?

8 The owner of a movie theater was counting the money from 1 day’s ticket sales. He knew that a total of 150 tickets were sold. Adult tickets cost $7.50 each and children’s tickets cost $4.75 each. If the total receipts for the day were $891.25, how many of each kind of ticket were sold?

9 The tickets for a dance recital cost $5.00 for adults and $2.00 for children. If the total number of tickets sold was 295 and the total amount collected was $1,220, how many adult tickets were sold? [Only an algebraic solution can receive full credit.]

10 There were 100 more balcony tickets than main-floor tickets sold for a concert. The balcony tickets sold for $4 and the main-floor tickets sold for $12. The total amount of sales for both types of tickets was $3,056. Write an equation or a system of equations that describes the given situation. Define the variables. Find the number of balcony tickets that were sold.

11 The ninth graders at a high school are raising money by selling T-shirts and baseball caps. The number of T-shirts sold was three times the number of caps. The profit they received for each T-shirt sold was $5.00, and the profit on each cap was $2.50. If the students made a total profit of $210, how many T-shirts and how many caps were sold?


2

12 When Tony received his weekly allowance, he decided to purchase candy bars for all his friends. Tony bought three Milk Chocolate bars and four Creamy Nougat bars, which cost a total of $4.25 without tax. Then he realized this candy would not be enough for all his friends, so he returned to the store and bought an additional six Milk Chocolate bars and four Creamy Nougat bars, which cost a total of $6.50 without tax. How much did each type of candy bar cost?

13 Tanisha and Rachel had lunch at the mall. Tanisha ordered three slices of pizza and two colas. Rachel ordered two slices of pizza and three colas. Tanisha’s bill was $6.00, and Rachel’s bill was $5.25. What was the price of one slice of pizza? What was the price of one cola?

14 Alexandra purchases two doughnuts and three cookies at a doughnut shop and is charged $3.30. Briana purchases five doughnuts and two cookies at the same shop for $4.95. All the doughnuts have the same price and all the cookies have the same price. Find the cost of one doughnut and find the cost of one cookie.

15 Using only 32-cent and 20-cent stamps, Charlie put $3.36 postage on a package he sent to his sister. He used twice as many 32-cent stamps as 20-cent stamps. Determine how many of each type of stamp he used.

16 The cost of a long-distance telephone call is determined by a flat fee for the first 5 minutes and a fixed amount for each additional minute. If a 15-minute telephone call costs $3.25 and a 23-minute call costs $5.17, find the cost of a 30-minute call.

17 At the local video rental store, José rents two movies and three games for a total of $15.50. At the same time, Meg rents three movies and one game for a total of $12.05. How much money is needed to rent a combination of one game and one movie?

18 Seth has one less than twice the number of compact discs (CDs) that Jason has. Raoul has 53 more CDs than Jason has. If Seth gives Jason 25 CDs, Seth and Jason will have the same number of CDs. How many CDs did each of the three boys have to begin with?

19 A total of 800 votes were cast in an election. The table below represents the votes that were received by the candidates. Candidate D got at least 30 votes more than Candidate E. What is the least number of votes that Candidate D could have received? Show how you arrived at your answer.

20 A group of 148 people is spending five days at a summer camp. The cook ordered 12 pounds of food for each adult and 9 pounds of food for each child. A total of 1,410 pounds of food was ordered. Write an equation or a system of equations that describes the above situation and define your variables. Find the total number of adults in the group and the total number of children in the group.

ID: A

1


1 ANS:

14 and 42. . .

PTS: 2 REF: 060531a 2 ANS:

4.5. .

PTS: 2 REF: 010022a 3 ANS:

374 grasshoppers and 187 crickets. . .

PTS: 3 REF: 010327a 4 ANS:

$5 for sprayer and $10 for generator. . .

PTS: 4 REF: 060133a 5 ANS:

17 nickels and 15 dimes. . .

PTS: 4 REF: 060638a

ID: A

2

6 ANS:

42 nickels and 21 dimes. . .

PTS: 2 REF: 060123a 7 ANS:

$16,400. . . . 200(32) + 400(25) = 16,400

PTS: 3 REF: 010228a 8 ANS:

65 adult and 85 children. . .

PTS: 4 REF: 060031a 9 ANS:

210. .

PTS: 4 REF: 010539a 10 ANS:

b = balcony m = main-floor b −m= 100

4b +12m= 3056

, 266. .

PTS: 4 REF: 010134a 11 ANS:

36 T-shirts and 12 caps. . .

PTS: 4 REF: 080132a

ID: A

3

12 ANS:

Milk Chocolate, $0.75 and Creamy Nougat, $0.50. . .

PTS: 4 REF: 010232a 13 ANS:

$1.50 for pizza and $0.75 for cola. . .

PTS: 4 REF: 080233a 14 ANS:

doughnut = $0.75, cookie = $0.60. . .

PTS: 4 REF: 010332a 15 ANS:

Four 20-cent and eight 32-cent stamps. . .

PTS: 3 REF: 010436a 16 ANS:

$6.85. . . .

PTS: 2 REF: 060123b 17 ANS:

$6.15. . . .

PTS: 4 REF: 010228b

ID: A

4

18 ANS:

Seth=101, Jason=51, Raoul=104. . . .

PTS: 3 REF: 060326a 19 ANS:

125. . .


a = adults c = children a + c = 148

12a +9c = 1410

, 26, 122. .

PTS: 4 REF: 010033a


1


1 Divide 46 into two parts such that the sum of the quotients obtained by dividing one part by 7 and the other part by 3 may be equal to 10.

2 One half the sum of two numbers is equal to one and one half times their difference. Twice the larger number exceeds three times the smaller by 12. Find the numbers.

3 The sum of two numbers is 20 and one half the larger is equal to three fourths the smaller. Find the numbers.

4 The age of the elder of two boys is twice that of the younger. Three years ago it was three times that of the younger. Find the age of each.

5 A man has two kinds of money, dimes and half dimes. If he is offered $1.35 for 20 coins, how many of each kind must he give?

6 A man had a surplus of $5000 after the purchase of a farm at $150 an acre. Had the rate been $180 an acre he would have needed $1000 more for the purchase. How many acres were there in the farm?

7 If a certain number is increased by the sum of its digits the sum is 21. If the number is diminished by twice the sum of its digits the result is 3. Find the number.

8 A number expressed by two digits is equal to six times the sum of its digits plus 2. If the order is reversed the resulting number will be 9 less than the original. Find the number.

9 In a number of two digits the first digit is twice the second, and if 18 be subtracted from the number the order of the digits will be inverted. Find the number.

10 A number is expressed by two digits whose sum is 12. If the digits are interchanged the resulting number is less than the original number by 36. Find the number.

11 A number is composed of two digits whose sum is equal to four times the tens digit. If the digits are interchanged the resulting number exceeds the original number by 36. Find the number.

12 The digits in the units place of a certain number of two figures is 7 less than the digit in the tens place. If the order of the digits is reversed, the resulting

number will be 29

the original number. Find the

number.

ID: A

1


1 ANS: 18 and 28


12 and 24

PTS: 10 REF: 039307al 3 ANS:

8 and 12

PTS: 10 REF: 069506al 4 ANS:

12 and 6

PTS: 10 REF: 060007al 5 ANS:

7 dimes and 13 half dimes


200

PTS: 10 REF: 119405al 7 ANS:

15

PTS: 20 REF: 069514al 8 ANS:

32

PTS: 10 REF: 119314al 9 ANS:

42

PTS: 20 REF: 089612al 10 ANS:

84

PTS: 10 REF: 019807al 11 ANS:

26

PTS: 10 REF: 069907al

ID: A

2

12 ANS: 81

PTS: 12 REF: 090512al


1


1 The sum of two numbers is 47, and their difference is 15. What is the larger number?

2 The total score in a football game was 72 points. The winning team scored 12 points more than the losing team. How many points did the winning team score?

3 Michael is 25 years younger than his father. The sum of their ages is 53. What is Michael’s age?

4 Ben has four more than twice as many CDs as Jake. If they have a total of 31 CDs, how many CDs does Jake have?

5 Pam is playing with red and black marbles. The number of red marbles she has is three more than twice the number of black marbles she has. She has 42 marbles in all. How many red marbles does Pam have?

6 Sam and Odel have been selling frozen pizzas for a class fundraiser. Sam has sold half as many pizzas as Odel. Together they have sold a total of 126 pizzas. How many pizzas did Sam sell?

7 At Genesee High School, the sophomore class has 60 more students than the freshman class. The junior class has 50 fewer students than twice the students in the freshman class. The senior class is three times as large as the freshman class. If there are a total of 1,424 students at Genesee High School, how many students are in the freshman class?

8 Josh and Mae work at a concession stand. They each earn $8 per hour. Josh worked three hours more than Mae. If Josh and Mae earned a total of $120, how many hours did Josh work?

9 Julia went to the movies and bought one jumbo popcorn and two chocolate chip cookies for $5.00. Marvin went to the same movie and bought one jumbo popcorn and four chocolate chip cookies for $6.00. How much does one chocolate chip cookie cost?

10 Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?

11 The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90. What is the cost of each item? Include appropriate units in your answer.

ID: A

1


1 ANS: 31L S 47

L S 15

2L 62

L 31


42W L 72

W L 12

2W 84

W 42


14f m 53

f m 25

2m 28

m 14


9b 2j 4

b j 31

b 31 j

2j 4 31 j

3j 27

j 9

REF: 081119ia

ID: A

2

5 ANS: 29b 42 r

r 2b 3

r 2b 3

r 2(42 r) 3

r 84 2r 3

3r 87

r 29


42s o 126

o 2s

. s 2s 126

s 42


202so f 60 j 2f 50 se 3f . f (f 60) (2f 50) 3f 1424

7f 10 1424

f 202


9J M 3

8J 8M 120

8J 8M 24

16J 144

J 9


$0.501P 2C 5

1P 4C 6

2C 1

C 0.5

REF: 011003ia

ID: A

3

10 ANS: $2.003c 4m 12.50

3c 2m 8.50

2m 4.00

m 2.00

REF: 060806ia 11 ANS:

m = 50¢, p = 15¢. 3m 2p 1.80

4m 6p 2.90

. 9m 6p 5.40

4m 6p 2.90

5m 2.50

m $0.50

. 4(.50) 6p 2.90

6p .90

p $0.15

REF: 080837ia

Regents Exam Questions Name: ________________________ A.A.8: Geometric Applications of Quadratics 1www.jmap.org

1

A.A.8: Geometric Applications of Quadratics 1: Analyze and solve verbal problems that involve quadratic equations

1 What is the length of one side of the square whose perimeter has the same numerical value as its area?1) 52) 63) 34) 4

2 A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle?1) 62) 83) 34) 19

3 The length of a rectangle is 3 inches more than its width. The area of the rectangle is 40 square inches. What is the length, in inches, of the rectangle?1) 52) 83) 8.54) 11.5

4 A contractor needs 54 square feet of brick to construct a rectangular walkway. The length of the walkway is 15 feet more than the width. Write an equation that could be used to determine the dimensions of the walkway. Solve this equation to find the length and width, in feet, of the walkway.

5 Jack is building a rectangular dog pen that he wishes to enclose. The width of the pen is 2 yards less than the length. If the area of the dog pen is 15 square yards, how many yards of fencing would he need to completely enclose the pen?

6 The area of the rectangular playground enclosure at South School is 500 square meters. The length of the playground is 5 meters longer than the width. Find the dimensions of the playground, in meters. [Only an algebraic solution will be accepted.]

7 Javon’s homework is to determine the dimensions of his rectangular backyard. He knows that the length is 10 feet more than the width, and the total area is 144 square feet. Write an equation that Javon could use to solve this problem. Then find the dimensions, in feet, of his backyard.

8 A rectangular piece of cardboard is to be formed into an uncovered box. The piece of cardboard is 2 centimeters longer than it is wide. A square that measures 3 centimeters on a side is cut from each corner. When the sides are turned up to form the box, its volume is 765 cubic centimeters. Find the dimensions, in centimeters, of the original piece of cardboard.

ID: A

1

A.A.8: Geometric Applications of Quadratics 1: Analyze and solve verbal problems that involve quadratic equationsAnswer Section

1 ANS: 4

PTS: 2 REF: 060608a 2 ANS: 2

l(l 5) 24

l2 5l 24 0

(l 8)(l 3) 0

l 8

PTS: 2 REF: 080817ia 3 ANS: 2

l(l 3) 40

l2 3l 40 0

(l 8)(l 5) 0

l 8

PTS: 2 REF: 081116ia 4 ANS:

w(w 15) 54, 3, 18. w(w 15) 54

w2 15w 54 0

(w 18)(w 3) 0

w 3

PTS: 4 REF: 060837ia 5 ANS:

16. . If w=3, then l=5.

PTS: 4 REF: 080035a

ID: A

2

6 ANS:

w 20, l 25.

PTS: 4 REF: 060035a 7 ANS:

w(w 10) 144; w 8, l 18.

PTS: 4 REF: 010233a 8 ANS:

21x23. If the width of the box is 15, adding the widths of the cutout squares

means the width of the original sheet of cardboard is 21 (15 + 3 + 3). The length is 2 more, or 23.

PTS: 4 REF: 080431b

Regents Exam Questions Name: ________________________ A.A.8: Geometric Applications of Quadratics 2www.jmap.org

1

A.A.8: Geometric Applications of Quadratics 2: Analyze and solve verbal problems that involve quadratic equations

1 Two floors, each square in form and one 7 feet wider than the other, contain together 1429 square feet. How many square feet in each?

2 The distance around a rectangular field is 100 rods; the area is 589 square rods. Find the length and breadth of the field.

3 The area of a rectangle is 48 sq. ft. Its perimeter (sum of its sides) is 32 feet. Find its length and width.

4 The length of a rectangular field is three times its width, and the number of square rods in its area is

712

times the number of rods around the field. Find

its length and width.

5 The length of a certain rectangle is to its width as 8 to 5 and the number of square feet in its area is equal to the number of linear feet in its perimeter less three. Find its length and width.

6 The length of a floor exceeds its width by 2 feet. If each dimension is increased 2 feet the area of the floor will be increased 48 square feet. Find the dimensions of the floor.

7 The perimeter of a rectangular lot is 220 feet and its area is 2925 square feet. Find its length and breadth.

8 A rectangular yard is 20 rods longer than it is wide. Its area is 2400 square rods. Find the dimensions of the yard.

9 If the sides of an equilateral triangle are increased by 7 inches, 4 inches and 1 inch respectively, a right triangle is formed. Find the length of a side of the equilateral triangle.

ID: A

1

A.A.8: Geometric Applications of Quadratics 2: Analyze and solve verbal problems that involve quadratic equationsAnswer Section

1 ANS: 529 and 900


31 and 19


4 and 12

PTS: 10 REF: 019402al 4 ANS:

60 and 20

PTS: 10 REF: 039411al 5 ANS:

4 and 2.5 or 1.2 and 0.75

PTS: 10 REF: 019512al 6 ANS:

width = 10 and length = 12

PTS: 10 REF: 019815al 7 ANS:

45 and 65

PTS: 10 REF: 039815al 8 ANS:

40 and 60

PTS: 12 REF: 030506al 9 ANS:

8

PTS: 12 REF: 060510al

Regents Exam Questions A.A.8: Writing Quadratics Name: ________________________ www.jmap.org

1

A.A.8: Writing Quadratics: Analyze and solve verbal problems that involve quadratic equations

1 When 36 is subtracted from the square of a number, the result is five times the number. What is the positive solution?1) 92) 63) 34) 4

2 Byron is 3 years older than Doug. The product of their ages is 40. How old is Doug?1) 102) 83) 54) 4

3 Find two consecutive numbers whose product is 306.

4 Find three consecutive positive even integers such that the product of the second and third integers is twenty more than ten times the first integer. [Only an algebraic solution can receive full credit.]

5 Find three consecutive odd integers such that the product of the first and the second exceeds the third by 8.

6 Three brothers have ages that are consecutive even integers. The product of the first and third boys’ ages is 20 more than twice the second boy’s age. Find the age of each of the three boys.

7 Tamara has two sisters. One of the sisters is 7 years older than Tamara. The other sister is 3 years younger than Tamara. The product of Tamara’s sisters' ages is 24. How old is Tamara?

ID: A

1

A.A.8: Writing Quadratics: Analyze and solve verbal problems that involve quadratic equationsAnswer Section

1 ANS: 1

x 2 36 5x

x 2 5x 36 0

(x 9)(x 4) 0

x 9

REF: 061020ia 2 ANS: 3

b 3 d

bd 40

(3 d)d 40

d 2 3d 40 0

(d 8)(d 5) 0

d 5


17 and 18


6, 8, 10. Three consecutive even integers are x, x 2 and x 4. (x 2)(x 4) 10x 20

x 2 6x 8 10x 20

x 2 4x 12 0

(x 6)(x 2) 0

x 6


3, 5, 7. x = first odd integer, x + 2 = second odd integer, x + 4 = third odd integer.

REF: 060131a

ID: A

2

6 ANS:

4, 6, 8. x = youngest brother, x + 2 = middle brother, x + 4 = oldest brother.

REF: 010326a 7 ANS:

5. x = Tamara’s age, x + 7 = Tamara’s older sister, x - 3 = Tamara’s younger sister.

REF: 060636a

Regents Exam Questions A.A.9: Exponential Functions 1 Name: ________________________ www.jmap.org

1

A.A.9: Exponential Functions 1: Analyze and solve verbal problems that involve exponential growth and decay

1 Is the equation A = 21000(1 − 0.12) t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period?1) exponential growth and 12%2) exponential growth and 88%3) exponential decay and 12%4) exponential decay and 88%

2 Mr. Smith invested $2,500 in a savings account that earns 3% interest compounded annually. He made no additional deposits or withdrawals. Which expression can be used to determine the number of dollars in this account at the end of 4 years?1) 2500(1 + 0.03)4

2) 2500(1 + 0.3)4

3) 2500(1 + 0.04)3

4) 2500(1 + 0.4)3

3 The current student population of the Brentwood Student Center is 2,000. The enrollment at the center increases at a rate of 4% each year. To the nearest whole number, what will the student population be closest to in 3 years'?1) 2,2402) 2,2503) 5,4884) 6,240

4 Cassandra bought an antique dresser for $500. If the value of her dresser increases 6% annually, what will be the value of Cassandra's dresser at the end of 3 years to the nearest dollar?1) $4152) $5903) $5964) $770

5 The value, y, of a $15,000 investment over x years

is represented by the equation y = 15000(1.2)x3 .

What is the profit (interest) on a 6-year investment?1) $6,6002) $10,7993) $21,6004) $25,799

6 A bank is advertising that new customers can open

a savings account with a 3 34 % interest rate

compounded annually. Robert invests $5,000 in an account at this rate. If he makes no additional deposits or withdrawals on his account, find the amount of money he will have, to the nearest cent, after three years.


2

7 The New York Volleyball Association invited 64 teams to compete in a tournament. After each round, half of the teams were eliminated. Which equation represents the number of teams, t, that remained in the tournament after r rounds?1) t = 64(r)0.5

2) t = 64(−0.5)r

3) t = 64(1.5)r

4) t = 64(0.5)r

8 Kathy plans to purchase a car that depreciates (loses value) at a rate of 14% per year. The initial cost of the car is $21,000. Which equation represents the value, v, of the car after 3 years?1) v = 21,000(0.14)3

2) v = 21,000(0.86)3

3) v = 21,000(1.14)3

4) v = 21,000(0.86)(3)

9 A car depreciates (loses value) at a rate of 4.5% annually. Greg purchased a car for $12,500. Which equation can be used to determine the value of the car, V, after 5 years?1) V = 12,500(0.55)5

2) V = 12,500(0.955)5

3) V = 12,500(1.045)5

4) V = 12,500(1.45)5

10 Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates (loses value) at a rate of 5%. What will its approximate value be at the end of the fourth year?1) $33,250.002) $30,008.133) $28,507.724) $27,082.33

11 The value of a car purchased for $20,000 decreases at a rate of 12% per year. What will be the value of the car after 3 years?1) $12,800.002) $13,629.443) $17,600.004) $28,098.56

12 In a science fiction novel, the main character found a mysterious rock that decreased in size each day. The table below shows the part of the rock that remained at noon on successive days.

Which fractional part of the rock will remain at noon on day 7?

1) 1128

2) 164

3) 114

4) 112

13 The Booster Club raised $30,000 for a sports fund. No more money will be placed into the fund. Each year the fund will decrease by 5%. Determine the amount of money, to the nearest cent, that will be left in the sports fund after 4 years.

ID: A

1

A.A.9: Exponential Functions 1: Analyze and solve verbal problems that involve exponential growth and decayAnswer Section

1 ANS: 3 REF: 081211ia 2 ANS: 1 REF: 011202ia 3 ANS: 2

2000(1 + 0.04)3 ≈ 2249

REF: 081124ia 4 ANS: 3

500(1 + 0.06)3 ≈ 596

REF: 080929ia 5 ANS: 1

15000(1.2)63 = 21,600. 21,600 − 15,000 = 6,600


5,583.86. A = P(1+ R) t = 5000(1+ 0.0375)3 ≈ 5583.86

REF: 060935ia 7 ANS: 4 REF: 010908ia 8 ANS: 2 REF: 060830ia 9 ANS: 2 REF: 061229ia 10 ANS: 3

35000(1− 0.05)4 ≈ 28507.72


20000(.88)3 = 13629.44

REF: 061124ia 12 ANS: 2

R = 0.5d − 1

REF: 011006ia 13 ANS:

24,435.19. 30000(.95)4 ≈ 24435.19

REF: 011138ia


1

A.A.9: Exponential Functions 2: Analyze and solve verbal problems that involve exponential growth and decay

1 The population of Henderson City was 3,381,000 in 1994, and is growing at an annual rate of 1.8%. If this growth rate continues, what will the approximate population of Henderson City be in the year 2000?1) 3,696,0002) 3,763,0003) 3,798,0004) 3,831,000

2 Kathy deposits $25 into an investment account with an annual rate of 5%, compounded annually. The amount in her account can be determined by the

formula A P(1 R) t , where P is the amount deposited, R is the annual interest rate, and t is the number of years the money is invested. If she makes no other deposits or withdrawals, how much money will be in her account at the end of 15 years?1) $25.752) $43.753) $51.974) $393.97

3 On January 1, 1999, the price of gasoline was $1.39 per gallon. If the price of gasoline increased by 0.5% per month, what was the cost of one gallon of gasoline, to the nearest cent, on January 1 one year later?

4 A radioactive substance has an initial mass of 100 grams and its mass halves every 4 years. Which expression shows the number of grams remaining after t years?

1) 100(4)

t

4

2) 100(4)2t

3) 10012

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

t

4

4) 10012

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

4t

5 A used car was purchased in July 1999 for $11,900. If the car depreciates 13% of its value each year, what is the value of the car, to the nearest hundred dollars, in July 2002?

ID: A

1

A.A.9: Exponential Functions 2: Analyze and solve verbal problems that involve exponential growth and decayAnswer Section

1 ANS: 2

REF: fall9916b 2 ANS: 3

REF: 060803b 3 ANS:

1.48.

REF: 010525b 4 ANS: 3 REF: 010813b 5 ANS:

$7,800.

REF: 080221b

Regents Exam Questions A.A.10: Solving Linear Systems 1 Name: ________________________ www.jmap.org

1

A.A.10: Solving Linear Systems 1: Solve systems of two linear equations in two variables algebraically

1 What is the value of the y-coordinate of the solution to the system of equations x 2y 9 and x y 3?1) 62) 23) 34) 5

2 What is the value of the y-coordinate of the solution to the system of equations x 2y 1 and x 4y 7?1) 12) 13) 34) 4

3 What is the solution of the system of equations c 3d 8 and c 4d 6?1) c 14, d 22) c 2, d 23) c 2, d 24) c 14, d 2

4 What is the value of the y-coordinate of the solution to the system of equations 2x y 8 and x 3y 3?1) 22) 23) 34) 3

5 What is the solution of the system of equations 2x 5y 11 and 2x 3y 9?1) (3,1)2) (1,3)3) (3,1)4) (3,1)

6 The equations 5x 2y 48 and 3x 2y 32 represent the money collected from school concert ticket sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?1) $202) $103) $84) $4

7 Solve the following system of equations algebraically for y:

2x 2y 9

2x y 3

8 Solve the following system of equations algebraically:

3x 2y 4

4x 3y 7[Only an algebraic solution can receive full credit.]

ID: A

1

A.A.10: Solving Linear Systems 1: Solve systems of two linear equations in two variables algebraicallyAnswer Section

1 ANS: 2x 2y 9

x y 3

3y 6

y 2

REF: 060925ia 2 ANS: 1

x 2y 1

x 4y 7

6y 6

y 1

REF: 080920ia 3 ANS: 3

c 3d 8

4d 6 3d 8

7d 14

d 2

c 4d 6

c 4(2) 6

c 2

REF: 061012ia 4 ANS: 2

2(x 3y 3)

2x y 8

2x 6y 6

7y 14

y 2

REF: 081021ia 5 ANS: 3

2x 5y 11

2x 3y 9

2y 2

y 1

2x 5(1) 11

2x 6

x 3

REF: 081109ia

ID: A

2

6 ANS: 35x 2y 48

3x 2y 32

2x 16

x 8


2. Subtracting the equations: 3y 6

y 2


(2,5). 3x 2y 4 12x 8y 16

4x 3y 7 12x 9y 21

y 5

. 3x 2y 4

3x 2(5) 4

3x 6

x 2

REF: 010937ia


1


1 What is the value of the y-coordinate of the solution to the system of equations x 2y 9 and x y 3?

2 What is the value of the y-coordinate of the solution to the system of equations x 2y 1 and x 4y 7?

3 What is the solution of the system of equations c 3d 8 and c 4d 6?

4 What is the value of the y-coordinate of the solution to the system of equations 2x y 8 and x 3y 3?

5 What is the solution of the system of equations 2x 5y 11 and 2x 3y 9?

6 The equations 5x 2y 48 and 3x 2y 32 represent the money collected from school concert ticket sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?

7 Solve the following system of equations algebraically for y:

2x 2y 9

2x y 3

8 Solve the following system of equations algebraically:

3x 2y 4

4x 3y 7[Only an algebraic solution can receive full credit.]

ID: A

1


1 ANS: 2x 2y 9

x y 3

3y 6

y 2


1x 2y 1

x 4y 7

6y 6

y 1


c 2, d 2c 3d 8

4d 6 3d 8

7d 14

d 2

c 4d 6

c 4(2) 6

c 2


22(x 3y 3)

2x y 8

2x 6y 6

7y 14

y 2

REF: 081021ia

ID: A

2

5 ANS: (3,1)

2x 5y 11

2x 3y 9

2y 2

y 1

2x 5(1) 11

2x 6

x 3


$85x 2y 48

3x 2y 32

2x 16

x 8


2. Subtracting the equations: 3y 6

y 2


(2,5). 3x 2y 4 12x 8y 16

4x 3y 7 12x 9y 21

y 5

. 3x 2y 4

3x 2(5) 4

3x 6

x 2

REF: 010937ia


1


1 What is the value of y in the following system of equations?

2x 3y 6

2x y 21) 12) 23) 34) 4

2 If a 3b 13 and a b 5, the value of b is1) 12) 73) 4.54) 4

3 If x y 10 and x y 2, what is the value of x?1) 62) 63) 44) 4

4 Which ordered pair is the solution of the following system of equations?

3x 2y 4

2x 2y 241) (2,1)2) (2,5)3) (4,8)4) (4,8)

5 Which ordered pair satisfies the system of equations below?

3x y 8

x y 21) (3,1)2) (2.5,0.5)3) (2.5,0.5)4) (5,3)

6 What point is the intersection of the graphs of the lines 2x y 3 and x y 3?1) (2,1)2) (1,2)3) (3,0)4) (3,3)

7 When solved graphically, which system of equations will have exactly one point of intersection?1) y x 20

y x 172) y 0.5x 30

y 0.5x 30

3) y 35

x 12

y 0.6x 194) y x 15

y x 25

ID: A

1


1 ANS: 42x 3y 6

2x y 2

2y 8

y 4

REF: 080013a 2 ANS: 4

REF: 080706a 3 ANS: 3

REF: 060824a 4 ANS: 3

3x 2y 4

2x 2y 24

5x 20

x 4

. 3x 2y 4

3(4) 2y 4

12 2y 4

y 8

REF: 060007a 5 ANS: 2

.

REF: 060716a

ID: A

2

6 ANS: 12x y 3

x y 3

3x 6

x 2

. x y 3

2 y 3

y 1

REF: 080429a 7 ANS: 1

In (2) – (4), the equations in each system have equal slope, and therefore do not intersect.

REF: 080529a


1


1 What is the value of y in the following system of equations?

2x 3y 6

2x y 2

2 If a 3b 13 and a b 5, the value of b is

3 If x y 10 and x y 2, what is the value of x?

4 Which ordered pair is the solution of the following system of equations?

3x 2y 4

2x 2y 24

5 Which ordered pair satisfies the system of equations below?

3x y 8

x y 2

6 What point is the intersection of the graphs of the lines 2x y 3 and x y 3?

7 When solved graphically, which system of equations will have exactly one point of intersection?1) y x 20

y x 172) y 0.5x 30

y 0.5x 30

3) y 35

x 12

y 0.6x 194) y x 15

y x 25

ID: A

1


1 ANS: 42x 3y 6

2x y 2

2y 8

y 4

REF: 080013a 2 ANS:

4

REF: 080706a 3 ANS:

4

REF: 060824a 4 ANS:

(4,8)3x 2y 4

2x 2y 24

5x 20

x 4

. 3x 2y 4

3(4) 2y 4

12 2y 4

y 8

REF: 060007a

ID: A

2

5 ANS: (2.5,0.5)

.

REF: 060716a 6 ANS:

(2,1)2x y 3

x y 3

3x 6

x 2

. x y 3

2 y 3

y 1

REF: 080429a 7 ANS: 1

In (2) – (4), the equations in each system have equal slope, and therefore do not intersect.

REF: 080529a

Regents Exam Questions A.A.11: Quadratic-Linear Systems Name: ________________________ www.jmap.org

1

A.A.11: Quadratic-Linear Systems:Solve a system of one linear and one quadratic equation in two variables, where only factoring is required

1 Which ordered pair is a solution to the system of

equations y x and y x 2 2?1) (2,2)2) (1,1)3) (0,0)4) (2,2)

2 Which ordered pair is a solution to the system of

equations y x 3 and y x 2 x?1) (6,9)2) (3,6)3) (3,1)4) (2,5)

3 Which ordered pair is in the solution set of the

system of equations y x 1 and y x 2 5x 6?1) (5,1)2) (5,6)3) (5,4)4) (5,2)

4 Which ordered pair is a solution of the system of

equations y x 2 x 20 and y 3x 15?1) (5,30)2) (1,18)3) (0,5)4) (5,1)

5 The graphs of the equations y x 2 4x 1 and y 3 x are drawn on the same set of axes. At which point do the graphs intersect?1) (1,4)2) (1. 2)3) (2,1)4) (2,5)

6 What is the solution set of the system of equations

x y 5 and y x 2 25?1) {(0,5),(11,6)}2) {(5,0),(6,11)}3) {(5,0),(6,11)}4) {(5,10),(6,1)}

7 Solve the following system of equations algebraically.

y x 2 4x 2

y 2x 1

8 Solve the following system of equations algebraically for all values of x and y.

y x 2 2x 8

y 2x 1

ID: A

1

A.A.11: Quadratic-Linear Systems:Solve a system of one linear and one quadratic equation in two variables, where only factoring is required

Answer Section

1 ANS: 4

x 2 2 x

x 2 x 2 0

(x 2)(x 1) 0

x 2 or 1

Since y x , the solutions are (2,2) and (1,1).

REF: 060810ia 2 ANS: 2

x 2 x x 3

x 2 2x 3 0

(x 3)(x 1) 0

x 3 or 1

. Since y x 3, the solutions are (3,6) and (1,2).

REF: 061118ia 3 ANS: 2

x 2 5x 6 x 1

x 2 6x 5 0

(x 5)(x 1) 0

x 5 or 1

. y x 1

(5) 1

6

REF: 080812ia

ID: A

2

4 ANS: 2

x 2 x 20 3x 15

x 2 4x 6 0

(x 5)(x 1) 0

x 5 or 1

. y 3x 15

3(1) 15

18

.

REF: 010922ia 5 ANS: 4

y 3 x

y x 3

. . y 3 x

y 2 3

y 5

. .

REF: 060018a 6 ANS: 2

y x 5. x 5 x 2 25

0 x 2 x 30

0 (x 6)(x 5)

x 6,5

. y (6) 5 11

y 5 5 0

.


(3,5), (1,3). . y 2(3) 1 5

2(1) 1 3

. .

REF: 080135a

ID: A

3

8 ANS:

(3,5), (3,7). x 2 2x 8 2x 1

x2 9 0

x 3

. y 2(3) 1 7

y 2(3) 1 5

REF: 081236ia

Regents Exam Questions A.A.12: Division of Powers 1 Name: ________________________ www.jmap.org

1

A.A.12: Division of Powers 1: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents only

1 What is half of 26?

1) 13 2) 16 3) 23 4) 25

2 What is one-third of 36?

1) 12 2) 32 3) 35 4) 96

3 The quotient of 15x 8

5x 2, x 0, is

1) 3x 4 2) 10x 4 3) 3x 6 4) 10x 6

4 The expression 32x 8

4x 2, x 0, is equivalent to

1) 8x 4 2) 8x 6 3) 8x 4 4) 8x 6

5 When 9x 5 is divided by 3x 3 , x 0, the quotient is

1) 3x 2 2) 3x 2 3) 27x 15 4) 27x 8

6 Which expression represents (2x 3 )(8x 5 )

4x 6 in simplest

form?

1) x 2 2) x 9 3) 4x 2 4) 4x 9

7 The expression 12w9 y3

3w3 y 3 is equivalent to

1) 4w6 2) 4w3 y 3) 9w6 4) 9w3y

8 Which expression represents 27x 18 y 5

9x 6y in simplest

form?

1) 3x 12 y 4 2) 3x 3 y 5 3) 18x 12 y 4 4) 18x 3 y 5

9 Which expression represents 14a 2 c 8

7a 3 c 2 in simplest

form?

1) 2ac4 2) 2ac6 3) 2c 4

a 4)

2c 6

a

10 The expression 5x 6 y 2

x 8 y is equivalent to

1) 5x 2 y 2) 5y

x 2 3) 5x 14 y 3 4) 5y 3

x 14

11 The expression 4x 2 y 3

2xy 4 is equivalent to

1) 2xy

2) 2yx

3) 2xy 4) 2xy

12 Simplify: 27k 5 m8

(4k 3 )(9m2 )

ID: A

1

A.A.12: Division of Powers 1: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents onlyAnswer Section

1 ANS: 4

26

21 25

REF: 060813ia 2 ANS: 3

36

31 35

REF: 061219ia 3 ANS: 3 REF: 060005a 4 ANS: 4 REF: 060707a 5 ANS: 2 REF: 080405a 6 ANS: 3

(2x 3 )(8x 5 )

4x 6 16x 8

4x 6 4x 2

REF: fall0703ia 7 ANS: 1 REF: 061103ia 8 ANS: 1 REF: 060903ia 9 ANS: 4 REF: 061018ia 10 ANS: 2 REF: 080526a 11 ANS: 1 REF: 010817a 12 ANS:

3k 2 m6

4

REF: 010932ia

Regents Exam Questions A.A.12: Division of Powers 2 Name: ________________________ www.jmap.org

1

A.A.12: Division of Powers 2: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents only

1 What is half of 26?

2 What is one-third of 36?

3 The quotient of 15x 8

5x 2, x 0, is

4 The expression 32x 8

4x 2, x 0, is equivalent to

5 When 9x 5 is divided by 3x 3 , x 0, the quotient is

6 Which expression represents (2x 3 )(8x 5 )

4x 6 in simplest

form?

7 The expression 12w9y3

3w3y 3 is equivalent to

8 Which expression represents 27x 18y 5

9x 6y in simplest

form?

9 Which expression represents 14a 2c 8

7a 3c 2 in simplest

form?

10 The expression 5x 6y 2

x 8y is equivalent to

11 The expression 4x 2y 3

2xy 4 is equivalent to

12 Simplify: 27k 5m8

(4k 3 )(9m2 )

ID: A

1

A.A.12: Division of Powers 2: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents onlyAnswer Section

1 ANS:

25

26

21 25


35

36

31 35


3x 6

REF: 060005a 4 ANS:

8x 6

REF: 060707a 5 ANS:

3x 2

REF: 080405a 6 ANS:

4x 2

(2x 3 )(8x 5 )

4x 6 16x 8

4x 6 4x 2


4w6


3x 12y 4

REF: 060903ia

ID: A

2

9 ANS:

2c 6

a

REF: 061018ia 10 ANS:

5y

x 2

REF: 080526a 11 ANS:

2xy

REF: 010817a 12 ANS:

3k 2m6

4

REF: 010932ia

Regents Exam Questions A.A.12: Multiplication of Powers 1 Name: ________________________ www.jmap.org

1

A.A.12: Multiplication of Powers 1: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents only

1 Which expression is equivalent to 33 34 ?

1) 912

2) 97

3) 312

4) 37

2 The expression 32 33 34 is equivalent to

1) 279

2) 2724

3) 39

4) 324

3 Which expression represents (3x 2y4 )(4xy 2 ) in simplest form?

1) 12x 2y 8

2) 12x 2y 6

3) 12x 3y 8

4) 12x 3y 6

4 The product of 4x 2y and 2xy 3 is

1) 8x 2y 3

2) 8x 3y 3

3) 8x 3y 4

4) 8x 2y 4

5 The expression (x 2z3 )(xy 2z) is equivalent to

1) x 2y 2z3

2) x 3y 2z4

3) x 3y 3z4

4) x 4y 2z5

6 The product of 2x 3 and 6x 5 is

1) 10x 8

2) 12x 8

3) 10x15

4) 12x15


1) 12x 3y 4

2) 12x 3y 4

3) 12x 2y 3

4) 12x 2y 3


1) 5x 9

2) 5x 20

3) 6x 9

4) 6x 20


2

9 What is the product of 10x 4y 2 and 3xy 3?

1) 30x 4y 5

2) 30x 4y 6

3) 30x 5y 5

4) 30x 5y 6

10 The expression (2a 2b 3 )(4ab 5 )(6a 3b 2 ) is equivalent to

1) 8a 6b 30

2) 48a 5b 10

3) 48a 6b 10

4) 48a 5b 10

11 What is the product of 13

x 2y and 16

xy 3?

1)12

x 2y 3

2)19

x 3y 4

3)118

x 2y3

4)118

x 3y4

12 The product of 6xa and x is

1) 6xa

2) 6xa 1

3) 6xa2

4) 6x 2a

13 If x 5a , then the value of 5x is1) x 12) 6a

3) a 54) 5a 1

ID: A

1

A.A.12: Multiplication of Powers 1: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents onlyAnswer Section

1 ANS: 4 REF: 011020ia 2 ANS: 3 REF: 060312a 3 ANS: 4 REF: 080903ia 4 ANS: 3 REF: 089906a 5 ANS: 2 REF: 010008a 6 ANS: 2 REF: 080001a 7 ANS: 1 REF: 010205a 8 ANS: 3 REF: 010306a 9 ANS: 3 REF: 080605a 10 ANS: 3 REF: 010910a 11 ANS: 4 REF: 060604a 12 ANS: 2 REF: 060328siii 13 ANS: 4 REF: 018926siii


1

A.A.12: Multiplication of Powers 2: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents only

1 Which expression is equivalent to 33 34 ?

2 The expression 32 33 34 is equivalent to

3 Which expression represents (3x 2y4 )(4xy 2 ) in simplest form?


5 The expression (x 2z3 )(xy 2z) is equivalent to




9 What is the product of 10x 4y 2 and 3xy 3?

10 The expression (2a 2b 3 )(4ab 5 )(6a 3b 2 ) is equivalent to

11 What is the product of 13

x 2y and 16

xy 3?

12 The product of 6xa and x is

13 If x 5a , then the value of 5x is

ID: A

1

A.A.12: Multiplication of Powers 2: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents onlyAnswer Section

1 ANS:

37


39

REF: 060312a 3 ANS:

12x 3y 6


8x 3y 4

REF: 089906a 5 ANS:

x 3y 2z4

REF: 010008a 6 ANS:

12x 8

REF: 080001a 7 ANS:

12x 3y 4

REF: 010205a 8 ANS:

6x 9

REF: 010306a 9 ANS:

30x 5y 5

REF: 080605a 10 ANS:

48a 6b 10

REF: 010910a

ID: A

2

11 ANS: 118

x 3y4

REF: 060604a 12 ANS:

6xa 1


5a 1

REF: 018926siii

Regents Exam Questions A.A.12: Powers of Powers 1 Name: ________________________ www.jmap.org

1

A.A.12: Powers of Powers 1: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents only

1 Which expression is equivalent to (3x 2 )3?

1) 9x 5

2) 9x 6

3) 27x 5

4) 27x 6

2 Expressed in simplest form, (3x 3 )(2y)2 (4x 4 ) is equivalent to

1) 24x 12y 2

2) 24x 7y 2

3) 48x 12y 2

4) 48x 7y 2

3 The expression (6x 3y 6 )2 is equivalent to

1) 36x 6y 12

2) 36x 5y 8

3) 12x 6y 12

4) 6x 6y 12

4 The expression (4a 3b)2 is equivalent to

1) 16a 6b 2

2) 16a 6b 2

3) 16a 5b 2

4) 8a 6b 2

5 The product of (5ab) and (2a 2b)3 is

1) 30a 6b 4

2) 30a 7b 4

3) 40a 6b 4

4) 40a 7b 4

6 If x 0, then (x 2 )3

x 5 1000 is equivalent to

1) 1000x2) 1000 x3) 10004) 0

7 The expression 4x 3Ê

ËÁÁÁ

ˆ¯˜̃̃

2

2x is equivalent to

1) 4x 4

2) 4x 5

3) 8x 4

4) 8x 5

8 The expression (10w3 )2

5w is equivalent to

1) 2w5

2) 2w8

3) 20w5

4) 20w8

9 The expression b 2n 1Ê

ËÁÁÁ

ˆ¯˜̃̃

3

bn b 4n 3 is equivalent to

1)bn

2

2) bn

3) b 3n

4) b 3n 1

ID: A

1

A.A.12: Powers of Powers 1: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents onlyAnswer Section

1 ANS: 4 REF: 080827ia 2 ANS: 4

REF: 010529a 3 ANS: 1 REF: 010728a 4 ANS: 2 REF: 080824a 5 ANS: 4

REF: 010506b 6 ANS: 1

REF: 060518a 7 ANS: 4

4x 3ÊËÁÁÁ

ˆ¯˜̃̃

2

2x 16x 6

2x 8x 5

REF: 011216ia 8 ANS: 3

(10w3 )2

5w 100w6

5w 20w5

REF: 011124ia 9 ANS: 2

REF: 080415b

Regents Exam Questions A.A.12: Powers of Powers 2 Name: ________________________ www.jmap.org

1

A.A.12: Powers of Powers 2: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents only

1 Which expression is equivalent to (3x 2 )3?

2 Expressed in simplest form, (3x 3 )(2y)2 (4x 4 ) is equivalent to

3 The expression (6x 3y 6 )2 is equivalent to

4 The expression (4a 3b)2 is equivalent to

5 The product of (5ab) and (2a 2b)3 is

6 If x 0, then (x 2 )3

x 5 1000 is equivalent to

7 The expression 4x 3Ê

ËÁÁÁ

ˆ¯˜̃̃

2

2x is equivalent to

8 The expression (10w3 )2

5w is equivalent to

9 The expression b 2n 1Ê

ËÁÁÁ

ˆ¯˜̃̃

3

bn b 4n 3 is equivalent to

ID: A

1

A.A.12: Powers of Powers 2: Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents onlyAnswer Section

1 ANS:

27x 6


48x 7y 2

REF: 010529a 3 ANS:

36x 6y 12

REF: 010728a 4 ANS:

16a 6b 2

REF: 080824a 5 ANS:

40a 7b 4

REF: 010506b 6 ANS:

1000x

REF: 060518a 7 ANS:

8x 5

4x 3ÊËÁÁÁ

ˆ¯˜̃̃

2

2x 16x 6

2x 8x 5


20w5

(10w3 )2

5w 100w6

5w 20w5

REF: 011124ia

ID: A

2

9 ANS:

bn

REF: 080415b

Regents Exam Questions Name: ________________________ A.A.13: Addition and Subtraction of Monomialswww.jmap.org

1

A.A.13: Addition and Subtraction of Monomials: Add, subtract, and multiply monomials and polynomials

1 The expression 2x 2 x 2 is equivalent to

1) x 0

2) 2

3) x 2

4) 2x 4

2 Which expression is equivalent to 3x(x 4) 2x(x 3)?

1) x 2 12) x 2 18x3) 5x 2 6x4) 5x 2 6x

ID: A

1

A.A.13: Addition and Subtraction of Monomials: Add, subtract, and multiply monomials and polynomialsAnswer Section

1 ANS: 3 REF: 080623a 2 ANS: 4

3x(x 4) 2x(x 3) 3x 2 12x 2x2 6x 5x 2 6x

REF: 081114ia

Regents Exam Questions Name: ________________________ A.A.13: Addition and Subtraction of Polynomials 1www.jmap.org

1

A.A.13: Addition and Subtraction of Polynomials 1: Add, subtract, and multiply monomials and polynomials

1 The sum of 3x 2 x 8 and x 2 9 can be expressed as

1) 4x 2 x 12) 4x 2 x 173) 4x 4 x 14) 3x 4 x 1

2 The sum of 3x 2 4x 2 and x 2 5x 3 is

1) 4x 2 x 12) 4x 2 x 13) 4x 2 x 14) 4x 2 x 1

3 The sum of 8x 2 x 4 and x 5 is

1) 8x 2 92) 8x 2 13) 8x 2 2x 94) 8x 2 2x 1

4 What is the sum of x 2 3x 7 and 3x 2 5x 9?

1) 4x 2 8x 22) 4x 2 2x 163) 4x 2 2x 24) 4x 2 2x 2

5 What is the sum of 2m2 3m 4 and m2 3m 2?

1) m2 62) 3m2 63) 3m2 6m 64) m2 6m 2

6 The sum of 4x 3 6x 2 2x 3 and

3x 3 3x 2 5x 5 is

1) 7x 3 3x 2 3x 82) 7x 3 3x 2 7x 23) 7x 3 9x 2 3x 84) 7x 6 9x 4 3x2 8

7 What is the sum of 3x 2 7x 9 and 5x 2 6x 4?

1) 8x 2 x 52) 8x 4 x 53) 8x 2 13x 134) 8x 4 13x2 13


1) 2x 2 8x 152) 2x 2 8x 33) 2x 4 8x 2 34) 4x 2 2x 15

ID: A

1

A.A.13: Addition and Subtraction of Polynomials 1: Add, subtract, and multiply monomials and polynomialsAnswer Section

1 ANS: 1 REF: 069904a 2 ANS: 2 REF: 010108a 3 ANS: 2 REF: 080710a 4 ANS: 4 REF: 060805a 5 ANS: 2 REF: 080807a 6 ANS: 3 REF: 061003ia 7 ANS: 1 REF: 011213ia 8 ANS: 2 REF: 081205ia


1


1 The sum of 3x 2 x 8 and x 2 9 can be expressed as


3 The sum of 8x 2 x 4 and x 5 is

4 What is the sum of x 2 3x 7 and 3x 2 5x 9?

5 What is the sum of 2m2 3m 4 and m2 3m 2?

6 The sum of 4x 3 6x 2 2x 3 and 3x 3 3x 2 5x 5 is

7 What is the sum of 3x 2 7x 9 and 5x 2 6x 4?


ID: A

1


1 ANS:

4x 2 x 1

REF: 069904a 2 ANS:

4x 2 x 1

REF: 010108a 3 ANS:

8x 2 1

REF: 080710a 4 ANS:

4x 2 2x 2

REF: 060805a 5 ANS:

3m2 6

REF: 080807a 6 ANS:

7x 3 9x 2 3x 8


8x 2 x 5


2x 2 8x 3

REF: 081205ia


1


1 The expression (3x 2 2xy 7) (6x 2 4xy 3) is equivalent to

1) 3x 2 2xy 4

2) 3x 2 2xy 4

3) 3x 2 6xy 4

4) 3x 2 6xy 4

2 The expression (x 2 5x 2) (6x 2 7x 3) is equivalent to

1) 7x 2 12x 52) 7x 2 2x 13) 7x 2 2x 14) 7x 2 2x 5

3 The expression (2x 2 6x 5) (6x 2 3x 5) is equivalent to

1) 4x 2 3x2) 4x 2 3x3) 4x 2 3x 104) 4x 2 3x 10

4 When 3x 2 8x is subtracted from 2x 2 3x, the difference is

1) x 2 11x2) x 2 11x3) x 2 5x4) x 2 5x

5 When 5x 4y is subtracted from 5x 4y, the difference is1) 02) 10x3) 8y4) 8y

6 When 3g 2 4g 2 is subtracted from 7g 2 5g 1, the difference is

1) 4g 2 9g 3

2) 4g 2 g 1

3) 4g 2 9g 3

4) 10g 2 g 1

7 When 4x 2 7x 5 is subtracted from 9x 2 2x 3, the result is

1) 5x 2 5x 22) 5x 2 9x 83) 5x 2 5x 24) 5x 2 9x 8

8 When 3a 2 2a 5 is subtracted from a 2 a 1, the result is

1) 2a 2 3a 62) 2a 2 3a 63) 2a 2 3a 64) 2a 2 3a 6


2

9 If 2x 2 4x 6 is subtracted from 5x 2 8x 2, the difference is

1) 3x 2 12x 82) 3x 2 12x 83) 3x 2 4x 44) 3x 2 4x 4

10 When 3x 2 2x 1 is subtracted from 2x 2 7x 5, the result will be

1) x 2 9x 42) x 2 9x 43) x 2 5x 64) x 2 5x 6

11 When 2x 2 4x 2 is subtracted from x 2 6x 4, the result is

1) 3x 2 2x 62) x 2 10x 23) 2x 2 2x 64) 3x 2 2x 6

12 If 2x 2 x 6 is subtracted from x 2 3x 2, the result is

1) x 2 2x 82) x 2 4x 83) x 2 2x 84) x 2 4x 8

13 When 3a 2 7a 6 is subtracted from 4a 2 3a 4, the result is

1) a 2 4a 22) a 2 10a 23) a 2 4a 24) 7a 2 10a 10

14 If 2a 2 6a 5 is subtracted from 3a 2 2a 3, the result is

1) 5a 2 8a 82) a 2 4a 23) a 2 4a 24) a 2 8a 8


1) x 2 22) 17x 2 23) x 2 6x 64) x 2 6x 6

16 What is the result when 2x 2 3xy 6 is subtracted

from x 2 7xy 2?

1) x 2 10xy 8

2) x 2 10xy 8

3) x 2 4xy 4

4) x 2 4xy 4

17 Subtract 5x 2 7x 6 from 9x 2 3x 4.

18 Subtract 2x 2 5x 8 from 6x 2 3x 2 and express the answer as a trinomial.

ID: A

1


1 ANS: 3 REF: 080423a 2 ANS: 3 REF: 060511a 3 ANS: 1 REF: 010707a 4 ANS: 1 REF: 010523a 5 ANS: 4 REF: 061130ia 6 ANS: 3 REF: 080819ia 7 ANS: 2 REF: 060923ia 8 ANS: 2 REF: 010019a 9 ANS: 1 REF: 060019a 10 ANS: 1 REF: 080020a 11 ANS: 4 REF: 080209a 12 ANS: 4 REF: 010429a 13 ANS: 1 REF: 010619a 14 ANS: 2 REF: spring9805a 15 ANS: 4 REF: 061226ia 16 ANS: 1 REF: 011126ia 17 ANS:

4x 2 10x 2

REF: 080123a 18 ANS:

4x 2 8x 10

REF: 010934a


1


1 The expression (3x 2 2xy 7) (6x 2 4xy 3) is equivalent to

2 The expression (x 2 5x 2) (6x 2 7x 3) is equivalent to

3 The expression (2x 2 6x 5) (6x 2 3x 5) is equivalent to

4 When 3x 2 8x is subtracted from 2x 2 3x, the difference is

5 When 5x 4y is subtracted from 5x 4y, the difference is

6 When 3g 2 4g 2 is subtracted from 7g 2 5g 1, the difference is


8 When 3a 2 2a 5 is subtracted from a 2 a 1, the result is

9 If 2x 2 4x 6 is subtracted from 5x 2 8x 2, the difference is

10 When 3x 2 2x 1 is subtracted from 2x 2 7x 5, the result will be

11 When 2x 2 4x 2 is subtracted from x 2 6x 4, the result is

12 If 2x 2 x 6 is subtracted from x 2 3x 2, the result is

13 When 3a 2 7a 6 is subtracted from 4a 2 3a 4, the result is

14 If 2a 2 6a 5 is subtracted from 3a 2 2a 3, the result is


16 What is the result when 2x 2 3xy 6 is subtracted

from x 2 7xy 2?

17 Subtract 5x 2 7x 6 from 9x 2 3x 4.

18 Subtract 2x 2 5x 8 from 6x 2 3x 2 and express the answer as a trinomial.

ID: A

1


1 ANS:

3x 2 6xy 4

REF: 080423a 2 ANS:

7x 2 2x 1

REF: 060511a 3 ANS:

4x 2 3x

REF: 010707a 4 ANS:

x 2 11x

REF: 010523a 5 ANS:

8y


4g 2 9g 3


5x 2 9x 8


2a 2 3a 6

REF: 010019a 9 ANS:

3x 2 12x 8

REF: 060019a 10 ANS:

x 2 9x 4

REF: 080020a

ID: A

2

11 ANS:

3x 2 2x 6

REF: 080209a 12 ANS:

x 2 4x 8

REF: 010429a 13 ANS:

a 2 4a 2

REF: 010619a 14 ANS:

a 2 4a 2


x 2 6x 6

REF: 061226ia 16 ANS:

x 2 10xy 8

REF: 011126ia 17 ANS:

4x 2 10x 2

REF: 080123a 18 ANS:

4x 2 8x 10

REF: 010934a

Regents Exam Questions A.A.13: Multiplication of Polynomials 1 Name: ________________________ www.jmap.org

1

A.A.13: Multiplication of Polynomials 1: Add, subtract, and multiply monomials and polynomials

1 What is the product of 2r2 5 and 3r?

1) 6r3 15r2) 6r3 53) 6r2 15r4) 6r2 15

2 What is the product of 3x 2 y and (5xy 2 xy)?

1) 15x 3y 3 3x 3 y 2

2) 15x 3 y3 3x3 y

3) 15x 2 y2 3x2 y

4) 15x 3 y 3 xy

3 What is the product of (c 8) and (c 5)?

1) c 2 3c 402) c 2 3c 403) c 2 13c 404) c 2 40

4 What is the product of (3x 2) and (x 7)?

1) 3x 2 142) 3x 2 5x 143) 3x 2 19x 144) 3x 2 23x 14

5 The expression (x 6)2 is equivalent to

1) x 2 362) x 2 363) x 2 12x 364) x 2 12x 36

6 The expression a 2 b 2ÊËÁÁÁ

ˆ¯˜̃̃

2

is equivalent to

1) a 4 b 4

2) a 4 a 2b 2 b 4

3) a 4 2a 2 b 2 b 4

4) a 4 4a 2 b 2 b 4

7 The expression (2x 1)2 2(2x 2 1) is equivalent to1) 4x 32) 2x 33) 34) 1

ID: A

1

A.A.13: Multiplication of Polynomials 1: Add, subtract, and multiply monomials and polynomialsAnswer Section

1 ANS: 1 REF: 010819a 2 ANS: 1 REF: 060807ia 3 ANS: 1

REF: 060708a 4 ANS: 3

(3x 2)(x 7) 3x 2 21x 2x 14 3x2 19x 14

REF: 061210ia 5 ANS: 3

REF: 060015a 6 ANS: 3

REF: 010430a 7 ANS: 1 REF: 088917siii

Regents Exam Questions A.A.13: Multiplication of Polynomials 2 Name: ________________________ www.jmap.org

1

A.A.13: Multiplication of Polynomials 2: Add, subtract, and multiply monomials and polynomials

1 What is the product of 2r2 5 and 3r?

2 What is the product of 3x 2 y and (5xy 2 xy)?

3 What is the product of (c 8) and (c 5)?

4 What is the product of (3x 2) and (x 7)?

5 The expression (x 6)2 is equivalent to

6 The expression a 2 b 2ÊËÁÁÁ

ˆ¯˜̃̃

2

is equivalent to

7 The expression (2x 1)2 2(2x 2 1) is equivalent to

ID: A

1

A.A.13: Multiplication of Polynomials 2: Add, subtract, and multiply monomials and polynomialsAnswer Section

1 ANS:

6r3 15r

REF: 010819a 2 ANS:

15x 3y 3 3x 3 y 2


c 2 3c 40

REF: 060708a 4 ANS:

3x 2 19x 14(3x 2)(x 7) 3x 2 21x 2x 14 3x2 19x 14


x 2 12x 36

REF: 060015a 6 ANS:

a 4 2a 2 b 2 b 4

REF: 010430a 7 ANS:

4x 3

REF: 088917siii

Regents Exam Questions A.A.14: Division of Polynomials Name: ________________________ www.jmap.org

1

A.A.14: Division of Polynomials: Divide a polynomial by a monomial or binomial, where the quotient has no remainder

1 When 3x 2 6x is divided by 3x, the result is1) 2x2) 2x3) x 24) x 2

2 What is 6x 3 4x2 2x divided by 2x?

1) 3x 2 2x2) 3x 2 2x 13) 4x 2 2x4) 4x 2 2x 1

3 When 6y 6 18y3 12y 2 is divided by 3y 2 , the quotient is

1) 2y 4 6y2 4y

2) 3y 4 6y 4

3) 2y 4 6y 4

4) 2y 3 6y 2 4y

4 The expression (50x 3 60x 2 10x) 10x

1) 5x 2 6x 12) 5x 3 6x 2 x3) 5x 2 60x2 10x4) 5x 2 6x

5 If x 0, the expression x 2 2x

x is equivalent to

1) x 22) 23) 3x4) 4

6 Which expression represents 12x 3 6x 2 2x

2x in

simplest form?

1) 6x 2 3x2) 10x 2 4x3) 6x 2 3x 14) 10x 2 4x 1

7 Which polynomial is the quotient of

6x 3 9x 2 3x3x

?

1) 2x 2 3x 12) 2x 2 3x3) 2x 34) 6x 2 9x

8 The quotient of 8x 5 2x4 4x3 6x 2

2x 2 is

1) 16x 7 4x 6 8x 5 12x 4

2) `4x 7 x 6 2x 5 3x 4

3) 4x 3 x 2 2x 3x4) 4x 3 x 2 2x 3

9 Express in simplest form: 45a 4b 3 90a 3b

15a 2b

ID: A

1

A.A.14: Division of Polynomials: Divide a polynomial by a monomial or binomial, where the quotient has no remainderAnswer Section

1 ANS: 4 REF: 060506a 2 ANS: 2 REF: 080817a 3 ANS: 3 REF: spring9807a 4 ANS: 1 REF: 010724a 5 ANS: 1

x 2 2xx

x 2

REF: 010109a 6 ANS: 3

12x 3 6x 2 2x2x

2x(6x 2 3x 1)

2x 6x 2 3x 1

REF: 011011ia 7 ANS: 1

REF: 060102a 8 ANS: 4 REF: 061203ia 9 ANS:

3a 2b 2 6a. 45a 4b 3 90a 3b

15a 2b 45a 4b 3

15a 2b 90a 3b

15a 2b 3a 2b 2 6a

REF: 081031ia

Regents Exam Questions A.A.15: Undefined Rationals 1 Name: ________________________ www.jmap.org

1

A.A.15: Undefined Rationals 1: Find values of a variable for which an algebraic fraction is undefined

1 Which value of x makes the expression x 4x 3

undefined?1) 42) 33) 34) 0

2 Which value of n makes the expression 5n

2n 1

undefined?1) 12) 0

3) 12

4)12

3 For which value of x is x 3

x 2 4 undefined?

1) 22) 03) 34) 4

4 The expression 14 x

x 2 4 is undefined when x is

1) 14, only2) 2, only3) 2 or 24) 14, 2, or 2

5 The function y x

x2 9 is undefined when the

value of x is1) 0 or 32) 3 or 33) 3, only4) 3, only

6 The algebraic expression x 2

x 2 9 is undefined when

x is 1) 02) 23) 34) 9

7 Which value of x makes the expression

x 2 9

x 2 7x 10 undefined?

1) 52) 23) 34) 3

8 For which set of values of x is the algebraic

expression x 2 16


1) {6,2}2) {4,3}3) {4,4}4) {2,6}

9 For which values of x is the fraction x 2 x 6

x 2 5x 6

undefined?1) 1 and 62) 2 and 33) 3 and 24) 6 and 1

ID: A

1

A.A.15: Undefined Rationals 1: Find values of a variable for which an algebraic fraction is undefinedAnswer Section

1 ANS: 3 REF: 060817ia 2 ANS: 4 REF: 060916ia 3 ANS: 1 REF: fall0728ia 4 ANS: 3

x 2 4 0

(x 2)(x 2) 0

x 2


x 2 9 0

(x 3)(x 3) 0

x 3

REF: 061014ia 7 ANS: 1

x 2 7x 10 0

(x 5)(x 2) 0

x 5 or 2

REF: 080918ia 8 ANS: 4

x 2 4x 12 0

(x 6)(x 2) 0

x 6 x 2

REF: 061125ia 9 ANS: 1

x 2 5x 6 0

(x 6)(x 1) 0

x 6, 1

REF: 011214ia


1


1 Which value of x makes the expression x 4x 3

undefined?

2 Which value of n makes the expression 5n

2n 1

undefined?

3 For which value of x is x 3

x 2 4 undefined?

4 The expression 14 x

x 2 4 is undefined when x is

5 The function y x

x2 9 is undefined when the

value of x is

6 The algebraic expression x 2

x 2 9 is undefined when

x is

7 Which value of x makes the expression

x 2 9


8 For which set of values of x is the algebraic

expression x 2 16


9 For which values of x is the fraction x 2 x 6

x 2 5x 6

undefined?

ID: A

1


1 ANS: 3


12


2


2 or 2

x 2 4 0

(x 2)(x 2) 0

x 2


3 or 3


3

x 2 9 0

(x 3)(x 3) 0

x 3


5x 2 7x 10 0

(x 5)(x 2) 0

x 5 or 2

REF: 080918ia

ID: A

2

8 ANS: {2,6}

x 2 4x 12 0

(x 6)(x 2) 0

x 6 x 2


1 and 6x 2 5x 6 0

(x 6)(x 1) 0

x 6, 1

REF: 011214ia


1


1 For which value of x is the expression 3x 6x 4

undefined?1) 02) 23) 44) 4

2 For which value of x is the expression x 7x 2

undefined?1) 22) 23) 74) 0

3 For which value of x is the expression 3

x 2

undefined?1) 22) 23) 34) 0

4 For which value of x is the expression 6 xx 2

undefined?1) 22) 23) 04) 6


undefined?1) 12) 13) 54) 5

6 For which value of m is the expression 15m2 n3 m

undefined?1) 12) 03) 34) 3

7 For which value of x will the fraction 3

2x 4 be

undefined?1) 22) 23) 04) 4

8 For which value or values of n is the expression n 12n 4

undefined?

1) 1, only2) 2, only3) 1 and 24) 0

9 For which value of x is 1

27 3x undefined?

1) 12) 03) 34) 3

10 Which expression is undefined when w 3?

1)w 3w 1

2)w2 2w

5w

3)w 1

w2 3w

4)3w

3w2

11 For what values of x is the fraction 4 x

x 2 4

undefined?

12 For which negative values of x is the fraction x 5

x 2 x 6 undefined?

ID: A

1


1 ANS: 4 REF: 060319a 2 ANS: 1 REF: 080422a 3 ANS: 2 REF: 080610a 4 ANS: 1 REF: 010822a 5 ANS: 3 REF: 080821a 6 ANS: 3 REF: 010917a 7 ANS: 1 REF: 010607a 8 ANS: 2 REF: 060217siii 9 ANS: 3 REF: 060801b 10 ANS: 3 REF: 010716a 11 ANS:

2, 2


2

REF: 089906siii


1



undefined?

2 For which value of x is the expression x 7x 2

undefined?

3 For which value of x is the expression 3

x 2

undefined?

4 For which value of x is the expression 6 xx 2

undefined?


undefined?

6 For which value of m is the expression 15m2 n3 m

undefined?

7 For which value of x will the fraction 3

2x 4 be

undefined?

8 For which value or values of n is the expression n 12n 4

undefined?

9 For which value of x is 1

27 3x undefined?

10 Which expression is undefined when w 3?

1)w 3w 1

2)w2 2w

5w

3)w 1

w2 3w

4)3w

3w2

11 For what values of x is the fraction 4 x

x 2 4

undefined?

12 For which negative values of x is the fraction x 5

x 2 x 6 undefined?

ID: A

1


1 ANS: 4

REF: 060319a 2 ANS:

2

REF: 080422a 3 ANS:

2

REF: 080610a 4 ANS:

2

REF: 010822a 5 ANS:

5

REF: 080821a 6 ANS:

3

REF: 010917a 7 ANS:

2

REF: 010607a 8 ANS:

2, only


3

REF: 060801b 10 ANS: 3 REF: 010716a 11 ANS:

2, 2


2

REF: 089906siii

alg 1 worksheet pkt. with answers 345 pgs

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