Problems on Quadratics, Straight Lines, Polynomials, Logs

and Exponentials

1. (10 points) Express A and B as simplified, improper fraction: For the calculation of A, cancel

common factors in numerators and denominators before multiplication. For the calculation of B, use the least

common denominator.

A = 25

27

. 81

100

B = 3

26

7

10

For A and B, there is 1 point for right answer and 4 points for following instruction on how to

arrive at the answer. Show work! If you use a calculator (not recommended), show the

reasoning needed to arrive at your solution without its use.

2. (10 points) Use algebra to find the intersection point of the two lines

y = ¾x - ¼

y = ¼x + 2

3. (4 points) (a) Find the slope of the straight line K if K is perpendicular to a line L with slope

2.

(6 points) (b) Find the slope and an equation for a straight line T which passes through [3,5]

and [8, 20].

Express the equation in slope intercept form y= m x + b

4. (10 points) Compute product (x4+3x

3+6x

2 + 3x + 1)(x

2 + 2x + 1) using a column method.

5. (10 points) Use the polynomial long division to find polynomials a(x) (the quotient) and r(x)

(the remainder) such that

x4+3x

3+6x

2 + 4x + 2= a(x)(x

2 + 2x + 1) + r(x)

with degree (r(x)) < 2.

6. (2 points) (i) Use the ln(x) button on your calculator to fill in the table (or a copy of it)

x 1/6 0.2 0.25 1/3 0.5 1 2 3 4 5 6

ln(x) 0

(3 points) (i) Use the ex button on your calculator to complete in the table (or a copy of it).

x -1.792 -1.61 -1.39 -1.099 -0.693 0 0.693 1.099 1.39 1.61 1.79

exp(x) 1

(5 points) (iii) Draw the straight line y = x from [-2,-2] to [6,6] on graph paper. Then on the

same graph, use the above points to sketch graph of y = ln(x) for x in the interval [1/6, 6] and y

= exp(x) = ex for x in the interval [-1.79, 1.79]. Label all curves.

7. (3 points) (i) Solve x2-5x+ 4 =0 using factorization by inspection. Show all ways for 4 to

equal the product AB of two integers A and B.

(3 points) (ii) Solve x2-5x+4 = 0 with the quadratic formula. Show work.

(4 points) (iii) Solve x2

- 5x + 4 =0 starting with the method of completing the square. Show

work.

8. (4 points) (i) Find the x- and y-intercepts of the quadratic y = x2-5x+4 and the straight line

y = -2x + 8 with the x- and y-axes. Hint: See 7(ii) or (iii).

(3 points) (ii) Sketch the curves y = x2-5x+4 and y = -2x + 8. Identify the axis of symmetry

for the quadratic. Label axes and all intercepts.

(3 points) (iii) Find the coordinates of the intersection points for the quadratic y = x2-5x+4

and line y = -2x + 8. Show reasoning. Hint: x2-3x-4 = (x-4)(x+1).

_______

| | |

// _ _ \\

/\ /\

<| (o) (o) |>

\ | | /

\___ _/ ||

-/[]\-

|| / \_

Professor Whyslopes:

Site value lies in the

difference between

its ideas and yours. If one site

explanation is not to

your liking, try

another. Each one is

different.

Two gaps The Old Algebra Gap: Algebra appears with too few words of

explanation in high school and college mathematics. Online Volumes 2

and 3 offer remedies. Chapters 8 to 12 in Volume 2 put more words into

the explanation and comprehension of algebra. Chapter 14 in Volume 2

with its explicit discussion of the direct and indirect use a formulas

identifies a unifying theme for mathematics and logic - all rules and

patterns will be used forward and backwards. Chapters 2 to 6 and 12 to 18

in Volume 3 may further ease or avoid the very challenging use of algebra

in the high level mathematics: calculus. Calculus requires earlier high

school mathematics at full strength: (i) This logically complete but long

lesson on complex numbers shows how to simplify the senior high school

exposition of circular trig functions upto to formulas in the plane for

vectors dot and cross-products. The lesson provides the route that would

have been taken in course design if the key element of the lesson, a

December 2009 invention, had been available in the 1950s. For further

algebra skill development. See the site coverage of fraction with units,

proportionality, ratios and rates, polynomials, quadratics functions and

straight line slopes and equations. The Arithmetic Gap: An exact and efficient mastery of arithmetic with

decimals and fractions is best (required) for the high level study of

mathematics alone and in science, technology and business. Pages here on

arithmetic with decimals and integers, on fractions and solving linear

equations with fractional operations on stick diagrams may help fill the

gap. That exact and efficient command should be obtained in the last years

of primary school and the first years of secondary school.

Skill mastery in mathematics has to be seen to believed. To that end, learn or

teach how-to write and draw the steps in mathematical figuring or reasoning

clearly. Do not try to save space by doing a sequence of step in one place. Instead,

do or record the steps in sequence on a separate lines to make each step obvious

and verifiable.

Algebra 1

Chapter 1

1. Which of the following sentences is true?

A.

when x = 4.

B.

when x = 6.

C.

when x = 5.

D.

3x + 5 < x2 when x = 4.

Hint

2. Which statement illustrates the additive identity?

A.

3 - 3 = 0

B.

C.

3 × 1 = 3

D.

3 + 0 = 3

Hint

3. Which statement illustrates the commutative property of addition?

A.

(5 + 3) + 6 = 14

B.

(5 + 3) + 6 = (3 + 5) + 6

C.

(5 + 3) + 6 = 8 + 6

D.

(5 + 3) + 6 = 5 + (3 + 6)

Hint

4. Simplify 3 + 2(xy+ 3z) + 4xy.

A.

9xy + 15z

B.

5xy + 3z + 3

C.

6xy + 3z + 3

D.

6xy + 6z + 3

Hint

5. Evaluate 34.

A.

64

B.

3

C.

12

D.

81

Hint

6. Write the following expression with exponents.

b × b × b × b × b × b × b × b × b

A.

b2

B.

b18

C.

b9

D.

9b

Hint

7. Which statement is best illustrated by the graph?

A.

walking up steps

B.

jogging

C.

driving through the city

D.

driving on the highway

Hint

8. Evaluate a2 - (b + c) if a = 8, b = 17, and c = 21.

A.

34

B.

12

C.

18

D.

26

Hint

9. Evaluate 5(11 + 22 - 10) – 19.

A.

6

B.

66

C.

44

D.

106

Hint

10. Solve = x.

A.

x = 0

B.

x = 10

C.

x = 5

D.

x = 25

Hint

11. Name the property demonstrated by 15 × 1 = 15.

A.

Transitive Property

B.

Multiplicative Identity

C.

Reflexive Property

D.

Multiplicative Inverse

Hint

12. Use the Distributive Property to simplify 11(v – 2).

A.

11v + 22

B.

11v – 22

C.

11v – 2

D.

22 – 11v

Hint

13. Use the Distributive Property to simplify 7(6x2 + 5x + 4).

A.

42x2 + 35x + 4

B.

42x2 + 35x + 28

C.

42x2 + 5x + 4

D.

42x2 +35x + 21

Hint

14. Which values are a counterexample to the given statement?

If x + y = an even number, then x is even and y is even.

A.

x = 10, y = 9

B.

x = 21, y = 3

C.

x = 12, y = 6

D.

x = 7, y = 12

Hint

15. Which values are a counterexample to the given statement?

If x × y = 0, then x must be 0.

A.

x = 0, y = 1

B.

x = 5, y = 0

C.

x = 0, y = 0

D.

x = -1, y = 1

Hint

16. Make a table showing the cost of buying 1 to 5 CDs if CDs cost $12 each.

A.

B.

C.

D.

Hint

17. Rico took a survey to find out the number of family members in each of his

classmates' households. The results of the survey are shown in the graph.

How many total people responded to the survey?

A.

90

B.

100

C.

95

D.

85

Hint

18. Rico took a survey to find out the number of family members in each of his

classmates' households. The results of the survey are shown in the graph.

How many more students said they have 4 family members in their

household than 5?

A.

10

B.

20

C.

5

D.

15

Hint

Algebra 1 Chapter 3

1. Translate ''two times a number is six times the sum of z and y'' into an

equation, inequality, or formula.

A. 2x = 6z + y

B. 2x = 6(z + y)

C. 2 + x = 6 + z + y

D. 2x = 6 (zy)

Hint

2. Solve 15 + a = 10.

A. a = -25

B. a = 150

C. a = -5

D. a = 25

Hint

3. Solve 115 - b = 200.

A. 85

B.

C.

D. -85

Hint

4. Write an equation for the following sentence. Two-thirds of a number is 24.

A.

B.

C.

D.

Hint

5. Solve the equation 3b - 5 = 18.

A. b = B. b = 20

C. b = D. b = 26

Hint

6. Three times the greater of two consecutive odd integers is five less than four

times the smaller. Find the two numbers.

A. 8, 9

B. 15, 17

C. 8, 10

D. 11, 13

Hint

7. Solve the equation 3x + y = 6 for x.

A. x = 6 - 3x

B. x = 2 - y

C. x = 5y

D.

Hint

8. A 50-mile trip uses 2 gallons of gas. How much gas would you use on a

115-mile trip?

A. 4 gallons

B. 5 gallons

C. 25 gallons

D. 4.6 gallons

Hint

9. A person biking uphill travels 15 miles in 1hour.

The same person biking downhill travels 15 miles

in hour. Find this person's average speed.

A. 22.5 mph

B. 20 mph

C. 15 mph

D. 30 mph

Hint

10. Translate the sentence into an equation. Seven times v subtracted from 102

equals 53.

A. 7v – 102 = 53

B. 7(102 – v) = 53

C. 7(102) – v = 53

D. 102 – 7v = 53

Hint

11. Solve –14n = -112.

A. n = 8

B. n = 1568

C. n = -8

D. n = -1568

Hint

12. Solve

A. a = 90

B.

C.

D. a = -90

Hint

13. Solve

A.

B. No Solution

C.

D. All Real Numbers

Hint

14. Andre mows lawns as a summer job. On average, he can mow 3 lawns in 2

hours and 15 minutes. At this rate, how long would it take Andre to mow 5

lawns?

A. 3 hours and 30 minutes

B. 3 hours and 58 minutes

C. 3 hours and 45 minutes

D. 4 hours and 15 minutes

Hint

15. A department store is having a 30% off sale for all clothing items. What is

the discount price of a pair of blue jeans that normally cost $39.99?

A. $27.99

B. $25.99

C. $11.98

D. $29.99

Hint

16. Last year, an internet service provider's fee was $17.99 per month. This

year, the same internet service provider charges $19.99 per month. Rounded

to the nearest percent, what is the percent of increase for internet service?

A. 11%

B. 9%

C. 15%

D. 2%

Hint

17. Solve 2x + 8y = 48 for y.

A. y = -2x + 6

B. y = -2x + 48

C.

D.

Hint

18. Xenxang drove 60 miles to visit his daughter. On the way to his daughter's

house the trip took 1 hour and 15 minutes. On the way back from his

daughter's house the trip took 1 hour and 30 minutes. Rounded to the nearest

mile per hour, what was Xenxang's average speed for the round trip?

A. 46 miles per hour

B. 40 miles per hour

C. 48 miles per hour

D. 44 miles per hour

Algebra 1

Chapter 4

1. How many diagonals are there in an 11-sided figure?

A. 44

B. 43

C. 11

D. 22

Hint

2. What is the perimeter of the pattern consisting of 8 trapezoids?

A. 23

B. 26

C. 29

D. 8

Hint

3. Name the quadrant that contains point Q.

A. IV

B. III

C. I

D. II

Hint

4. What ordered pair represents a point 13 units to the left and 2 units above

the origin?

A. (-13, -2)

B. (13, -2)

C. (-13, 2)

D. (13, 2)

Hint

5. State the range of the relation {(1, 6), (-2, 3), (5, 7), (5, 9)}.

A. {1, -2, 5}

B. {3, 6, 7}

C. {3, 6, 7, 9}

D. {3, 6, 9}

Hint

6. Express the relation in the table as a set of ordered pairs.

A. {(-1, 5), (0, 2), (1, 2, 6)}

B. {(-1, 5), (0, 2), (1, 6)}

C. {(-1, 5), (0, 2), (1, 6), (2, 6)}

D. {(5, 1), (2, 0), (6, 1), (6, 2)}

Hint

7. Find the range of y = 3x + 2 if the domain is {-3, -1, 0, 1, 3}.

A. {2, 5, 11}

B. {-7, -1, 2}

C. {-7, -1, 2, 5, 11}

D. {-11, -5, 2, 5, 11}

Hint

8. If h(z) = 2z2 - 5z + 7, find h(3c).

A. 9c

2 - 15c + 7

B. c + 7

C. 18c

2 - 15c + 7

D. 18c

2 - 3c + 7

Hint

9. What are the coordinates of A´ if trapezoid ABCD is reflected over the x-

axis?

A. A'(7, -5)

B. A'(-7, -5)

C. A'(7, 5)

D. A'(-7, 5)

Hint

10. Triangle DEF has vertices D(-6, -1), E(-4, -8), and F(-2, -5). Find the

coordinates of the image of triangle DEF after it is rotated 180° about the

origin.

A. D´(1, 6), E´(8, 4), F´(5, 2)

B. D´(1, -6), E´(8, -4), F´(5, -2)

C. D´(-1, -6), E´(-8, -4), F´(-5, -2)

D. D´(6, 1), E´(4, 8), F´(2, 5)

Hint

11. Match the given graph with its corresponding equation.

A. x + y = -1

B. x + 4y = -4

C. x + 2y = -2

D. 4x + y = -1

Hint

12. Determine the coordinates of the y-intercept of 2x + 4y = 8.

A. (0, 2)

B. (4, 0)

C. (0, 4)

D. (2, 0)

Hint

13. Find f(-11) if f(x) = -3x – 25.

A. 58

B. -8

C. -58

D. 8

Hint

14. Find h(3a) if h(z) = z2 - 9z – 10.

A. -24a – 10

B. -18a – 10

C. 9a

2 - 27a – 10

D. 3a

2 - 27a – 10

Hint

15. Find the next three terms of the arithmetic sequence 101, 93, 85, 77, ….

A. 68, 59, 50

B. 71, 65, 59

C. 69, 61, 53

D. 70, 63, 56

Hint

16. Find the next three terms in the arithmetic sequence 2, -1.5, -5, -8.5, ….

A. -13, -17.5, -22

B. -11.5, -14.5, -17.5

C. -12, -15.5, -19

D. -11, -13.5, -16

Algebra 1 Chapter 5

1. Jim's wages vary directly as the numbers of hours he works. For 7 hours, he

makes $38.85. How much will he make in 37 hours?

A. $207.20

B. $194.25

C. $205.35

D.

$1437.45

Hint

2. What is the slope of the line that passes through (8, 4) and (6, 7)?

A.

B.

C.

D.

Hint

3. Write the standard form of an equation of the line that passes through

(-2, 5) and has an undefined slope.

A. -2x + 5y = 0

B. x = -2

C. y = 5

D.

x - y = 3

Hint

4. Write the point-slope form of an equation of the line that passes through (4,

-3) and (2, 1).

A.

B.

C.

D.

Hint

5. What is implied when it is said that x and y have a negative correlation?

A. When the value of x is negative, the value of y negative.

B. When the value of x increases, the value of y increases.

C. When the value of x increases, the value of y decreases.

D. When the value of x increases, the value of y does not necessarily

increase or decrease.

Hint

6. A direct variation equation has (-2, 4) and (n, -8) as solutions. Find the

missing value.

A. 4

B. -2

C. 16

D.

1

Hint

7. Which equation has a graph perpendicular to the graph 3y = 2x - 9?

A.

B. y = 2x + 5

C. 2x + 3y = 4

D.

3x + 2y = 7

Hint

8. Which equation is the slope-intercept form of the equation of the line that

passes through (1, 2) and is parallel to 4x - 2y = 6?

A. y = 4x + 3

B. y = -2x + 1

C. y = 2x

D.

Hint

9. Which scatter plot shows that x and y have no correlation?

A.

B.

C.

D.

Hint

10. Find the slope of the line that passes through (-2, 9.5) and (4, 5).

A. undefined

B. 0

C.

D.

Hint

11. Write an equation of the line shown in the graph.

A. y = 2x + 5

B. y = 2x – 5

C. y = -2x – 5

D.

y = -2x + 5

Hint

12.

Write an equation of the line whose slope is and whose

y-intercept is –2.

A.

B.

C.

D.

Hint

13. Which equation describes the line that contains the points (-1, -8) and (-9, -

21)?

A.

B.

C.

D.

Hint

14. A ticket service is selling tickets to a concert. An order of 4 tickets has a

price of $63 and an order of 6 tickets has a price of $92. Write an equation

to find the price of any amount of tickets.

A.

B.

C.

D.

Hint

Algebra 1

Chapter 6

1. Choose the inequality that corresponds with the sentence ''Twice a number

increased by four is less than the difference of three times that number and

five. ''

A. 2x + 4 < 5 - 3x

B. 2(x + 4) < 3(x + 5)

C. 2x + 4 > 3x - 5

D. 2x + 4 < 3x - 5

Hint

2. Solve

A. {x | x > 0.43}

B. {x | x < 23.68}

C. {x | x > 23.68}

D. {x | x < 2.31}

Hint

3. The opposite of two thirds of a number x is at least 18. What are the possible

values of x?

A.

B.

C.

D. {x | x > -27}

Hint

4. Solve -3x - 5 > 22.

A.

B. {x | x > -9}

C. {x | x < -9}

D. {x | x < -81}

Hint

5. Which graph is the graph of the solution set of |6x - 4| > 14?

A.

B.

C.

D.

Hint

6. Which graph is the graph of the inequality 4x + 3y > -15?

A.

B.

C.

D.

Hint

7. Solve c + 49 -16.

A.

B.

C.

D.

Hint

8. Solve –4(10 – n) – 6n > 8(n + 3) – 7n + 2.

A. n < -6

B. n > -22

C. n < -22

D. n > -6

Hint

9. Solve –10 < 2x – 8 < 8.

A. {x| -1 < x < 6}

B. {x| -1 < x < 8}

C. {x| -9 < x < 8}

D. {x| -9 < x < 0}

Hint

10. Solve or

A. {x| x > 12}

B. {x| x < 15}

C. {x| x < 12}

D. {x| x > 15}

Hint

11. Solve

A. or B.

C. or D.

Hint

12. From the set {(-2, -5), (0, 10), (5, 8), (8, -3)}, which ordered pairs are a part

of the solution set for 5x + 5y > 45?

A. {(-2, -5), (8, -3)}

B. {(0, 10), (8, -3)}

C. {(-2, -5), (5, 8)}

D. {(0, 10), (5, 8)}

Hint

Chapter 7

Solving Systems of Linear Equations and Inequalities

1. Which ordered pair is the solution to the given system of equations?

x - 3y = 9

x - 2y = 5

A.

(-3, -4) B.

(-6, 1)

C. (9, -3)

D.

(3, -2)

Hint

2. Use substitution to solve the system of equations given below.

A.

(-5, 5) B.

no solution

C.

D.

infinitely many solutions

Hint

3. Students from the local high school are selling tickets to the town's annual

carnival. Adult admission is $5.00 and child admission is $2.50. Two hours

after the carnival opened its first day, 440 tickets had been sold totaling

$1900. How many adults and how many children entered the carnival

during the first two hours it was open?

A.

220 adults, 220 children

B. 320 adults, 120 children

C. 380 adults, 760 children

D.

293 adults, 147 children

Hint

4. Use elimination to solve the system given below.

5x - 2y = 25

5x + 3y = 5

A.

(13, 20) B.

C. (3, -5)

D.

(4, -5)

Hint

5. The sum of two numbers is –11. Twice the first number minus four times

the second number is –10. What are the two numbers?

A.

-8, -3 B.

-15, 4

C. -9, -2

D.

-6, -5

Hint

6. Use the graph below to determine if the given system of equations has one

solution, no solution, or infinitely many solutions. If the system has one

solution, name it.

A.

no solution B.

one solution at (-6, 0)

C. infinitely many solutions

D.

one solution at

Hint

7. Use elimination to solve the system of equations given by 7x + 23y = 12 and

3x + 23y = -8.

A.

B.

no solution

C. infinitely many solutions

D.

(5, -1)

Hint

8. Use elimination to solve the system of equations given by 6x + 2y = 0 and

3x + 7y = 24.

A.

infinitely many solutions B.

C. (-1, 3)

D.

no solution

Hint

9. Use graphing to solve the system of inequalities given by y < x + 1 and

A.

B.

C.

D.

Hint

10. Which point is in the solution set of and

A.

(-1, -5) B.

(2, 1)

C. (-4, 6)

D.

(3, 4)

Hint

Algebra 1

Chapter 8

1. Simplify (7a4b) (8a

7b

6).

A. 15a

28b

6

B. 56a

28b

6

C. 56a

11b

7

D. 15a

11b

7

Hint

2. Simplify (4x2y) (2xy

2z

3)3.

A. 32x

6y

6z

9

B. 32x

5y

7z

9

C. 24x

5y

7z

9

D. 8x

5y

7z

9

Hint

3. Simplify . Assume the denominator is not equal to zero.

A.

B.

C.

D.

Hint

4. The area of the rectangle shown below is 4x

3y

2, and its base b is 2x

5y. Find

the height, h.

A. 8x

8y

3

B.

C.

D. 2x

2y

Hint

5. Express 765,000,000,000 in scientific notation.

A. 7.65 × 10

10

B. 7.65 × 10

-11

C. 7.65 × 10

11

D. 0.765 × 10

12

Hint

6. What is the degree of 4x5 – 5xy

4 + 3xy

2 – 1?

A. 0

B. 4

C. 3

D. 5

Hint

7. Find the sum (4xy2 – 3x

2y – 5xy – 6) + (-5xy

2 – 2xy + 3).

A. 4xy

2 – 7xy – 3

B. -xy

2 – 3x

2y – 7xy – 3

C. -xy

2 – 3x

2y – 3xy – 3

D. 4xy

2 – 8x

2y – 7xy – 3

Hint

8. Solve 4a(a – 4) – 7a = a(4a – 3) + 20.

A.

B. a = -1

C. a = -2

D. a = -6

Hint

9. Find (5t2 - 2w)

2

A. 25t

4 – 20t

2w + 4w

2

B. 25t

4 – 10t

2w + 4w

2

C. 25t

4 + 4w

2

D. 25t

4 – 4w

2

Hint

10. Express 4.67 × 10-7

in standard notation.

A. 0.000000467

B. 0.0000000467

C. 0.00000467

D. 46,700,000

Hint

11. Write a polynomial to represent the area of a square with a side x minus the

area of a triangle with a base 2x and a height of 5.

A. 4x

B. x

2 – 2x + 5

C. x

2 – 10x

D. x

2 – 5x

Hint

12. Anthony and Sanford each throw a football. The height of Anthony's throw

can represented by the equation A = –10x2 + 15x + 22, where A is height and

x is the time in seconds. The height of Sanford's throw can represented by

the equation S = –9x2 + 14x + 23. At time x, what is the combined height of

the throws?

A. 19x

2 + 29x + 45

B. –x

2 + x – 1

C. –19x

2 + 29x + 45

D. x

2 – x + 1

Hint

13. Multiply 4x2 (–x

2 – 3x + 2).

A. –4x

2 – 7x + 8

B. –4x

4 – 7x

3 + 8x

2

C. –4x

4 – 12x

3 + 8x

2

D. –4x

2 – 12x + 8

Hint

14. Find the product (2x - 3)(2x2 + 5x - 1).

A. 8x

2 – 17x + 3

B. 8x

2 – 17x – 3

C. 4x

3 + 4x

2 – 17x + 3

D. 4x

3 + 4x

2 – 17x – 3

Hint

15. Find the product (x2 – 3x +6)(2x

2 + 3x + 4).

A. 2x

4 + 3x

3 + 7x

2 + 6x + 24

B. 2x

4 – 3x

3 + 7x

2 + 6x + 24

C. 2x

4 – 3x

3 – 5x

2 + 6x + 24

D. 2x

4 + 3x

3 – 5x

2 + 6x + 24

Hint

16. Which of the following is a difference of two squares?

A. x

2 + 6x + 9

B. x

2 – 9

C. x

2 – 8x – 16

D. x

2 + 36

Hint

Algebra 1

Chapter 9

1. An expression for the area of a rectangle is xy – 2x + 3y – 6. Express this area in

factored form.

A. x(y – 2) + 3(y – 2)

B. (xy – 2x)( 3y – 6)

C. (x – 2)(y + 3)

D. (x + 3)(y – 2)

Hint

2. Factor 4y2 – 3y – 1.

A. (2y + 1)(2y – 1)

B. (4y + 1)(y – 1)

C. prime

D. (4y – 1)(y + 1)

Hint

3. Factor 6a3b

5 – 15a

2b.

A. 3a

3b(2ab

2 - 5)

B. 3a

2b(2ab

4 - 5)

C. ab(6a

2b

4 - 15a)

D. 3(2a

3b

5 - 5a

2b)

Hint

4. Solve 5x2 – 10x = 0.

A. x = 0

B. x = 0 or x = -2

C. x = 2

D. x = 0 or x = 2

Hint

5. Solve a2 – 12a = -27.

A. a = 9

B. a = -27 or a = -15

C. a = 3

D. a = 3 or a = 9

Hint

6. Is 57 prime or composite? If it is composite, what is its factorization?

A. composite, 3 × 19

B. composite, 2 × 29

C. prime

D. composite, 3 × 17

Hint

7. Is 79 prime or composite? If it is composite, what is its factorization?

A. composite, 13 × 6

B. composite, 3 × 23

C. prime

D. composite, 7 × 11

Hint

8. Suppose the area of a square isx2 – 10x + 25. What is the perimeter of the square?

A. 2x – 10

B. 4x – 20

C. 2x

D. 4x

Hint

9. Factor 3x2 – 8x + 3.

A. (x – 1)(3x – 3)

B. not factorable

C. (3x – 5)(x – 1)

D. (3x – 1)(x – 3)

Hint

10. Solve 27x3 = 147x.

A.

B.

C.

D.

Hint

11. Suppose that we have a 3 ft. × 3 ft. piece of paper, and we cut out a square piece so that

the area of the remaining piece is 5 feet. What is the length of a side of the square?

A. 4 ft.

B.

C. D. 2 ft.

Hint

12. Solve the equation x

2 – x + = 0.

A.

B.

C.

D.

Hint

Algebra Practice Questions

1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?

A. 5/p

B. p - 5

C. p + 5

D. p/5

E. 1- p + 5

2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long

will it take for both of them to paint the house together?

A. 2 hours and 24 minutes

B. 3 hours and 12 minutes

C. 3 hours and 44 minutes

D. 4 hours and 10 minutes

E. 4 hours and 33 minutes

3. Employees of a discount appliance store receive an additional 20% off of the lowest price on

an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if

the dishwasher originally cost $450?

A. $280.90

B. $287

C. $292.50

D. $306

E. $333.89

4. The sales price of a car is $12,590, which is 20% off the original price. What is the original

price?

A. $14,310.40

B. $14,990.90

C. $15,290.70

D. $15,737.50

E. $16,935.80

5. Solve the following equation for A : 2A/3 = 8 + 4A

A. -2.4

B. 2.4

C. 1.3

D. -1.3

E. 0

6. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their

ages is 41. Then how old is Sue?

A. 8

B. 10

C. 14

D. 19

E. 21

7. Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he

receive?

A. $240

B. $480

C. $720

D. $960

E. $1,200

8. Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How

much did the statue originally cost him?

A. $496.30

B. $512.40

C. $555.40

D. $574.90

E. $588.20

9. The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends

the night in a motel room that costs $55 before taxes, how much will the city receive in taxes

from him?

A. 10 cents

B. 11 cents

C. 15 cents

D. 17 cents

E. 21 cents

10. A student receives his grade report from a local community college, but the GPA is smudged.

He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science

course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a “B” in the art

class, an “A” in the history class, a “C” in the science class, a “B” in the mathematics class, and

an “A” in the science lab. What was his GPA if the letter grades are based on a 4 point scale?

(A=4, B=3, C=2, D=1, F=0)

A. 2.7

B. 2.8

C. 3.0

D. 3.1

E. 3.2

11. Simon arrived at work at 8:15 A.M. and left work at 10: 30 P.M. If Simon gets paid by the

hour at a rate of $10 and time and ½ for any hours worked over 8 in a day. How much did Simon

get paid?

A. $120.25

B. $160.75

C. $173.75

D. $180

E. $182.50

12. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones.

What is the minimum number of jellybeans she must take out of her pocket to ensure that she has

one of each color?

A. 4

B. 8

C. 12

D. 13

E. 16

13. If r = 5 z then 15 z = 3 y, then r =

A. y

B. 2 y

C. 5 y

D. 10 y

E. 15 y

14. If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at

the same rate?

A. 150/x

B. 150x

C. 6x

D. 1500/x

E. 600x

15. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same

pay rate, how much will she make?

A. $57

B. $90

C. $104

D. $112

E. $122

16. If 8x + 5x + 2x + 4x = 114, the 5x + 3 =

A. 12

B. 25

C. 33

D. 47

E. 86

17. You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax

where you are purchasing the book is 8.25%. You have $100. How much change will you

receive back?

A. $5.20

B. $7.35

C. $13.40

D. $19.95

E. $21.25

18. You purchase a car making a down payment of $3,000 and 6 monthly payments of $225.

How much have you paid so far for the car?

A. $3225

B. $4350

C. $5375

D. $6550

E. $6398

19. Your supervisor instructs you to purchase 240 pens and 6 staplers for the nurse's station. Pens

are purchased in sets of 6 for $2.35 per pack. Staplers are sold in sets of 2 for 12.95. How much

will purchasing these products cost?

A. $132.85

B. $145.75

C. $162.90

D. $225.25

E. $226.75

20. If y = 3, then y3(y

3-y)=

A. 300

B. 459

C. 648

D. 999

E. 1099

Answer Key

1. A

2. A

3. D, Sale Price = $450 - 0.15*$450 = $382.50, Employee Price = $382.50 - 0.2*$382.50 = $306

4. D, $12,590 = Original Price - 0.2*Original Price = 0.8*Original Price, Original Price =

$12,590/0.8 = $15,737.50

5. A

6. A

7. E

8. A, $670 = Cost + 0.35*Cost = 1.35*Cost, Cost = $670/1.35 = $496.30

9. D

10. C

11. C

12. D

13. A

14. A

15. B

16. C

17. C

18. B

19. A

20. C