This assignment is expected to take 7 hours of work.

CP Algebra II

Summer Assignment

Directions:

Students must complete all problems and show all work to receive full credit. All work should

be completed prior to the beginning of the 2018-2019 school year. Khan Academy links are

included and should be used as a reference when completing each set of problems. Khan

Academy is not a mandatory part of the summer assignment. The packet will be due

Wednesday, September 5, 2018. Students should be prepared to take an assessment on the

material outlined in this packet. If you have any questions please see Ms. Della Fortuna.

Pacing Guide:

Section Anticipated Time Requirement (hrs)

Complete by

Linear Equations 2 July 13, 2018

Exponents 1 July 27, 2018 Quadratic Expressions and Equations 2.5 August 17, 2018

Polynomial Operations 1.5 August 31, 2018

Total: 7

Linear Equations:

1. Find the slope and state whether the line rises, falls, is horizontal or vertical.

a. 2, 4( ), 4, -1( )

b. -3, - 2( ), 3, - 2( )

c. -1, 4( ), 1, - 4( )

d. 4, 4( ), 4, 9( )

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/two-var-linear-equations/slope/v/introduction-to-slope

• https://www.khanacademy.org/math/algebra/two-var-linear-equations/hor-and-ver-lines-alg1/v/slope-of-a-line-3

2. Tell whether the lines are parallel or perpendicular

a. Line 1: through 3, -1( ) and 6, - 4( )

Line 2: through -4, 5( ) and -2, 7( )

b. Line 1: through -1, 4( ) and 2, 5( )

Line 2: through -6, 2( ) and 0, 4( )

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-lines/v/parallel-and-perpendicular-lines-intro

• https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/parallel-lines

3. Find the value of k so that the line through the given points has the given slope.

2, - 3( ) and k, 7( ) ; m = -2

4. Graph the following equations. Label the intercepts.

a. y = -x - 3 b. y =3

2x - 3 c. x = 4

d. x + 4y = 8 e. 1

2x + 2y = -2 f. y = -1

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-solutions-to-two-var-linear-equations/v/graphs-of-linear-equations

5. Write the equation of a line that passes through 5, 4( ) and has a slope of -3.

6. Write the equation of the line shown.

a.

b.

c.

7. Write an equation of the line that passes through -2, 3( ) and is:

a. Parallel to y = -4x +1

b. Perpendicular to y = -4x +1

8. Write an equation of the line that passes through 5, - 2( ) and 2, 10( )

9. Write an equation of the line that passes through the given point and satisfies the given condition.

a. -6, 2( ); perpendicular to y = -2

b. 3, -1( ) ; perpendicular to y = -1

4x -

1

4

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/two-var-linear-equations/forms-of-two-var-linear-equations/v/point-slope-and-standard-form

10. Solve the system by graphing

a. 4x + y = 8

2x - 3y = 18

ìíî

b. 4x - 5y = -10

2x - 7y = 4

ìíî

c. 4x - 3y = 8

8x - 6y = 16

ìíî

d. 2x + y = 4

2x + y = 1

ìíî

11. Solve the following systems using the substitution or elimination method.

a. 3x + y = 16

2x - 3y = -4

ìíî

b. 6x - 2y = 5

-3x + y = 7

ìíî

c.

5x - 3y = -3

2x + 6y = 0

ìíî d.

4x - 3y = 10

8x - 6y = 20

ìíî

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic

12. Solve the following equations

a. 4

5x + 8 = 20

b. 2

3x - 7 = 5

c. 7p+13 = 9p- 5

d. 8y-16 =13y+ 9

e. 3 5x- 8( ) = -2 -x+ 7( )-12x

f. 4 2x - 9( )+ 5x = -3 10 - x( )

g. 1

4x +

2

5x = 39

h. 2

3a+

5

6= a -

1

2

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-two-steps-equations-intro/v/why-we-do-the-same-thing-to-both-sides-two-step-equations

Exponent Expressions:

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/pre-algebra/pre-algebra-exponents-radicals/pre-algebra-exponents/v/exponents-warmup

• https://www.khanacademy.org/math/pre-algebra/pre-algebra-exponents-radicals/pre-algebra-exponent-properties/v/exponent-properties-involving-products

• https://www.khanacademy.org/math/pre-algebra/pre-algebra-exponents-radicals/pre-algebra-negative-exponents/v/negative-exponents

• https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-exp-prop-review/v/multiplying-and-dividing-powers-with-integer-exponents

• https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/rational-exponents-intro/v/basic-fractional-exponents

Directions for #1 – 12: Simplify the following exponential expressions.

1. y3 • y5

2. x7 • x3 • x

3. (a2b4) (a3b)

4. 4

9

a

a

5. 32

79

yx

yx

6. y-2

7. a0

8. (x6)2

9. (3a)2

10. 2

1

122

105

ba

ba

11. nm

nm5

212

6

24

−

−

12. (𝑥2

5𝑦1

5)−5

13. For each exercise, identify the error(s) in planning the solution or solving the problem. Then write the

correct solution.

14. For each exercise, identify the error(s) in planning the solution or solving the problem. Then write the

correct solution.

Directions for #15 – 18: Simplify the following exponential expressions.

15. 2

32

1

−

−

b

ba

16. (𝑥1

3𝑦2

3)6

17. 3

1

126

93

ba

ba

18. 𝑥3

4 ∙ 𝑥1

2

19. The number of bacteria in a culture quadruples every hour. There were 65,536 bacteria in the culture

at 8:00 a.m. The expression 65,536●4h models the number of bacteria in the culture h hours after 8:00

a.m.

a. What is the value of the expression for h = -4?

b. What does the value of the expression in part a represent?

20. Which of the following statements is not true regarding operations with exponents?

a. To divide powers with the same base, subtract the exponents.

b. To subtract powers with the same base, divide the exponents.

c. To multiply powers with the same base, add the exponents.

d. To raise a power to a power, multiply the exponents.

Quadratic Expressions and Equations: Factoring

1. Factor the following quadratics using the GCF.

a. 10𝑛𝑚3 − 15𝑛2𝑚

b. 16𝑥3𝑦2 − 20𝑥2𝑦3 + 12𝑥4𝑦

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-polynomials-1-

common-factors/v/factoring-and-the-distributive-property-3

2. Factor the following quadratics completely.

a. 𝑥2 + 𝑥 − 90

b. 𝑎2 + 10𝑎 + 16

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-

1/a/factoring-quadratics-leading-coefficient-1

• https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-

1/v/factoring-polynomials-1

3. Factor the following quadratics completely.

a. 5𝑥2 − 17𝑥 − 12

b. 2𝑛2 + 15𝑛 + 7

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-

2/v/factoring-trinomials-by-grouping-4

• https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-polynomials-2-

quadratic-forms/v/factoring-trinomials-by-grouping-5

4. Factor the following quadratics using the grouping method.

a. 4𝑥3 − 12𝑥2 + 3𝑥 − 9

b. 10𝑥3 − 12𝑥2 + 5𝑥 − 6

c. 𝑥2 − 3𝑥 + 4𝑎𝑥 − 12𝑎

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-

2/a/factoring-by-grouping

5. Factor the following quadratics. Recognize that they are difference of squares.

a. 𝑎2 − 121

b. 16𝑥2 − 49𝑦2

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-polynomials-3-special-product-forms/v/factoring-difference-of-squares

Directions for #6 – 10: Factor the following quadratics completely using the appropriate method(s).

6. 5𝑦2 − 20

7. 2𝑥3 + 18𝑥2 − 72𝑥

8. 3𝑏3 − 13𝑏2 + 10𝑏

9. 𝑝3 − 49𝑝

10. 50𝑥3 − 40𝑥2 + 8𝑥

11. A dentist’s office and parking lot are on a rectangular piece of land. The area (in square meters) of the land

is represented by 𝑥2 + 𝑥 − 30. Write the two binomials that represent the width and length of the land.

Solving Quadratic Equations

Directions for # 12- 17: Solve each of the following polynomials for x.

12. (𝑥 − 8)(𝑥 + 2)(𝑥 − 7) = 0

13. (𝑥 + 10)(𝑥2 − 25) = 0

14. 𝑥2 + 81 = 18𝑥

15. 3𝑥4 + 27𝑥3 + 60𝑥2 = 0

16. 𝑥3 − 6𝑥2 − 4𝑥 + 24 = 0

17. 𝑥4 − 5𝑥2 + 4 = 0

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/quadratics/solving-quadratic-equations-by-

factoring/v/example-1-solving-a-quadratic-equation-by-factoring

18. A bird picks up a golf ball and drops it while flying. The function 𝑦 = 81 − 16𝑡2 represents the height y (in

feet) of the golf ball t seconds after it is dropped. The ball hits the top of a 32-foot-tall pine tree. After how

many seconds does the ball hit the tree?

19. You are building a brick patio. The length of the patio is (x+11) feet.

a. The total area of the patio can be represented by 𝑥2 + 14𝑥 + 33. Write an expression for the width

of the patio.

b. The area of the patio is 48 square feet. Find the value of x.

20. A terrarium in the shape of a rectangular prism has a volume of 180 cubic inches. Its length is at least 4

inches. The dimensions of the terrarium in terms of its width are shown. Find the length, width and height of

the terrarium. (Hint: 𝑣𝑜𝑙𝑢𝑚𝑒 = 𝑙𝑒𝑛𝑔𝑡ℎ ∙ 𝑤𝑖𝑑𝑡ℎ ∙ ℎ𝑒𝑖𝑔ℎ𝑡)

(9 - w) in

Polynomial Operations:

Khan Academy Videos/Practice:

• https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/adding-and-subtracting-polynomials/v/adding-and-subtracting-polynomials-1

• https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/add-subtract-poly-two-var/v/example-adding-polynomials-with-multiple-variables

• https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-monomials/v/multiply-monomials-intro

• https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-binomials-2/v/area-model-for-multiplying-binomials

• https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-polynomials-by-binomials/v/more-multiplying-polynomials

1. Find the expression which represents the perimeter of the rectangle?

2. Find the expression which represents the perimeter of the triangle shown below?

3. The function ( )g x is the amount of money Shawn has in the bank at the beginning of the month.

The function ( )f x is the amount of money withdrawn from the account during the month. Which

expression represents the amount of money left at the end of the month?

2

2

( ) 3 12

( ) 6 2 20

f x x x

g x x x

= − +

= − +

4x + 5

2x + 3

4x + 1 x2 + 3

2x2 – x + 4

4. Subtract the following polynomials: ( ) ( )2 24 7 5 2 5 3y y y y+ − − − +

5. Find the product: (x – 4) (2x – 1)

6. Find the product: ( )( )3 22 3 4x x x x− + + −

7. Multiply the polynomials: ( ) ( )3 23 1 2 4 7x x x x− + − +

8. Multiply the polynomials: ( ) ( ) ( )5 2 1 4x x x− + +

9. Simplify the expression: (3y – 2)2

10. Find a polynomial expression for the volume of a rectangular prism with sides (x + 1) (x + 3) and (x + 4).

11. Distribute: 3x²(4x³ – 5x + 10)

12. Subtract: (-18x2 + 4x - 16) - (15x2 + 4x - 13)

13. Add: )141510()49( 4556 +−+− xxxx

14. Find the product: (1

2𝑥 + 3) (

1

3𝑥 − 1)

15. Find the sum: (3

4𝑥2 +

1

3𝑥 − 4) + (

1

4𝑥2 −

2

3𝑥 + 5)

16. Find the difference: (1

5𝑥2 +

2

5𝑥 − 5) − (

1

5𝑥2 −

2

5𝑥 + 6)

17. The length, width, and height of the box are shown below. Write the polynomial which represents its

volume.

18. The length of a rectangle swimming pool is 2x – 1 meters, and the width is x + 2 meters.

a. Write the polynomial that represents the area.

b. Find the area if x is 5 meters.

19. The length of a professor’s office is x feet, and the width is x + 4 feet.

a. Write the polynomial that represents the area.

b. Find the area if x = 10 ft.

20. A roof truss is in the shape of a triangle with height x feet and a base of 2x + 1 feet.

a. Write the polynomial that represents the area of the triangle.

b. What is the area if x = 5ft.