checkpoint 1 simplifying like terms and distributive property

Checkpoint 1 – Simplifying Like Terms and Distributive Property

Simplify the following expressions completely.

1. 2

3 2. 3( 2) 3. 25 4. 2

7 3 5. 3 2

1 6

6. (8x – 5) + (4x – 6) 7. (6t + 1)(t – 2) 8. (2k + 11) – (4 – 7k)

9. (x2 – x + 9) – (5x2 + 5x – 7) 10. (w + 4)(w – 6) 11. (3r – 5) 2

12. (2a – 4b)(a + 5b) 13. 4x2(3x2 – x + 2) 14. 2a – 3(a + 5)

x

3x

x + 6

3x + 6

15. (2a2 + 3)(5a2 – 2) 16. 3

3x 17. (2a – 5)(a2 – 4a + 1)

18. If the length of a rectangle can be represented as 2x – 3 and the width is 4x + 5, write an

expression that represents the perimeter of the rectangle.

19. Write the expression that represents the area of the rectangle above.

20. Kurtis is building a walkway that surrounds a rectangular garden.

The shaded area in the picture represents this walkway.

Write an expression that represents the area of the walkway using

the information provided.

21. Suppose the width of the garden is 4 feet and the length of the garden is 12 feet. The

walkway is to be 3 feet wide all the way around the garden. If bricks for the walkway sell at

$1.50 per square foot, what would be the total cost of bricks for the walkway.

Checkpoint 2 – Solving Equations

Solve the following equations.

1. 33 = 3x 2. x – 6 = –6 3. –6x = 20 1.

2.

3.

4. 5 = 3x + 4 5. 3 – 5x < –12 6. 3

2x = 8 4.

5.

6.

7. 1 2

2 3y 8. 5 = x25 9. 1.1 = 3x – 2.5 7.

8.

9.

10. x 2

3

= 4 11. 7x – 13 – x = 32 12. 4a – 13 = 7a + 20 10.

11.

12.

13. 1 2 1

42 3 2

x x 14. 5(2 ) 3 2 7 3x x x 15. 13 + 6x = 6x + 1 13.

14.

15.

16. 38 = 4(2f – 3) – 3f 17. 5(3y + 2) – 6 > 15y + 4 16.

17.

Solve the following formulas for the variable indicated.

18. y = mx + b; solve for x 19. x m

zs

; solve for x 18.

19.

20. The volume of a pyramid is given by the formula 21

3V b h , where V is the volume of the

pyramid, b is the length of one side of the base, and h is the height of the pyramid. Rewrite

the equation so that it would give you the height of the pyramid, for a known volume and

base length.

20.

Checkpoint 3 – Graph and Write the Equations of Lines

Graph the following functions.

1. 𝑦 = 3𝑥 − 7 2. 𝑦 =2

3𝑥 − 5 3. 𝑓(𝑥) = −

𝑥

3+ 8

m = m = m =

b = b = b =

4. 𝑔(𝑥) = −𝑥 − 8 5. 5𝑥 − 10𝑦 = 15 6. 1

2𝑦 = 2𝑥

m = m = m =

b = b = b =

7. 3𝑥 − 4𝑦 = 12 8. 𝑦 = −7 9. 2𝑥 = 16

m = m = m =

b = b = b =

Write the equation of a line given the following information.

10. 11. 12.

13. The line with slope = 3 passing through (6, 2) 14. The line with slope = –3 passing

through (5, 1)

15. A line with m= -2 passing through (0,2) 16. The line that goes through (6, 1)

and (3, 3).

17. A line passing through the origin and (8, 2) 18. A line passing through (-1, 3)

and (-1, 5)

19. A line passing through (0, 10) and (-5,0) 20. A with an x-intercept of -2, and a

y-intercept of 6

Checkpoint 4 – Solve Systems by Graphing and Substitution

Solve the following systems of equations by graphing.

1. y = x – 1 and x + y = 3 2. y = 2x and 2x + 5y = –12

Solve the following systems of equations by substitution.

3. y = 4x and x + y = 5 4. x = –4y and 3x + 2y = 20

5. 3x – y = 4 and 2x – 3y = –9 6. x + 3y = 8 and 2x – 4y = –9

7. x + 14y = 84 and 2x – 7y = –7 8. 2x – y = –11 and 3x – 6y = 6

9. 4x – 2y = –60 and 5x – 3y = –78 10. y + 2x = 2 and y + x = 1

Checkpoint 5 – Solve Systems by Elimination

Solve the following systems of equations by graphing.

1. –x + 2y = 12 and x + 6y = 20 2. x – y = 9 and x + y = 7

3. 2x + 5y = 14 and 4x + 5y = 8 4. x + 3y = 7 and 2x – 3y = –4

5. x + y = 1 and x – 2y = 2 6. 2x + 5y = 3 and –x + 3y = –7

7. y = –2x + 8 and y = –3x + 13 8. 2x – y = 6 and –2x + y = 15

9. –2x + 7y = –2 and 2x – 7y = 2 10. y = 9x – 35 and 5x + 8y = 28

11. –5x + 8y = 29 and 7x + 3y = 2 12. 9x + 8y = 7 and 18x – 15y = 14

Checkpoint 6 – Solve Systems of Equations with 3 Variables

Tell whether the given ordered triple is a solution to the system.

1. 1,4, 3 2. 6,0, 3

2 5

5 2 2 19

3 5

x y z

x y z

x y z

4 2 12

3 4 6

3 9

x y z

x y z

x y z

Solve the following systems of equations.

3.

2 2 7

2 4 5

4 6 1

x y z

x y z

x y z

4.

5 2 1

2 6

2 7 3 7

x y z

x y z

x y z

5.

5 6

2

3 4

x y z

x y z

x y

6.

3 12

2 4 2 6

2 6

x y z

x y z

x y z

Checkpoint 7 – Domain and Range

Given the following information, find the domain and range for the following.

1. (1,6) , (2, −7) , (−1,8) , (8, −3) 2. (7,7) , (2,6) , (−4, −3) , (11, −8)

3. (−8,8), (7,0), (−6, −7), (1,4), (0,5)

Find the domain and range of each function

4. Domain: __________ 5. Domain: __________ 6. Domain: __________

Range: __________ Range: __________ Range: __________

7. Domain: __________ 8. Domain: __________ 9. Domain: __________

Range: __________ Range: __________ Range: __________

10. Domain: __________ Range: __________ 11. Domain: __________ Range: __________



16. Eric wants to buy T-shirts for homecoming. It costs $20 for a design fee, and each T-shirt is

$5. Eric knows that the amount of money it costs to produce the homecoming T-shirts is

dependent on the number of T-shirts he orders. Write a function for Eric, and then state the

domain and range of that function.

Checkpoint 8 – Notation Given the following graph, write the domain and range in inequality, set, and interval notation. Also, describe

using words.

1.

2.

3.

4.

Words Inequality Set Interval

D

R


D

R


D

R

5.

6.

7. A movie theater seats 200 people. For any particular show, the amount of money the

theater makes is a function of the number of people, n, in attendance. If a ticket costs

$4.00…

A) Write a function that illustrates the amount of money made by the movie theater.

B) Sketch a rough graph


D

R


D

R

Checkpoint 9 – Piecewise Functions part 1

Evaluating the piecewise functions given the following domains

1. when x = 3 2. when x = –4

3. Find f(5) 4. Find f(2)

Graph the following functions:

5. 2

= 1, 33

f x x if x

6. = 4 5, 1f x x if x

7. 1

= -6 02

f x x if x

8. = 2 4 , 2 6f x x if x

4 2

2 10 2 5

2 5 10

x if x

f x x if x

if x

9. = 2 3 4f x if x 10. = 1 +2 4f x x if x

11. A gourmet coffee store sells the house blend of coffee beans at $9.89 per pound of

coffee for quantities up to and including 5 pounds. For each additional pound after the 5

pounds, the price is $7.98 per pound.

a. Write a function that relates the cost and the number of pounds of coffee beans

being purchased.

b. Determine the cost for 3 pounds of coffee beans

c. Determine the cost for 7 pounds of coffee beans.

d. Determine the cost for 5.5 pounds of coffee beans.

Checkpoint 10 – Piecewise Functions part 2

Graph the following functions:

1. 2. 3.

4. 5. 6.

2 1

= 2 , 1 3

17, 3

3

if x

f x x if x

x if x

4 , 0 2

= 2 10, 2 5

2, 5 10

x if x

f x x if x

if x

1, 2 1

= 2, 1 4

5, 4 7

if x

f x if x

if x

2 1, 0

= 1, 0

x if xf x

x if x

11, 2

= 2

3 7, 2

x if xf x

x if x

9, 1 2

= 3 5 , 2 6

x if xf x

x if x

For #7-8 Write and Graph the piecewise function described using the domain 3 3x .

7. Rounding Function. The output f x is the input x rounded to

the nearest integer. If the decimal part of x is 0.5, then x is rounded

up when x is positive and x is rounded down when x is negative.

8. Greatest Integer Function. The output f x is the greatest integer

Less than or equal to the input x.

9. An air-conditioning salesperson receives a base salary of $2850 per month plus a

commission. The commission is 2% of the sales up to and including $25,000 for the month and

5% of sales over $25,000 for the month

a. Write a function that relates the salesperson’s total monthly income with his or her sales

for the month.

b. Determine the salesperson’s total monthly income if his or her sales were $19,500 for

the month.

c. Determine the salesperson’s total monthly income if his or her sales were $43,000 for

the month

d. Graph the piecewise function.

checkpoint 1 simplifying like terms and distributive property

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