Name____________________________________________Period _________ Jan 2019

COMMON CORE ALGEBRA MIDTERM REVIEW

Unit 1: Chapter 1

Write the letter of the property which is illustrated in the example given in the first

column. Explain your choice.

___1. abc = cba A. Commutative Property of Addition

B. Commutative Property of Multiplication

___2. k 0 = 0 C. Associative Property of Addition

D. Associative Property of Multiplication

___3. m(x + 7) = mx + 7m E. Distributive Property of Multiplication and Addition

___4. 1a b

b a F. Additive Identity Property

G. Multiplicative Identity Property

___5. (9 + y )+ 6 = 9 + (y + 6) H. Additive Inverse Property

I. Multiplicative Inverse Property

___6. 9 – 9 = 0 J. Multiplication Property of Zero

K. Multiplication Property of –1

___7. m + 0 = m

___8. 3 + (x + 2) = (x + 2) + 3

___9. 1w = w

Write the word or expression that best completes the statement.

10. The additive identity is ________.

11. The multiplicative identity is _______.

12. The additive inverse is also called the __________________.

13. The multiplicative inverse is also called the ____________________.

14. The sign of the product of eight negative numbers is ____.

15. The coefficient of the term –x is ______.

16. Write a verbal expression for 2 + 5p

17. Write an algebraic expression for this “8 to the fourth power increased by 6”

18. Evaluate the following expressions:

a. 62 – 32 8 +11 b. 3

5 3 15

19. Evaluate a(4b + c2) if a = 2 , and b = 5 , and c = 1

20. Solve for x. Then name the property used.

1

13x

21. Simplify 16a2 – 7b2 + 3b – 2a2

22. a. Write an algebraic expression for this situation:

Silly Steve made a down payment of $300 on a new TV. He paid $37 per month

for x months to finish paying it off.

b. If x = 9 , how much did he pay altogether?

Unit 1: Chapter 2

23. Translate “six times the sum of x and y” and “five less than y.” Which algebraic

expression represents the sum of these two verbal expressions?

(1) 6x + 5 (2) 6x + 2y – 5 (3) 6x + 5y + 5 (4) 6x + 7y – 5

24. The bill (parts and labor) for the repair of a car is $458. The cost for the parts is

$339. The labor charge is $34 per hour. Which equation could be used to

determine the number of hours of labor?

(1) 34(x + 339) = 458 (2) 34 + 339x = 458

(3) 34x + 339 = 458 (4) 34 + x+ 339 = 458

25. Solve for x: 12x – 4 – 12 = 4x + 8 + 8x – 24

26. Solve for y: 32 – 3

8y =

3

4y + 5

27. Solve each of the following for the variable listed:

a. A = bh, for b b. P = 2l + 2w, for w c. ax

cb , for x

28. The school basketball team won 15 of their 20 games last season. What is the

ratio of games won to the number of games played in simplest form?

29. Find three consecutive integers such that the sum of the first two integers is 24

more than the third integer.

30. Find two consecutive even integers such that their sum is equal to the eight less than

three times the larger.

31. In a boy’s bank, there is a collection of nickels, dimes, and quarters which

amounts to $3.20. There are 3 times as many quarters as nickels, and 5 more

dimes than nickels. How many coins of each kind are there?

32. Grant’s change rack contained $8.80 in quarters, dimes and nickels. There were two

more than five times as many nickels as quarters and four less than twice as many

dimes as quarters. How many of each kind of coin was there in the change rack?

Unit 2: Chapter 3

33. Find the x-intercept and the y-intercept of the graph of the equation 2x + 3y = 6.

34. Is (2, -1) a solution of the equation 6y – 3x = -9?

35. Find the rate of change represented in each table or graph.

a. b.

36. Find the slope of the line passing through the following points:

a. (-3, -2) and (1, 6) b. (-6, 2) and (4, -2)

37. Determine the average rate of change for each function over the given interval.

a. 𝑔(𝑥) over the interval −2 ≤ 𝑥 ≤ 6 b. ℎ(𝑥) over the interval 2 ≤ 𝑥 ≤ 4

38. Music downloads are $0.99 per song. Write an equation for the total cost T of d songs.

Unit 2: Functions

39. State whether each of the following is a function or not a function.

a. b.

40. The function f x is defined by 2

62

xf x x . Find the value of 10f .

41. A function rule takes an input, x, and converts it into an output, y, by increasing

one half of the input by 10.

a. Write an equation for the rule.

b. Determine the output for this rule when the input is 50.

𝑥 ℎ(𝑥)

1 -6

2 -7

3 -6

4 -3

5 2

y

x

42. Based on the graph of the function y g x shown below, answer the following

questions.

a. Evaluate each of the following.

b. What are the zeroes (roots) of the function?

c. How many values of x solve the equation 2g x ? Illustrate your answer on

the graph.

d. Would you characterize the function as increasing or decreasing on the domain

interval 1 3x ?

e. Would you characterize the function as increasing or decreasing on the domain

interval 3 6x ?

f. Is the function positive or negative over the interval 3 1x ?

g. List all of the turning points shown in the graph.

h. What is the absolute minimum value of the function?

Unit 2: Chapter 4

43. Write an equation in slope-intercept form given the points (5, 3) and (7, -1).

44. What is the slope of the line with equation: x = 4

45. Write the equation y + 6 = -4(x – 3) in standard form.

46. Given a line whose slope is 1

4 and whose y-intercept is the origin. Write the

equation of the line in:

a. slope-intercept form

b. standard form

47. What is the slope-intercept equation of the line which passes through the point

(3, 4) and that is parallel to the line y = -2x + 5

48. a. Write a linear equation in slope-intercept form to model this situation. Define all

variables.

An internet cafe charges $6.00 to access a computer plus $2.50 for each hour of use.

b. How much would it cost to access a computer and play 3 hours of video games?

49. Which is an equation of the line that passes through (3, 5) and (-2, 5)?

(1) y = 3

x 25

(2) y = 0 (3) x = 5 (4) y = 5

50. Which is an equation of the line with slope -3 and y-intercept of 5?

(1) y = -3(x + 5) (2) y – 5 = -3x

(3) -3x + y = 5 (4) y = 5x – 3

51. What is an equation of the line through (0, -3) with slope 2

5?

(1) -5x + 2y = 15 (2) 2x – 5y = 15

(3) -5x – 2y = -15 (4) -2x + 5y = 15

52. Which equation is graphed at the right?

(1) 2y – x = 10 (2) 2x – y = 5

(3) 2x + y = -5 (4) 2y + x = -5

53. Graph the following equation:

3 4 24x y

Unit 2: Chapter 5

54. Solve the inequality and graph the solution on a number line. Write your solution using

interval notation. 2 5 7y

55. Solve the inequality and graph the solution on a number line: Write your solution using

set builder notation. 15 30 5(2 9) x x

56. Solve the compound inequality and graph the solution on a number line. Write your

solution using interval notation.

a. 2 3 8 10x b. 3 5 8x or 4x

57. Define a variable, write an inequality, and solve.

Three times a number increased by 8 is no more than the number decreased by 4.

58. Graph the inequality.

2 3 9x y

Unit 3: Chapter 6

59. Solve the following systems by graphing.

x + 2y = 8

y – 1 = x

60. Solve the system of equations using the substitution method.

y x 7

3x 7y 9

61. Solve the system of equations by using the elimination method.

2x 5y 18

9y 5x 24

62. Solve each word problem using a system of equations.

a. Abby goes to the Gap and buys 3 pairs of pants and 2 shirts for $140. Emily buys 2

pairs of the same pants and 4 of the same shirts for $160. How much does each item

of clothing cost?

b. Tickets for a high school dance cost $1.00 each if purchased in advance of the dance,

but $1.50 each if bought at the door. If 100 tickets were sold and $120 was collected,

how many tickets were sold in advance and how many were sold at the door?

63. Graph the solution to the system of inequalities.

2 8 12

25

5

y x

y x

64. John works part-time for a local contractor. He makes $10 an hour if he works with the

plumber, and $25 an hour if he works with the mason. John cannot work more than 10

hours per week. He plans to earn at least $150 per week.

a. Write a system of inequalities that models the situation. Let x be the number of

hours he works with the plumber and let y be the numbers of hours he works with

the mason.

b. Graph the system of inequalities.

c. State one combination of hours that would satisfy the problem.

65. Edith babysits for x hours a week after school at a job that pays $4 an hour. She has

accepted a job that pays $8 an hour as a library assistant working y hours a week. She

will work both jobs. She is able to work no more than 15 hours a week, due to school

commitments. Edith wants to earn at least $80 a week, working a combination of both

jobs.

a. Write a system of inequalities that can be used to represent this situation.

b. Graph these inequalities on the set of axes below.

c. Determine and state one combination of hours that will allow Edith to earn at least

$80 while working no more than 15 hours.