Free Printable PAP Algebra 2

Worksheets

PAP Algebra 2 - Module 1 Review

Total questions: 81

Worksheet time: 7hrs 19mins

Name

Class

Date

When you graph an inequality, you used a closed dot when you use which symbols?

≤, ≥

<, >

Solve the inequality.
x + 5 ≤ 13

x ≥ 8

x ≥ 18

x ≤ 8

x ≤ 18

Write an equation to represent this word problem.

40 - 2f = 8

40 + 2f = 8

8 - 2f = 40

40 = 2f - 8

Write an equation to represent this word problem.

5 + 4e = 25

5 = 4e + 25

5 + 4 + 25

4 - 4e = 25

Jim paid a gym membership fee of $50, plus $20 per month. Jim has paid a total of $290 to the gym. How many months has he been a member at the gym?

64.5

Jim paid a gym membership fee of $50, plus $20 per month. Jim has paid a total of $290 to the gym. Which equation matches this situation?

50 + 20m = 290

20 + 50m = 290

50 + 20 = m

50m - 20 = 290

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? Write an equation that matches this situation.

331=7x+6

331=13x

331=6x+7

331-7=6x

Which number line shows the solution set to the inequality below?
x - 3 > -3

Solve the equation:
3(x - 1) = 2x + 9

x = 12

no solution

x = 10

x = 6

10.

Solve:
8m - 9 > 71

m > 10

m > 1

m < 1

m > -48

11.

4x-7≥21

x≥7

x≥-8

x≤8

x≤7

12.

2x+6>12

x>9

x>3

x<9

x<3

13.

Pick the correct inequality.

14.

"At most" and "No more than" are both clue words for...

≤

≥

15.

What inequality does the number line graph represent.

x < 2

x > 2

x ≥ 2

x ≤ 2

16.

-4x + 14 ≤ 54

x ≥ - 10

x ≤ -10

x ≥ 10

x ≤ 10

17.

Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?

(-3,-8)

(-8,-3)

(3,-8)

(8,3)

18.

Give the solution to the system

(3,1)

(1,3)

(-1,3)

No solution

19.

Solve for x and y
5x + 3y = 7
y = 4

(4,1)

(4,-1)

(1,4)

(-1,4)

20.

Solve for x and y
2x − 3y = −1
y = x − 1

(-2,-3)

(0,-1)

(3,4)

(4,3)

21.

Solve for x and y
y = 2x + 1
y = 4x - 1

(1,3)

(-1,-3)

(-1,3)

(3,1)

22.

Solve:
y = 2x -11
-3y = -6x -15

(-1.5,-4)

(1.5,4)

No solution (parallel lines)

Infinitely many solutions

23.

Solve:
8x + 4y = 12
y = -2x + 3

(0,3)

(3,0)

No solution(parallel lines)

Infinitely many solutions

24.

4x - 2y = 7
x + 2y = 3
What are x and y?

x = 2, y = 2

x = 1/2, y = 2

x = 2, y = 1/2

x = 2, y = -2

25.

If 3x - 2y = 14 and 2x + 2y = 6,
what are x and y?

x = 1, y = 2

x = 2, y = 1

x = -4, y = 1

x = 4, y = -1

26.

If a system of equations has no solution, what does the graph look like?

intersecting lines

parallel lines

skew lines

the same line (coinciding lines)

27.

If a system of equations has infinitely many solutions, what does the graph look like?

intersecting lines

parallel lines

skew lines

the same line (coinciding lines)

28.

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?

x + y = 15
4x + 2y = 44

4x + 2y = 15
x + y = 44

x = 2y + 44
4x = y + 15

2x - 4y = 44
x - y = 15

29.

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

x + y = 33
y = 2x - 3

x + y = 33
x = 2y - 3

x + y = 33
x = 3 - 2y

x + y = 3
x = 33 - 2y

30.

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

4x + 6y = 3

13.5x - 13y = 6

x + y = 4

x - y = 6

4x + 6y = 13

3x + 7y = 13.5

4x - 6y = 13

3x - 7y = 13.5

31.

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

S + A = 530
3S + 4A = 1740

S + A = 530
4S + 3A = 1740

S + A = 1740
3S + 4A = 530

S + A = 1740
4S + 3A = 530

32.

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

x + y = 1430

20x + 50y = 49

x + y = 49

10x + 5y = 1430

x + y = 49

20x + 50y = 1430

x + y = 49

x + y = 1430

33.

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

5q + 2z = 1.32
1z = 0.75

5q + 2z = 1.32
3q + 1z = 0.75

q + z = 1.32
q + z = 0.75

5q + 2z = 0.75
3q + 1z = 1.32

34.

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

x+y=134
x+y=120

3x+3y=134
4x+3y=120

4x+3y=134
3x+3y=120

7xy=134
6xy=120

35.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

3H + 2D = 315

2H + 4D = 450

3H + 2D = 450

2H + 4D = 315

3H + 2D = 450

3H + 2D = 315

2H + 2D = 135

36.

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

1.5N+0.5S=78.5

N+S=87

1.5N+0.5S=78.5

1.5N+0.5S=87

N+S=78.5

1.5N+0.5S=87

N+S=78.5

N+S=87

37.

There are 50 donkeys and chickens on a far. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?

d + c = 174
4d + 2c = 50

d + c = 50
4d + 2c = 174

d + c = 50
2d + 4c = 174

d + c = 174
2d + 4c = 50

38.

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child ticket

3S+C=38

3S+2C=52

3S+C=52

3S+2C=38

3C+S=38

3C+2S=52

3C+S=52

3C+2S=38

39.

Choose the correct translated function.

f(x)= |x|+2

f(x)= |x|-2

f(x)= -|x|

f(x)= -|x|+2

40.

Describe the transformation of y = f(x) for the new function
y = 1/5f(x)

The graph of y = f(x) compressed horizontally by a factor of 1/5

The graph of y = f(x) was stretched horizontally by a factor of 5

The graph of y = f(x) was compressed vertically by a factor of 1/5

The graph of y = f(x) was stretched vertically by a factor of 5

41.

Write the equation for a graph that is vertically compressed by a factor of 2/5 and shifted up 6.

y=6|x|-2/5

y=2/5|x|+6

y=2/5|x+6|

y=2/5|x-6|

42.

What are the transformations of the equation: y = -¹/₂|x| + 3

Stretch

Reflect

Vertical shift

Shrink - Compress

43.

-|−2r − 1| = 11

{-6,5}

{5,-6}

-6

No Solution

44.

|−4 + 5x| = 16

{16/5,12/5}

{4,-5}

{-12/5, 4}

45.

−2|−2r − 4| = -12

{3,1}

{-3,-1}

{-3}

No Solution

46.

|−2n| + 10 = −50

{30, -30}

{20,-20}

{-5,5}

No Solution

47.

∣ 2x + 9 ∣ = 15

x = 3

x = 3
x = -6

x = 3
x = -12

x = 6
x = -12

48.

3| −8x| + 8 = 80

{-7/3, 7/3}

{-3,3}

{11/3,-11/3}

No Solution

49.

What is the reason that absolute value is always written as a positive?

Absolute value is talking about numbers so it must be positive.

Absolute value does not always have to be positive.

Absolute value is like a clock it has only positive numbers.

Absolute value is talking about distance, distance is always measured by positive numbers.

50.

Order the numbers from least to greatest.
-2, I8I, 5, I-10I, 6

-2, I8I, 5, I-10I, 6

-10, -2, 5, 6, 8

-2, 5, 6, 8, 10

I-10I, -2, 5, 6. I8I

51.

| x + 3 | ≤ 2

No Solution

x ≤ -1

-5 ≤ x and x ≤ -1

1 ≤ x and x ≤ 5

52.

| x + 3 | > 8

No Solution

All Real Numbers

x < -11 or x > 5

-5 < x < 11

53.

What is the correct first step?

divide by 10

multiply by 10

make it two inequalities with an "or"

make it two inequalities with and "and

54.

no solution

a> -1/6 or a< -5/6

a>1/2 or a< -3/2

all real numbers

55.

n > 1 or n < -7

n > -1 or n < -7

-7 < n < -1

no solution

56.

no solution

x > 2 or x < -22

-22 < x < 2

all real numbers

57.

Which compound inequality represents the graph?

m < -1 OR m > 2

-1 < m < 2

m > -1 OR m < 2

58.

Solve for n.

n ≥ 10 and n ≤ -6

n > 10 and n < -6

n ≥ 10 or n ≤ -6

n > 10 or n < -6

59.

Solve for r.

r ≥ -38 and r ≤ 32

r > -38 and r < 32

r ≥ -38 or r ≤ 32

r > -38 or r < 32

60.

61.

The radius of the gears produced at a factory must be 6 inches in length with a tolerance of 0.1 inches. The gears with radius beyond the tolerated lengths will be thrown away. Which of the following inequalities can be used to assess which gears are eligible? (x is the length of the radius)

|x – 6| ≤ 0.1

|x – 6| ≥ 0.1

|x – 0.1| ≤ 6

|x – 0.1| ≥ 6

62.

The average temperature in Las Vegas in July is 110 degrees. If the temperature can vary up to 10 degrees, which equation represents this situation?

| x - 10 | < 110

| 110 - x | < 10

| x - 110 | < 10

| 10 - x | < 110

63.

State the dimensions of the following matrix

(a)

64.

Name the dimensions:

6x2

2x6

65.

How many rows are in a 7 x 3 matrix?

66.

What is the value of element a₂₃?

-1

67.

What is the value of element a₃₄?

-3

68.

Solve, if possible:

-2x - 4y + 4z = 14

4x + 2y + 4z = -4

x + 2z = -2

x = 3, y = 1, z = 1

No solution

Infinitely many solutions

x = -3, y = -1, z = -1

69.

Solve, if possible:

3x + 2y - 3z = 13

4z + 4x = 12

-2x - y + z = 8

x = 3, y = 1, z = 1

No solution

Infinitely many solutions

x = -3, y = -1, z = -1

70.

Solve, if possible.

2x + 5y + z = -12

-x + 4y + 3z = -4

5x - 2z = -13

x = 3, y = 1, z = 1

No solution

Infinitely many solutions

x = -3, y = -1, z = -1

71.

Solve, if possible.

3x + 3y = -12

-4x - 2y + 2z = -14

x + 3y + 2z = 11

x = 1, y = 1, z = 4

No solution

Infinitely many solutions

x = -1, y = -1, z = 4

72.

Solve, if possible.

x - y + 2z = -1

-3x + 3y + 5z = 3

2x - 2y = -2

x = 1, y = 1, z = 4

No solution

Infinitely many solutions

x = -1, y = -1, z = 4

73.

Solve, if possible.

4x - 2y = 2

5x - 2y + z = 7

3x + 4y - z = 3

x = 1, y = 1, z = 4

No solution

Infinitely many solutions

x = -3, y = -1, z = -1

74.

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

x + y ≤ 8

x + y ≤ 6

2x + 3y ≤ 6

x + y ≤ 10

75.

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

2x + 3y ≤ 18

x + y ≤ 6

x + y ≤ 9

3x + 2y ≤ 18

76.

Which of the following inequalities matches the given graph?

x ≥ -1

x ≤ -1

x > -1

x < -1

77.

Which are vertices of the feasible region?

(0, 3) (3, 0) (5, 8)

(0, 6) (3, 5) (6, 5)

(3, 3) (8, 5) (5, 8)

(0, 5) (6, 0) (3, 3)

78.

Which of the following inequalities matches the given graph?

y ≤ -3/4 x + 3

y ≥ -3/4 x + 3

y < -3/4 x + 3

y > -3/4 x + 3

79.

What do you call the area where all the shading overlaps?

the answer

the feasible region

the void

the objective function

80.

Given the objective function: P = 30x + 50y

Which vertex maximizes the profit?

(0,0)

(6,2)

(8,0)

(0,6)

81.

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.

x+y≤300
7.5x+5.5y≥2000

x+y<300
7.5x+5.5y≥2000

x+y≤300
7.5x+5.5y≤2000

x+y>2000
7.5x+5.5y≤300

Reset

PAP Algebra 2 - Module 1 Review

Total questions: 81

Worksheet time: 7hrs 19mins

Similar Resources on Wayground