Free Printable First Quarter Review Algebra 2

1.

Define the fo0llowing:

1) Real Number

2) Rational Number

3)Irrational Number

4)Integer

5)Whole Number

6)Natural Number

4 lines

2.

Give one example of each of the above classifications:

4 lines

3.

Natural Numbers are also known as (a) numbers.

4.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

5.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

6.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

7.

Express the following in Interval Notation
-9 < x < -8.5

a)

[-9, -8.5]

b)

[-9, -8.5)

c)

(-9, -8.5]

d)

(-9, -8.5)

8.

Express the following interval in Set notation:
[3, 5]

a)

3 ≤ x ≤ 5

b)

3 < x ≤ 5

c)

3 ≤ x < 5

d)

3 < x < 5

9.

Express the following interval in Set notation:
(-7, 15]

a)

-7 ≤ x ≤ 15

b)

-7 < x ≤ 15

c)

-7 ≤ x < 15

d)

-7 < x < 15

10.

Express the following interval in Set notation:
[14.2, 19.6)

a)

14.2 ≤ x ≤ 19.6

b)

14.2 < x ≤ 19.6

c)

14.2 ≤ x < 19.6

d)

14.2 < x < 19.6

11.

Express the following interval in Set notation:
(-63, -62)

a)

-63 ≤ x ≤ -62

b)

-63 < x ≤ -62

c)

-63 ≤ x < -62

d)

-63 < x < -62

12.

Look at the graph. Write the inequality in interval notation.

a)

(-2,5)

b)

(-∞,-2)⋃(5,∞)

c)

[-2,5]

d)

(-∞,-2]∪[5,∞)

13.

Write the following in interval notation
-7 ≤ x < 8

a)

(-7, 8)

b)

[-7, 8)

c)

[-7, 8]

d)

(-7, 8]

14.

Write the following in interval notation
x < 8

a)

(8, ∞)

b)

(8, -∞)

c)

(-∞, 8)

d)

[-∞, 8]

15.

Write the following in interval notation
x < 3 or x ≥ 5

a)

(3, -∞) or (∞, 5]

b)

[-∞, 3) or [5, ∞]

c)

(-∞, 3) or [5, ∞)

d)

(3, -∞] or [∞, 5]

16.

Write the following in interval notation
x > 6 and x ≤ 10

a)

(-∞, 6) and (10, ∞)

b)

[6, 10)

c)

(-∞, 6] and [10, ∞)

d)

(6, 10]

17.

Write the following in interval notation
x ≥ 100

a)

(0, 100] (Real quick)

b)

(∞, 100]

c)

[100, ∞)

d)

(∞, 100)

18.

Look at the Graph. Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

19.

When graphing b< 6 would you use an open or closed circle?

a)

open

b)

closed

20.

(-2,12) can be written in inequality notation as:

a)

-2 < x > 12

b)

-2 > x > 12

c)

-2 < x <12

d)

None of these

21.

Look at the picture. Which number line corresponds to [-2, 5]?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

22.

Look at the picture. Which graph best represents the solution set (-∞, -2) U (5, ∞)?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

23.

Look at the picture. Select the correct interval notation for the given number line.

a)

(-∞, -8) U (-4, ∞)

b)

(-∞, -8] U [-4, ∞)

c)

(-8, -4)

d)

[-8, -4]

24.

What type of number is π ?

a)

Rational

b)

Irrational

25.

Which number is a rational number ?

a)

1/4

b)

π

c)

√3

d)

∛25

26.

√25

a)

Rational

b)

Irrational

27.

-17.565

a)

Rational

b)

Irrational

28.

.141414141414...

a)

Rational

b)

Irrational

29.

Zero

a)

Rational, integer

b)

Rational, integer, real

c)

Rational, integer, natural

d)

rational, integer, natural, real

30.

Choose the best definition of the term INTEGER...

a)

Positive numbers

b)

Positive numbers and zero

c)

Positive and negative whole numbers

d)

Positive and negative whole numbers, including zero

31.

Real Numbers are classified into 2 categories, what are they?

a)

Fractions and decimals

b)

Positive and Negative Numbers

c)

Rational and Irrational Numbers

d)

Whole Numbers and Integers

32.

Which of the following real numbers are integers?

a)

-3000

b)

2.5

c)

234

d)

8/4

33.

Which of the following real numbers are whole numbers?

a)

$-10$

b)

$2.5$

c)

$200$

d)

$\sqrt{100}$

34.

Are all whole numbers integers?

a)

yes

b)

no

35.

An integer is always a whole number.

a)

True

b)

False

36.

A fraction is which type of number?

a)

Rational

b)

Irrational

37.

Which set do I belong to?

(1, 2, 3, 4, 5...)

a)

Natural Numbers

b)

Rational Numbers

c)

Whole Numbers

d)

Integers

e)

Irrational Numbers

38.

Which set do I belong to?

(...-3, -2, -1, 0, 1,2 ...)

a)

Natural Numbers

b)

Rational Numbers

c)

Whole Numbers

d)

Integers

e)

Irrational Numbers

39.

a)

linear

b)

quadratic

c)

absolute value

d)

inverse

40.

a)

constant

b)

linear

c)

cubic

d)

square root

41.

a)

quadratic

b)

absolute value

c)

square root

d)

inverse

42.

a)

linear

b)

don't miss this one

c)

you know this one

d)

spell it RIGHT

43.

Which of the following is the graph of $y=\left(x+5\right)^2-3$

a)

b)

c)

d)

44.

Which of the following is the graph of $y=\left(x-5\right)^2+3$

a)

b)

c)

d)

45.

The blue graph is $y=\left|x\right|$
Which of the following could be the equation of the red graph?

a)

$y=\frac{1}{4}\left|x-2\right|-1$

b)

$y=-\frac{1}{4}\left|x-2\right|-1$

c)

$y=4\left|x-2\right|-1$

d)

$y=-4\left|x-2\right|-1$

46.

The blue graph is $y=\left|x\right|$
Which of the following could be the equation of the red graph?

a)

$y=\frac{1}{4}\left|x-2\right|-1$

b)

$y=-\frac{1}{4}\left|x-2\right|-1$

c)

$y=4\left|x-2\right|-1$

d)

$y=-4\left|x-2\right|-1$

47.

|v + 8| − 5 = 2

a)

{-1,-15}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

48.

-|−2r − 1| = 11

a)

{-6,5}

b)

{5,-6}

c)

-6

d)

No Solution

49.

|−4 + 5x| = 16

a)

{16/5,12/5}

b)

{4,-5}

c)

{-12/5, 4}

d)

4

50.

−2|−2r − 4| = -12

a)

{3,1}

b)

{-3,-1}

c)

{-3}

d)

No Solution

51.

|−2n| + 10 = −50

a)

{30, -30}

b)

{20,-20}

c)

{-5,5}

d)

No Solution

52.

|2a - 10| = 6

a)

a = 8, a = 5

b)

a = 2

c)

a = 8

d)

a = 8, a = 2

53.

| x – 3 |= 0

a)

3

b)

-3

c)

{-3, 3}

d)

no solution

54.

Solve for p. 9|9 - 2p| = 81

a)

p = 0, p = -9

b)

p = -63/2, p = 99/2

c)

p = 0, p = 9

d)

No Solution

55.

Solve.

8 - 9|10r - 9| = -73

a)

r = 9/5, r = 0

b)

r = 0, r = 5

c)

r = 9/5, r = 1

d)

r = -63/10, r= 0

56.

Solve for k. |6 - 2k| = 18

a)

k = -6, k = 6

b)

k = -6, k = 12

c)

k = -6, k = -12

d)

k = -6, k = 5

57.

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

a)

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

b)

Absolute value does not always have to be positive.

c)

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

d)

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

58.

What's a way to define absolute value?

a)

The value of a number

b)

The opposite of a number

c)

The distance of a number from zero

d)

The multiplicative inverse of a number

59.

3| −8x| + 8 = 80

a)

{-7/3, 7/3}

b)

{-3,3}

c)

{11/3,-11/3}

d)

No Solution

60.

8|-2x + 4| = 96

a)

x = -4, x = 8

b)

x = -4

c)

x = -4, x = -8

d)

x = 4, x = 8

61.

How many solutions does the following equation have?

0 = -6|9v - 7|

a)

no solution

b)

one solution

c)

two solutions

62.

solve for z.

|-4z|=7

a)

-7/4, 7/4

b)

-7/4

c)

11, 3

d)

-11, -3

63.

Solve the following equation:

∣ 2x + 9 ∣ = 15

a)

x = 3

b)

x = 3, x = −6

c)

x = 3, x = −12

d)

x = 6, x = −12

64.

Solve the following equation:

|−4 + 5x| = 16

a)

{16/5,12/5}

b)

{4, −5}

c)

{−12/5, 4}

d)

{4}

65.

8|-2x + 4| = 96

a)

x = -4, x = 8

b)

x = -4

c)

x = -4, x = -8

d)

x = 4, x = 8

66.

Connor has sold 15 cups of lemonade at his stand and will sell 5 more cups per hour. Write an equation to represent this situation.

a)

y = 10x + 5

b)

y = 20x

c)

y = 15x + 5

d)

y = 5x + 15

67.

Bob's Plumbing charges $15 per hour plus a service fee of $40 for coming out to your house. Which equation models this situation?

a)

y = 15x + 40

b)

y = 40x + 15

c)

y = 15x

d)

y = 15x - 40

68.

Ace Telecommunications charges $0.12 per minute of phone use plus a monthly service fee of $8.00 for it phone service. Which equation can be used to find c, the total cost for one month when m, minutes are used?

a)

c = 0.12m + 8m

b)

c = 8m + 0.12m

c)

c = 0.12m + 8

d)

c = 0.20m

69.

Write the equation of the line.

a)

y= -1x-3

b)

y= -3x-1

c)

y=-1/3x-1

d)

y= -3x-3

70.

Write a linear equation in the form of y=mx+b

a)

y = -2x - 3

b)

y = 2x - 3

c)

y = 3x -2

d)

y= -3x -2

71.

A holiday meal costs $12.50 a person plus a delivery fee of $30. Which equation represents the amount a holiday meal costs, including delivery, for x people?

a)

y = 12.5x + 30

b)

y = 12.5 + 30

c)

y = 30x + 12.5

d)

y = 30 - 12.5x

72.

Which equation matches the graph? (Click me to see the image)

a)

y = 2x

b)

y = 1/4 x + 2

c)

y = 1x + 4

d)

y = -2x

73.

Jerry has $20 and makes $7 per hour. Which equation represents the total amount of money Jerry has after working x hours?

a)

y = 7x + 20

b)

y = 20x + 7

c)

y = 20 + 7

d)

y = 7x - 20

74.

Write a linear equation in the form of y=mx+b

a)

y = 2x + 3

b)

y = -2x + 3

c)

y = 2x -3

d)

y = 3x - 4

75.

Eddie's Electric charges $90 per hour plus a $50 traveling fee. Which equation models this scenario?

a)

y = -50x + 90

b)

y = 90x + 50

c)

y = -90 - 50x

d)

y = 50 - 90x

76.

A man is climbing down from 100 feet high descending 30 feet per minute.

a)

y = 100 - 30x

b)

y = 100 + 30x

c)

y = 100x + 30

d)

y = 100x - 30

77.

Write the equation for the line in slope-intercept form.

a)

y= -1x+3

b)

y= 4x+3

c)

y=1/4x+3

d)

y= -4x+3

78.

Sandra has a $20 itunes gift card and spends $3 each month. Which equation can be used to find how much money Sandra has on her giftcard after x months?

a)

y = 3x + 20

b)

y = 3 + 20x

c)

y = -3x + 20

d)

y = -20x + 3

79.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

80.

When Phil started his new job, he owed the company $65 for his uniforms. He is earning $13 per hour. The cost of his uniforms is withheld from his earnings. Write an equation that models the total money he has y after x hours of work.

a)

y = 13x - 65

b)

y = 13x + 65

c)

y = 65x + 13

d)

y = 65x + 13

81.

Write an equation that could represent the amount of money in my account

a)

y = 0x + 3

b)

y = 3x

c)

y = x + 3

d)

y = 3x + 1

82.

Amelia has $100 in her savings account and plans on saving $20 per week. Write an equation to represent this situation.

a)

y = 100x

b)

y = 20x

c)

y = 20x + 100

d)

y = 100x + 20

83.

Solve the simultaneous equations

x+y=5

x-y=1

a)

x=2, y=3

b)

x=3, y=2

c)

x=3, y=-2

d)

x=-3, y=2

84.

Solve the simultaneous equations

a+b=11

a-b=3

a)

a=7, b = 4

b)

a=-4, b= 7

c)

a=4, b = 7

d)

a=4, b= -7

85.

Solve the Simultaneous Equations: a+b= 3; a-b= -7

a)

a=-2, b = 5

b)

a=2, b = -5

c)

a=2, b = 5

d)

a=-2, b = -5

86.

What is the solution?

a)

No solution

b)

(0, 2)

c)

(0, -4)

d)

(3, -3)

87.

Where do these two lines intersect?

a)

No solution

b)

(-2, 3)

c)

(3, -2)

d)

(2, 3)

88.

What is the solution?

a)

(6, 3)

b)

(3, 6)

c)

(-6, 3)

d)

No solution

89.

Solve the system of equations using substitution:

-4x + 4y = 8

y = -2x - 10

a)

(-4, -2)

b)

(12, -34)

c)

(4, -18)

d)

(-2, -6)

90.

What is the solution to the system?

8x + 4y = 12

y = -2x + 3

a)

(0,3)

b)

(3,0)

c)

No solution(parallel lines)

d)

Infinitely many solutions

91.

Solve the system of equations using substitution:

y = 2x + 5

2x + 2y = 4

a)

(1, 7)

b)

(7, 1)

c)

(2, 9)

d)

(-1, 3)

92.

Solve:

3x - y = 11

x + y = 5

a)

x = 4

y = 1

b)

x = 4

y = -1

c)

x = -4

y = 1

d)

x = -4

y = -1

93.

Solve:

3x + 5y = 4

4x - 5y = -18

a)

x = -2

y = 2

b)

x = -2

y = -2

c)

x = 2

y = -2

d)

x = 2

y = 2

94.

Which inequality describes this graph...

a)

y < 3x - 2

b)

y > 3x + 2

c)

y < 3x + 2

d)

y > 3x -2

95.

This is a graph of which inequality?

a)

y > 4x - 2

b)

y > -2x + 4

c)

y < -2x

d)

y < 4X - 2

96.

According to the graph, which point is a solution? Choose all that apply.

a)

(0, 0)

b)

(4, 2)

c)

(-1, -5)

d)

(-3, 0)

97.

Is the point (3, 1) a solution for the following inequality? Choose the best answer that has the best explanation.

a)

Yes because it is located in the shaded region.

b)

No because it is located on the line and the line is dotted.

c)

Yes because it is located on the line.

d)

No because it is in the shaded region.

98.

Which of the following is true of the given graph?

y ≥ -2x + 1

a)

The graph is a dotted line, shaded above.

b)

The graph is a solid line, shaded above.

c)

The graph is a dotted line, shaded below.

d)

The graph is a solid line, shaded below.

99.

Which inequality below is equivalent to

3x - y > 4

a)

y > 3x - 4

b)

y < -3x + 4

c)

y < 3x - 4

d)

y > -3x + 4

100.

Which of the following is "NOT" a solution for the inequality?

y ≤ 5x - 1

a)

(0, -3)

b)

(5, 24)

c)

(-2, -15)

d)

(1, 7)

101.

Choose the correct inequality for this graph.

a)

b)

c)

d)

102.

Which of the following is the graph of

3x - 2y < 10

a)

b)

c)

d)

103.

Where would you find a solution for

y < -x + 4

a)

In the shaded region above the line.

b)

In the shaded region below the line.

c)

On the line.

d)

On the origin.

104.

Which point is in the overlap of the shaded regions?

a)

(8,-5)

b)

(20,5)

c)

(9,10)

d)

(-7,1)

105.

Which point is a solution to both inequalities?

a)

(-10,-5)

b)

(-20,25)

c)

(40,30)

d)

(40,-10)

106.

Which point is in the overlap (solution) of the shaded region?

a)

(5,0)

b)

(-1,8)

c)

(1,15)

d)

(10,5)

107.

Which point is part of the solution?

a)

(4,0)

b)

(0,4)

c)

(10,5)

d)

(5,10)

108.

Use desmos. Which point is in the overlap of
$y\ >\ \frac{1}{2}x+1$
$y<\frac{1}{4}x+6$

a)

(5,3)

b)

(3,5)

c)

(1,6)

d)

(6,1)

109.

Use desmos to find a solution to the system:
$y\ge\frac{1}{2}x+2$
$2x+3y<12$

a)

(4,3)

b)

(-1,3)

c)

(2,-6)

d)

(0,0)

110.

Use desmos to pick the correct graph of the system:
$y<x$
$y\ge-\frac{1}{2}x+1$

a)

b)

c)

d)

111.

Use desmos. Which correctly shows the graph of the sytem:

$y<-\frac{3}{2}x+1$
$x\ge-2$

a)

b)

c)

d)

112.

Pick ALL correct answers.

Which are solutions to the system?

a)

(-5,4)

b)

(-5,-2)

c)

(0,10)

d)

(5,10)

e)

(0,-5)

113.

Pick ALL correct answers.

Which point are solutions to the system of inequalities?

a)

(0,6)

b)

(6,0)

c)

(4,0)

d)

(0,4)

e)

(0,-6)

114.

Pick ALL correct answers.

Use desmos to pick solutions to the system:
$y<x$

$y\ge\frac{1}{2}x-4$

a)

(2,0)

b)

(0,2)

c)

(-2,0)

d)

(0,-2)

e)

(10,0)

115.

Pick ALL correct answers.

Use desmos to select solutions to the system:
$y\ge-5x+1$

$3x+4y\le24$

a)

(5,1)

b)

(-1,5)

c)

(5,-1)

d)

(7,-2)

e)

(-2,7)

116.

The graph shows which system?

a)

y>\frac{2}{3}x+1

y\le-5x+10

b)

$y<\frac{2}{3}x+1$
$y\ge-5x+10$

c)

$y<\frac{2}{3}x+1$
$y\le-5x+10$

d)

$y>\frac{2}{3}x+1$
$y\ge-5x+10$

117.

Which system is graphed?

a)

y>-\frac{1}{4}x-3

y>2x+6

b)

$y>\frac{1}{4}x-3$
$y\le-2x+6$

c)

$y\le-2x+6$
$y<-\frac{1}{4}x-3$

d)

$y\le-2x+6$
$y>-\frac{1}{4}x-3$

118.

Solve the system for each variable:

4c+2y+4z = 28

6c+2y = 16

3c = 6

4 lines

119.

Solve the system for each variable:

2b+v+3y = 16

5b+v = 10

3b = 3

4 lines

120.