Free Printable 2021-2022 Algebra 1 Winter Exam Review

1.

Is the table linear, exponential, or quadratic?

a)

Linear

b)

Exponential

c)

Quadratic

d)

none of these

2.

This table represents what kind of function?

a)

Linear

b)

Exponential Growth

c)

Exponential Decay

d)

Quadratic

3.

y=x²

^{What type of equation is the above?}

a)

exponential

b)

linear

c)

quadratic

d)

neither

4.

This is a _______________ function.

a)

Linear

b)

Exponential

c)

Quadratic

5.

Pick a function that best models the following situation: A babysitter getting paid hourly.

a)

Exponential

b)

Linear

c)

Quadratic

d)

Neither

6.

abc=d

Solve for a:

a)

$a=bcd$

b)

$a=\frac{bc}{d}$

c)

$a=\frac{c}{bd}$

d)

$a=\frac{d}{bc}$

7.

$V=\pi r^2h$ solve for $\pi$

a)

$\pi=Vr^2h$

b)

$\pi=\frac{h}{Vr^2}$

c)

$\pi=\frac{r^2}{Vh}$

d)

$\pi=\frac{V}{r^2h}$

8.

ax + c = R
(solve for x)

a)

ax = R + c

b)

ax = R - c

c)

x = a(R-c)

d)

x = (R-c) / a

9.

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

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

10.

Write x ≤ 10

using interval notation:

a)

(-∞, 10]

b)

(-∞, 10)

c)

[10, ∞)

d)

(10, ∞)

11.

Rewrite for h:

A\ =\ \frac{1}{2}h\left(b_1+b_2\right)

a)

$h=2A\ -b_1-b_2$

b)

$h=\frac{A}{2\left(b_1+b_2\right)}$

c)

$h\ =\frac{2A}{b_1+b_2}$

d)

$h=\frac{2A}{-b_1-b_2}$

12.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

13.

Which is the closest to " [ a, b) "

a)

All values between a and b, including both a and b

b)

All values between a and b, excluding both a and b

c)

All values between a and b, including a, but excluding b

d)

All values between a and b, including b, but excluding a

14.

a)

Continuous

b)

Discrete

15.

a)

Continuous

b)

Discrete

16.

a)

Continuous

b)

Discrete

17.

a)

Continuous

b)

Discrete

18.

a)

Continuous

b)

Discrete

19.

What is a function?

a)

Every output has one input.

b)

Every input has one output.

c)

If there is a constant rate of change.

d)

If it is a line.

20.

You are laying bricks for a patio. Every row has 20 bricks in it. You have 400 bricks. How many rows of bricks did you lay?

a)

20

b)

2

c)

8000

d)

4

21.

Lee charges $3 for a basket and $2.50 for each pound of fruit picked at the orchard. Write an equation in y = mx + b form for the total cost of x pounds of fruit from the orchard.

a)

y = 3x + 2.5

b)

y = 2.50x + 3

c)

y = 2.50x

d)

y = 3x + 2.50

22.

The total cost (y) at an amusement park can be modeled by y=1.5x+20 where x is the number of rides you ride. What is the price per ride?

a)

1.5

b)

21.5

c)

0

d)

20

23.

A plumber charges $50 to make a house call. He also charges $25 per hour for labor.

How much would it cost for 2.5 hours of labor?

a)

$100

b)

4.50

c)

$112.50

d)

$65.00

e)

$123.45

24.

What type of function is f(x)=2(3^x) ?

a)

Quadratic

b)

Linear

c)

Exponential

25.

This function has the same rate of change.

a)

Linear

b)

Exponential

c)

Neither

26.

The graph of this function is a curve going up really fast or down really fast.

a)

Linear

b)

Exponential

c)

Neither

27.

The graph of this function is a straight line.

a)

Linear

b)

Exponential

c)

neither

28.

What type of function is this equation:
y= 4^x+1

a)

Linear

b)

Exponential

c)

Neither

29.

Is the table linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

30.

Is the table linear or exponential?

a)

Linear

b)

Exponential

31.

Which graph is linear?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

32.

Is the equation linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

33.

Is the equation linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

34.

Which function describes the table?

a)

Linear

b)

Exponential

c)

Neither

35.

Which statement below is TRUE regarding the two functions?

a)

Both functions are linear

b)

Both functions are increasing

c)

Both functions have a y-intercept of 1

d)

Both functions are exponential growth

36.

Which one means left

a)

x →-∞

b)

x →∞

37.

Which one means up

a)

y →-∞

b)

y →∞

38.

Which one means the function goes down on the left

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

39.

What is the End behavior on the left side

a)

x →-∞, y→∞

b)

x →∞, y→-∞

c)

x →-∞, y→-∞

d)

x →∞, y→∞

40.

What is the End behavior on the left side

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

c)

x →∞, y→∞

d)

x →∞, y→∞

41.

What is the end behavior on the left side

a)

x →∞, y→∞

b)

x →-∞, y→-∞

c)

x →-∞, y→∞

d)

x →∞, y→∞

42.

Is the sequence arithmetic: 37, 31, 25, 19, ...

a)

Yes

b)

No

43.

Is the sequence arithmetic: 78, 785, 7855, 78555, ...

a)

Yes

b)

No

44.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

45.

Which sequence is NOT an arithmetic sequence?

a)

-7, -13, -19, -25,...

b)

-10, -6, -2, 2,..

c)

6, 8, 10, 12,...

d)

3, 15, 75, 375,...

46.

Select the explicit rule that represents the sequence.

a)

a_n = 14(-3)(n - 1)

b)

a_n = 3 + (n - 1)(14)

c)

a_n = 14 + (n - 1)(-3)

d)

a_n = -3 + (n - 1)(14)

47.

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

(Hint: Write the explicit rule first, then use it to solve)

a)

-515

b)

-490

c)

-535

d)

460

48.

Find the 22nd term of the following sequence:

5, 8, 11, ...

(Hint: Write the explicit rule first, then use it to solve)

a)

14

b)

68

c)

63

d)

71

49.

Select the explicit rule that represents the sequence.

a)

a_n = 6 + 5(n - 1)

b)

a_n = 4 + 6(n - 1)

c)

a_n = 6 - 4(n - 1)

50.

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

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

51.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

52.

How many solutions does this system of equations have?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

d)

Two Solutions

53.

If a system of linear equations has one solution, what does this mean about the two lines?

a)

Parallel lines

b)

the same line

c)

Intersecting lines

54.

Solve the system of equations.
y = 4x+1
3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

55.

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?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

56.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

57.

√48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

58.

Simplify √60

a)

2√15

b)

12

c)

4√15

d)

3√5

59.

Simplify:

a)

4√30

b)

√4√30

c)

√2√30

d)

2√30

60.

Simplify:

a)

240

b)

300

c)

340

d)

360

61.

Simplify:

a)

A

b)

B

c)

C

d)

D

62.

√(45x⁴y⁷)

a)

3x²y³√5

b)

9x²y³√(5y)

c)

3x²y³√(5y)

d)

3x⁴y⁷

63.

Simplify:

a)

√5

b)

(√14)/2

c)

√7

d)

Cannot be simplified

64.

Simplify:

a)

2

b)

4√3

c)

2√3

d)

4

65.

√98 + 5√2

a)

8√3

b)

12√2

c)

7√2

d)

7√3

66.

Which is equivalent to √121p⁵r⁷s⁴?

a)

11prs √pr

b)

11p^2.5r^3.5s²√pr

c)

11p²r³s²√pr

d)

11p²r³s²

67.

Multiply, if possible. Then simplify.

a)

-4

b)

8

c)

4

d)

not possible

68.

Simplify. Assume that all variables are positive. $\sqrt{50x^5}$

a)

$5x^2\sqrt{2}$

b)

$10x\sqrt{2x}$

c)

$5\sqrt{2x^2}$

d)

$5x^2\sqrt{2x}$

69.

Simplify. Assume that all variable are positive. $\sqrt{200a^6b^7}$

a)

$10a^3b^3\sqrt{b}$

b)

$10a^3b^3\sqrt{2b}$

c)

$5a^3b^3\sqrt{2b}$

d)

$5a^3b^3\sqrt{b}$

70.

Simplify. Assume that all variables are positive.

a)

b)

c)

d)

71.

Multiply and simplify. Assume that all variables are positive. $\sqrt{8y^5}\cdot\sqrt{40y^2}$

a)

$8y^3\sqrt{5}$

b)

$8y^3\sqrt{5y}$

c)

$8y\sqrt{5y}$

d)

$8y^3\sqrt{5}$

72.

Multiply and simplify. Assume that all variables are positive.

a)

b)

c)

d)

73.

Divide and simplify. Assume that all variables are positive. $\frac{\sqrt{180x^5}}{\sqrt{5x^3}}$

a)

$6x^2$

b)

$12x$

c)

$6x$

d)

$12x^2$

74.

Divide and simplify. Assume that all variables are positive.

a)

b)

c)

d)

75.

Divide and simplify. Assume that all variables are positive.

a)

b)

c)

d)

76.

Divide and simplify. Assume that all variables are positive.

a)

$2x$

b)

$2x^2$

c)

$4x$

d)

$4x^2$

77.

a)

Function

b)

Not a Function

78.

Which of the following statements is true about a function?

a)

A graph passes the vertical line test

b)

A graph does not pass the veritcal line test.

79.

a)

Function

b)

Not a Function

80.

a)

Function

b)

Not a Function

81.

a)

Function

b)

Not a Function

82.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

83.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

84.

Factor 4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

85.

Factor by grouping:
3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the aboe

86.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

87.

Factor Completely.
8x³ - 18x

a)

2x(4x²-9)

b)

(4x²+3)(2x-3)

c)

2x(2x+3)(2x-3)

d)

PRIME

88.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

89.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

90.

Factor:
2x² - 3x - 2

a)

(2x - 2)(x + 1)

b)

(2x + 1)(x - 2)

c)

(2x - 1)(x - 2)

d)

(2x - 1) (x - 1)

91.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

92.

Factor
x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 10)(x + 2)

c)

(x + 8)(x + 3)

d)

(x + 2)(x + 12)

93.

Factor completely.
3x² + 10x - 8

a)

(3x + 2)(x + 4)

b)

(7x + 5)(x + 2)

c)

(3x - 2)(x + 4)

d)

(7x - 3)(x - 4)

94.

Factor completely.
5x² - 7x + 2

a)

5(x - 2)(x + 1)

b)

(5x - 2)(x + 1)

c)

(7x - 1)(x - 4)

d)

(5x - 2)(x - 1)

95.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

96.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

97.

Factor completely: 2x²+22x+60

a)

(2x+10)(x+6)

b)

(x+5)(x+6)

c)

2(x+1)(x+30)

d)

2(x+5)(x+6)

98.

Factor completely: x²-6x+8

a)

(x-2)(x-4)

b)

(x-1)(x-8)

c)

(x+2)(x+4)

d)

(x+1)(x+8)

99.

Factor completely: x²+16x+64

a)

(x+4)(x+16)

b)

(x-8)(x-8)

c)

(x+2)(x+32)

d)

(x+8)(x+8)

100.

Factor completely: x²-13x+40

a)

(x-5)(x-8)

b)

(x+5)(x+8)

c)

(x-4)(x-10)

d)

(x-2)(x-20)

101.

Factor completely: 3x²-8x+4

a)

(3x-4)(x-1)

b)

(3x-2)(x-2)

c)

(x+1)(3x+4)

d)

(x+2)(3x+2)

102.

Find the product.

(x+7)²

a)

x² + 49

b)

x²+ 7x + 7

c)

7x²+ x + 7

d)

x² + 14x + 49

103.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

104.

Multiply:
(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

105.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

106.

Simplify the expression.
(4n⁴-8n+4) - (8n²+4n⁴+1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

107.

(4x²+x) - (x²+2x)

a)

3x²- x

b)

4x²+ 2x

c)

3x² + 3x

d)

3x² + 2x

108.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

109.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

110.

Simplify:

a)

2

b)

4

c)

8

d)

16

111.

Simplify the following expression:

a)

16

b)

32

c)

40

d)

64

112.

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

113.

a)

2^3/5

b)

-2^3/5

c)

2^5/3

d)

8⁵

114.

a)

7³

b)

7

c)

7^3/4

d)

7^4/3

115.

a)

216

b)

6^1/2

c)

6²

d)

6^3/2

116.

Does this graph have a maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

117.

Using the graph of the quadratic function, identify the y-intercept.

a)

(4, -6)

b)

(0, 2)

c)

(.5, 0)

d)

(7.5, 0)

118.

What is the y-intercept of the graph?

a)

(-2,5)

b)

(1,0)

c)

(0,1)

d)

(-3.104, 0)

119.

What is the correct end behavior?

a)

As x → - ∞, f(x) → ∞

As x → ∞, f(x) → ∞

b)

As x → - ∞, f(x) → - ∞

As x → ∞, f(x) → ∞

c)

As x → - ∞, f(x) → ∞

As x → ∞, f(x) → - ∞

d)

As x → - ∞, f(x) → - ∞

As x → ∞, f(x) → - ∞

120.

What are the x-intercepts of the graph?

a)

(2, 0)

b)

(0, -2)

c)

(-1.225, -4.25) and (1.225, -4.25)

d)

(-1.887, 0) and (1.887, 0)

121.

Which ordered pair could represent a y-intercept?

a)

(-1, 0)

b)

(2, 4)

c)

(0,4)

d)

(-2, 4)

122.

True or False:

The x-intercept of a function ALWAYS has a zero as the y-coordinate.

a)

TRUE

b)

FALSE

123.

The lowest point of a graph is called the _________________.

a)

minimum

b)

maximum

c)

x-intercept

d)

y-intercept

124.

The point (-5.25, 0) represents ___________.

a)

a maximum

b)

a minimum

c)

a y-intercept

d)

an x-intercept

125.

What is the correct end behavior?

a)

As x → - ∞, f(x) → ∞

As x → ∞, f(x) → ∞

b)

As x → - ∞, f(x) → - ∞

As x → ∞, f(x) → ∞

c)

As x → - ∞, f(x) → ∞

As x → ∞, f(x) → - ∞

d)

As x → - ∞, f(x) → - ∞

As x → ∞, f(x) → - ∞

126.

What is the y-intercept of the graph?

a)

(2, 0)

b)

(0, -2)

c)

(-1.225, -4.25) and (1.225, -4.25)

d)

(-1.887, 0) and (1.887, 0)

127.

What is the range of the graph?

a)

y ≥ -1.225

b)

y ≥ -4.25

c)

All Real Numbers ℝ

d)

y ≤ -4.25

128.

What is the correct end behavior?

a)

As x → - ∞, f(x) → ∞

As x → ∞, f(x) → ∞

b)

As x → - ∞, f(x) → - ∞

As x → ∞, f(x) → ∞

c)

As x → - ∞, f(x) → ∞

As x → ∞, f(x) → - ∞

d)

As x → - ∞, f(x) → - ∞

As x → ∞, f(x) → - ∞

129.

What is the y-intercept of the graph?

a)

(0,5)

b)

(-5, 0)

c)

(-2, 9)

d)

(1, 0)

130.

What are the x-intercepts?

a)

(0,5) (-2, 9)

b)

(-5, 0) (1, 0)

c)

(-2, 9) (-5, 0)

d)

(1, 0) (0, 5)

131.

Which best describes the increasing and decreasing of the graph?

a)

Decreasing and then increasing

b)

Increasing and then decreasing

c)

Increasing Only

d)

Decreasing Only

132.

What best describes the increasing/decreasing of the graph?

a)

decreasing, increasing

b)

decreasing, increasing, decreasing

c)

increasing, decreasing, increasing

d)

increasing, decreasing

133.

What is the minimum of the graph?

a)

(0,5)

b)

(-5, 0) (1, 0)

c)

(-2, 9)

d)

It does not have one

134.

Determine the interval in which this function is DECREASING.

a)

(-3, ∞)

b)

(-3, ∞)

c)

(-∞, -4)

d)

(-∞, -3)

135.

Determine the interval in which this function is INCREASING.

a)

(-4, ∞)

b)

(-3, ∞)

c)

(∞, -3)

d)

(-∞, -4)

136.

Identify the increasing interval:

a)

(0, 4)

b)

(1, 0) U (1, 4)

c)

(-1, 1)

d)

(-∞, -1) U (1, ∞)

137.

Identify the decreasing interval:

a)

(0, 4)

b)

(1, 0) U (1, 4)

c)

(-1, 1)

d)

(-∞, -1) U (1, ∞)

138.

State the relative maximum y-value.

a)

$5$

b)

$9$

c)

$4$

d)

$1$

139.

List the types of intervals that the graph demonstrates in order.

a)

decreasing, constant, increasing, constant

b)

increasing, decreasing, constant

c)

increasing, constant, increasing, constant

d)

increasing, constant, decreasing, constant

140.

When is the function decreasing?

a)

(30, 55)

b)

(40, 60)

c)

(15, 40)

d)

(60, -40)

141.

Over what interval is this function constant?

a)

(−5, ∞)

b)

(−3, 4)

c)

(4,∞)

d)

(−5)

142.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

2021-2022 Algebra 1 Winter Exam Review

Total questions: 142

Worksheet time: 8hrs 7mins

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