Free Printable Algebra 1 Review

1.

Simplify

a)

9

b)

5√2 + 2

c)

10√2

d)

2√2 + 3√30

2.

Solve for x:

$4(2x-5)=7(2x+4)$

a)

x = 8

b)

x = -8

c)

x = -1.5

d)

x = 1.5

3.

Solve for y:

$4x+2y=16$

a)

$y=-4x+16$

b)

$y=-2x+8$

c)

$y=\frac{1}{2}x+4$

d)

$y=-2x+8$

4.

Solve for p.

HINT: SIMPLIFY first before you factor!!! :)

a)

A

b)

B

c)

C

d)

D

5.

$(x-7)(x+7)$

a)

$x^2+14x-49$

b)

$x^2-14x-49$

c)

$x^2-49$

d)

$x^2+49$

6.

-5x⁶(3x² - 12x + 30)

a)

-15x⁸+ 60x⁷- 150x⁶

b)

15x⁸- 60x⁷- 150x⁶

c)

8x⁶- 17x + 35

d)

-8x⁶+ 17x - 35x²

7.

Which of the following graphs best represents the solution to the system of linear equations shown below?

HINT: Change each equation into slope-intercept form first!

a)

A

b)

B

c)

C

d)

D

8.

Which of the following is the solution for this system of linear equations?

a)

No Solution

b)

( -3, 4 )

c)

( 1, -2 )

d)

( 2, 1 )

9.

Some of the values for two linear equations are shown in the tables below.

a)

( -2, 4 )

b)

( -2, -4 )

c)

( -6, 10 )

d)

(10, 2 )

10.

A coffee shop sells donuts for $2 and muffins for $3. On a very cold morning, the shop sold 10 more donuts than muffins and made $250. Which system of equations could be used to find the number of donuts, d, and muffins, m, that the shop sold that day?

a)

A

b)

B

c)

C

d)

D

11.

Which graph best represents the solution set of

−4x ≤ 6y − 54?

HINT: Write the linear inequality into slope-intercept form first. Be careful!!!

a)

A

b)

B

c)

C

d)

D

12.

What is the solution set for −4x + 10 ≥ 5x + 55?

a)

F

b)

G

c)

H

d)

J

13.

Which graph best represents the solution set of

$y\ ≤-4x$

a)

A

b)

B

c)

C

d)

D

14.

Which of the following is equivalent to
6x + 2y = 28

a)

y = 3x + 14

b)

y = -3x + 14

c)

y = 3x - 14

d)

y = -3x - 14

15.

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.
3x - 8 = 3(x - 4) + 1

a)

one

b)

no solutions

c)

infinite solutions

16.

What is the domain of the graph?

a)

-7 ≤ x < 5

b)

-3 ≤ x < 1

c)

-3 ≤ y < 1

d)

-7 ≤ y < 5

17.

What is the range of the graph?

a)

-7 ≤ x < 5

b)

-3 ≤ x < 1

c)

-3 ≤ y < 1

d)

-7 ≤ y < 5

18.

Is this a function?

a)

Function

b)

Not a Function

19.

a)

Function

b)

Not a Function

20.

For the function f(x) = -3x + 3 find f(0).

a)

0

b)

-3

c)

3

d)

-1

21.

Simplify. (x) (x⁵y) (y³)

a)

x⁵y³

b)

x⁶y⁴

c)

x⁶y³

d)

x⁵y⁴

22.

Simplify. (2x) (3x³y) (y³)

a)

6x⁴y³

b)

6x⁴y⁴

c)

5x⁴y⁴

d)

5x³y³

23.

(6x⁹y⁵)²

a)

6x¹⁸y¹⁰

b)

36x¹¹y⁷

c)

6x¹¹y⁷

d)

36x¹⁸y¹⁰

24.

Find the area of a rectangle that has a length of (3x - 1) and (2x + 5)

a)

6x²+ 17x + 5

b)

6x² + 13x + 5

c)

6x²+ 17x - 5

d)

6x²+ 13x - 5

25.

What are the zeroes for the quadratic function
f(x) = x² + 2x - 15?

a)

x = 5 and x = -3

b)

x = -5 and x = 3

c)

x = 5 and x = 3

d)

x = -5 and x = -3

26.

For what value of c will the graph of k be 9 units above the graph of g?

a)

9

b)

-3

c)

3

d)

21

27.

Based on the graph, what is the width in feet of the porch with the greatest area?

a)

175 ft

b)

50 ft

c)

25 ft

d)

350 ft

28.

In the equation y=mx+b, what does the m represent?

a)

slope

b)

y-intercept

c)

x-intercept

29.

Which line below would be parallel to y=2x + 3?

a)

$y=2x-7$

b)

$y=-2x+3$

c)

$y=\frac{1}{2}x+5$

d)

$y=-\frac{1}{2}x+2$

e)

None of these

30.

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

31.

Simplify:

√48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

32.

Simplify:

4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

33.

What is the x-intercept of the line pictured?

a)

(3,0)

b)

(0,-5)

c)

(0,3)

d)

(-5,0)

34.

Which compound inequality is represented by the number line shown?

a)

-6 < x < 0

b)

-6 < x ≤ 0

c)

-6 ≤ x ≤ 0

d)

-6 ≤ x < 0

35.

Which inequality is pictured?

a)

$y\ ≤\ \frac{4}{3}x-4$

b)

$y\ <\frac{4}{3}x-4$

c)

$y\ <\ \frac{3}{4}x-4$

d)

$y\ \le\ \frac{3}{4}x-4$

36.

Which relation is a function?

a)

A

b)

B

c)

C

d)

D

37.

What is the range of the graph?

a)

All real numbers

b)

y≤0

c)

y ≥ 0

d)

x ≥ 0

38.

Simplify: √28

a)

7√2

b)

7√4

c)

4√7

d)

2√7

39.

What is the equation that would represent all the ordered pairs below?

(-3, -14), (-1, -4), (0, 1), (2, 11), (5, 26)

a)

y = 5x + 1

b)

y = 3x - 5

c)

y = 4x

d)

y = x + 1

40.

What is the solution to the following inequality?

-4x + 10 < 6x - 10

a)

x > 2

b)

x < 2

c)

x > 10

d)

x < 10

41.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(-10, 20)

c)

(3, 5)

d)

(0, -2)

42.

Which is a zero of the graph?

a)

0

b)

-1

c)

1.5

d)

-3

43.

Which function is represented by the following equation.

y = 3^x

a)

Linear

b)

Quadratic

c)

Exponential

d)

None of these

e)

Absolute Value

44.

Where is the vertex of this quadratic?
$f\left(x\right)\ =\ (x-3)^2$

a)

(3, 0)

b)

(-3, 0)

c)

(0, 3)

d)

(0, -3)

45.

Select all the TRUE statements.

a)

$f\left(-2\right)\ =\ -5$

b)

$f\left(2\right)\ =\ 0$

c)

$f\left(3\right)\ =\ 3$

d)

$f\left(0\right)\ =\ -2$

e)

$f\left(-5\right)\ =\ -2$

46.

Find $f\left(10\right)$ :

$f(x)=-2x+13$

a)

-7

b)

1

c)

-8

d)

7

47.

In which step does a mistake first appear?

a)

Step 1

b)

Step 2

c)

Step 3

d)

Step 4

48.

Which inequality is equivalent to 7x - 2y > 8 ?

a)

b)

c)

d)

49.

What value of x makes the equation true?

a)

3

b)

5

c)

$\frac{1}{3}$

d)

$\frac{1}{5}$

50.

Which graph represents $-3x+5y=-15$ ?

a)

b)

c)

d)

51.

What is the 25th term of the sequence 6, 2, -2, -6, ...?

a)

-98

b)

-94

c)

-90

d)

-86

52.

What is the solution to the system?

a)

(3,1)

b)

(1,3)

c)

(-1,3)

53.

What type of function is $f(x)=2\left(\frac{1}{7}\right)^x$

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

Quadratic, upward facing

e)

Quadratic, downward facing

54.

What is the slope between the two points?

(2, 8) (3, 12)

a)

0

b)

-1

c)

undefined

d)

4

55.

Select the systems of equations that would have infinitely many solutions.

a)

$y=4x-3$ and $y=4x+2$

b)

$y=3x-1$ and $2y=6x-2$

c)

$y=\frac{1}{2}x+3$ and $2x+y=-1$

d)

$4x+y=7$ and $y=-4x+7$

e)

$y=6x-1$ and $y=\frac{1}{6}x$

56.

What is the shape of this data?

a)

Skewed Left

b)

Skewed Right

c)

Normal Distribution

57.

What percentage of the data is between 90 and 140?

a)

25 %

b)

50%

c)

75%

d)

100%

58.

What are the x-intercepts of this function?

$f\left(x\right)\ =\ \left(x-3\right)\left(x+7\right)\left(x-2\right)$

a)

-7

b)

3

c)

-3

d)

-2

e)

2

59.

Factor completely:
x² - 121

a)

(x + 11)(x - 11)

b)

(x + 11)(x +11)

c)

(x - 11)(x - 11)

d)

x(x - 121)

60.

Is this a function or not a function?

a)

Function

b)

Not a Function

61.

^{What is the x- intercept of the line?}

a)

x = 1

b)

x = 2

c)

x = -1

d)

x = -2

62.

What is the equation of this quadratic graph?

a)

y = (x + 4)²

b)

y = (x - 4)²

c)

y = x²

d)

y = x² - 4

63.

What is the equation of the graph?

a)

y = x²(quadratic)

b)

y = √x (square root)

c)

y = x³ (cubic)

d)

y = |x| (absolute value)

64.

What is the equation of g?

a)

x = 4

b)

y = x + 4

c)

y = 4x

d)

y = 4

65.

Solve by factoring: x² + 11x + 30 = 0

a)

x = 5,6

b)

x = 10, 3

c)

x = -5, -6

d)

x = -10, -3

66.

What equation matches the graph?

a)

$y=\sqrt{x+4}$

b)

$y=\sqrt{x-4}$

c)

$y=\sqrt{x}-4$

d)

$y=\sqrt{x}+4$

67.

Which function has the equation y = (x + 3)³?

a)

Red (C)

b)

Blue (B)

c)

Green (A)

d)

none of these match the equation

68.

Solve by factoring:

x²- 14x - 32 = 0

a)

2, -16

b)

-2, 16

c)

4, -8

d)

-4, 8

69.

What is the domain of this relation?

a)

{-4, -1, 1, 3, 4}

b)

{-3, -2, -1, 1, 2}

c)

All real numbers

d)

-4 ≤ x ≤ 4

70.

Solve:

2x + 3 = 2x + 3

a)

x = 0

b)

x = 1

c)

No solution

d)

Infinitely Many Solutions

71.

find g(2):
g(x) = 5 - 3x

a)

-11

b)

-1

c)

1

d)

11

72.

The graph of a quadratic function is shown on the grid. Which equations best represents the axis of symmetry?

a)

y = 6

b)

x = 2

c)

y = 4

d)

x = 0

73.

If p(x) = 5(x² + 1) + 16, what is the value of p(11)?

a)

690

b)

736

c)

622

d)

626

74.

Which quadratic function has a range:

$y\ge-6$

a)

b)

c)

d)

75.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

76.

Which transformation transforms the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a vertical translation 4 units up

b)

a vertical translation 4 units down

c)

a horizontal translation 4 units to the left

d)

a horizontal translation 4 units to the right

77.

What is the x and y intercept for the following equation ?
4x - 10y = 20

a)

x - int = 4
y-int = -10

b)

x-int = 5
y-int = 2

c)

x - int = 5
y int = -2

d)

x -int = 4
y -int = -10

78.

Solve for x.
x² - 14x + 24 = 0

a)

x = 2 or x = 12

b)

x = -2 or x = -12

c)

x = 4 or x = 6

d)

x = 3 or x = 8

79.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

80.

What kind of sequence is the pattern 15, 17, 20, 24, 29, ...?

a)

Arithmetic

b)

Geometric

c)

Neither

81.

What kind of sequence is the pattern 400, 200, 100, 50, 25, ...?

a)

Arithmetic

b)

Geometric

c)

Neither

82.

Which of the following is NOT an arithmetic sequence?

a)

1/2, 1, 3/2, 2

b)

11, 14, 17, 20

c)

2, 4, 8, 16

d)

5, 2, -1, -4

83.

Identify the common difference of the sequence below:

-2.3, -1.1, 0.1, 1.3,...

a)

-1.2

b)

1.3

c)

1.2

d)

-1.3

84.

Write the explicit formula for the sequence shown below.

3, -3, -9, -15...

a)

$a_n=3+6(n-1)$

b)

$a_n=3-6(n-1)$

c)

$a_n=6+3(n-1)$

d)

$a_n=6-3(n-1)$

85.

Write the explicit formula for the sequence shown below.
1, 6, 11, 16...

a)

$a_n=1+5(n-1)$

b)

$a_n=1-5(n-1)$

c)

$a_n=5+1(n-1)$

d)

$a_n=5-1(n-1)$

86.

What is the 20^thterm of the arithmetic sequence shown below.

7, 4, 1,...

a)

-49

b)

50

c)

-50

d)

-51

87.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

88.

a)

A

b)

B

c)

C

d)

D

89.

Simplify:

√45

a)

3√5

b)

5√3

c)

9√5

d)

5√9

90.

Simplify:

√72

a)

7√9

b)

4√6

c)

6√2

d)

3√4

Algebra 1 Review

Total questions: 90

Worksheet time: 7hrs 41mins

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