Free Printable Alg 1, Chapter 10 Review

1.

Find the product:
(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

2.

Find the product:
(3r-4)(7r-5)

a)

21r²-43r+20

b)

21r+43r²+9

c)

7r+12r

d)

r+2r

3.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

4.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

5.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

6.

Find the difference.
(7p + 4p³ - 8) - (-3p²+ 2 - 9p)

a)

-3p²+ 4p³ -15 + 9

b)

3p³ + 4p² - p + 3

c)

4p³ -3p² +16p -10

d)

4p³ +3p² + 16p + 10

7.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

8.

Simplify each expression.
(6x + 4x⁴ - 3x²) + (7x⁴ + 5x² + 8x)

a)

11x⁴ + 2x² + 14x

b)

16x⁴ + x² + 14x

c)

11x⁴ + x² + 14x

d)

11x⁴ + 2x² + 10x

9.

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

a)

4b⁴ - 2b³ + 7

b)

5b⁴ - 2b³ + 4

c)

b⁴ - 2b³ + 7

d)

5b⁴ - 2b³ + 7

10.

Simplify:
(x² - 3x - 2) + (5x² + 10x - 5)

a)

5x⁴ - 30x² + 10

b)

6x² + 7x - 7

c)

6x⁴+ 7x² - 7

d)

4x² + 13x + 7

11.

Which of these are like terms in the following expression:
3x + 7 - 9x + 24y + 2x²

a)

7, 24y

b)

3x, 9x

c)

3x, -9x

d)

3x, -9x, 2x²

12.

Simplify by combining like terms:
5a + 2b - 3a + 4

a)

8a + 2b + 4

b)

2a + 2b + 4

c)

8ab

d)

4ab + 4

13.

Simplify the expression: 7v + 2 + 12 + 2v

a)

23

b)

23v

c)

9 + 14v

d)

9v + 14

14.

Simplify the following expression:
-10x + 15 - 3x + 2

a)

13x² + 17

b)

-13x² + 13

c)

-13x + 17

d)

-7x + 17

15.

Simplify the following expression:
-6x + 4(-x - 3)

a)

-2x - 12

b)

10x + 12

c)

-10x - 12

d)

-2x + 12

16.

Simplify the following expression:
19 - ( 3 - 5b)

a)

16 + 5b

b)

21 + 5b

c)

16 - 5b

d)

21 - 5b

17.

Simplify the following expression:
-8 (5b + 2) -7 (b - 5)

a)

-33b + 19

b)

-47b² + 21

c)

33b - 19

d)

-47b -19

18.

Find the product:
(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

19.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

20.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

21.

Simplify:
(3x - 5) ( 4x² - 2x - 3)

a)

12x³ - 26x² - 25x + 15

b)

12x³ - 20x² - 5x + 15

c)

12x³ - 20x² - 6x + 15

d)

12x³ - 26x² + x + 15

22.

Multiply the polynomial
4(y-7) + 5y

a)

9y - 7

b)

9y - 28

c)

20y - 28

d)

9y + 28

23.

Multiply the Polynomials
2a²(3a - 5)-6a(8a² - 2a + 4)

a)

-42a³ + 2a²- 24a

b)

6a³- 10a²

c)

-48a³+ 12a²- 24a

d)

-42a³ - 22a² + 24a

24.

What are the inverse points for the coordinates:

(3, 0) , (2, -4), (5, 5) and (-6,8)

a)

(3,0) , (2, -4) , (5,5) , (6,8)

b)

(0,3) , (-4,2) , (5,5) , (8,-6)

c)

(3,2), (0, -4), (5, -6), (5,8)

25.

Are these inverse functions?

a)

yes

b)

no

26.

Are these functions inverses?

a)

No

b)

Yes

c)

No way to tell

27.

Are these functions inverses?

a)

Yes

b)

No

28.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

29.

Which graph represents the functions f(x) and f^-1(x)?

a)

b)

c)

d)

30.

Find the inverse of $f(x)=10+7x$

a)

$f^{-1}(x)=\frac{x-7}{10}$

b)

$f^{-1}(x)=\frac{x-10}{7}$

c)

$f^{-1}(x)=\frac{1}{10+7x}$

31.

Find the inverse of $f(x)=4x$

a)

$f^{-1}(x)=\frac{x}{4}$

b)

$f^{-1}(x)=4$

c)

$f^{-1}\left(x\right)=\frac{1}{4}$

32.

Find the inverse of $f(x)=\frac{x-5}{3}$

a)

$f^{-1}(x)=\frac{3}{5}+x$

b)

$f^{-1}(x)=3x+5$

c)

$f^{-1}(x)=5x+3$

33.

Find the inverse of $f(x)=2x+1$

a)

$f^{-1}(x)=2x$

b)

$f^{-1}(x)=\frac{x-1}{2}$

c)

$f^{-1}(x)=2$

34.

Find the inverse of $f(x)=3x+2$

a)

$f^{-1}(x)=3x-2$

b)

$f^{-1}(x)=2+3x$

c)

$f^{-1}(x)=\frac{x-2}{3}$

35.

The inverse of $f(x)=8x+30$ is $f^{-1}(x)=\frac{8}{30}$ .

a)

True

b)

False

36.

The inverse of $f(x)=x+30$ is $f^{-1}(x)=x-30$ .

a)

True

b)

False

c)

I have no idea how to do this.

37.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

38.

Find the inverse of $f\left(x\right)=\frac{1}{4}x-7$

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x+28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x+28

39.

$f\left(x\right)=\frac{x-2}{6}$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-6}{2}$

b)

$6x+2$

c)

$2x+6$

d)

$6\left(x+2\right)$

40.

Find the correct order to find the inverse of f(x)= 2x-5

a)

y=2x-5

b)

2y-5=x

c)

2y= x+5

d)

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

e)

$f^{-1}\left(x\right)=\frac{1}{2}x+\frac{5}{2}$

1)

2)

3)

4)

5)

41.

Find the inverse of $f(x)=10+7x$

a)

$f^{-1}(x)=\frac{x-7}{10}$

b)

$f^{-1}(x)=\frac{x-10}{7}$

c)

$f^{-1}(x)=\frac{1}{10+7x}$

42.

Find the inverse
f(x)= x⁴- 2

a)

∜(x+2)

b)

(x+2)⁴

c)

-1+2x⁴

d)

∜2x

43.

Find the inverse
f(x)=2x-2

a)

f^-1(x)=1/2x+1

b)

f^-1(x)=-2-1/2x

c)

f^-1(x)=-7/3x-20/3

d)

2-2/5x

44.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = - 4x - 3

45.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 1/4x + 7/4

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

46.

Find the inverse of $f(x)=4x$

a)

$f^{-1}(x)=\frac{x}{4}$

b)

$f^{-1}(x)=4$

c)

$f^{-1}\left(x\right)=\frac{1}{4}$

47.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

48.

Which is f ^-1(x)?

a)

f^-1(x) = 3x + 5

b)

f^-1(x) = 3x - 5

c)

f^-1(x) = 3x - 15

d)

f^-1(x) = 3x + 15

49.

$f\left(x\right)=3x$
Find $f^{-1}\left(x\right)$

a)

$\frac{x}{3}$

b)

$\frac{3}{x}$

c)

$0.3x$

d)

$x\times3$

50.

$f\left(x\right)=\frac{8x-3}{5}$
Find $f^{-1}\left(x\right)$

a)

$5\left(8x+3\right)$

b)

$\frac{5x}{8}+3$

c)

$\frac{5\left(x+3\right)}{8}$

d)

$\frac{5x+3}{8}$

51.

Is the inverse function found correctly?

a)

yes

b)

no

52.

Find the inverse of the function
f(x) = 3x − 5

a)

f^-1(x)=3x +5

b)

f^-1(x)=(x+5)/3

c)

f^-1(x)=3y-5

d)

f^-1(x)=3y+5

53.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

54.

a)

Inverse Functions

b)

Not Inverse Functions

55.

a)

Inverse Functions

b)

Not Inverse Functions

56.

a)

Inverse Functions

b)

Not Inverse Functions

57.

Identify the domain of the following relation:

a)

-6, 14, 2, 28

b)

(-6,14), (0,32), (2,38), (4,44)

c)

-6, 0, 2, 4

d)

14, 32, 38, 44

58.

Janice is working as a babysitter for the Harold Family. They plan to leave for their date at 7:00 pm and be back by 12:00 am. If the equation f(x) = 15x + 20 models the amount that Janice will earn, where x is the number of hours she works, and f(x) is the total money she earns, what is an appropriate domain?

a)

any value between 0 and 5

b)

any value between 15 and 20

c)

any value between -1 and 1

d)

any value greater than 0

59.

Janice is working as a babysitter for the Harold Family. They plan to leave for their date at 7:00 pm and be back by 12:00 am. If the equation f(x) = 15x + 20 models the amount that Janice will earn, where x is the number of hours she works, and f(x) is the total money she earns, what is an appropriate range?

a)

any value between 0 and 20

b)

any value between 0 and 125

c)

any value between 0 and 95

d)

any value greater than 0

60.

Identify the range of the following function when given the domain { 2, 3, 10}:
y = 4x - 12

a)

4, 12, 20

b)

-20, 0, 28

c)

-4, 0, 28

d)

8, 12, 40

61.

What is the range of the following graph?

a)

-5, -1, 0 , 1, 5

b)

-4, -2, 0, 3, 6

c)

(-4, 1) ( 6, 0)

d)

(6, 0)

62.

The lake has a depth of 45 feet below sea level. A scuba diver is taking a dive. His depth under water can be modeled by
D(x) = -4x - 2, where x represents the minutes. The diver starts at a depth of 2 feet and travels deeper at a speed of 4 feet every minute. What is the appropriate range for this function?

a)

from 0 to 2

b)

from -2 to -45

c)

from 2 to 45

d)

it can not be determined

63.

What is the range of the following relation:
(9, -2) (4, 3) ( 8, 10) ( -4, 8)

a)

-4, 4, 8, 9

b)

-2, 3, 8, 10

c)

(9, -2) ( 4, 3)

d)

(8, 10) (-4, 8)

64.

Which of the following best describes the domain of the relation graphed?

a)

all real numbers

b)

integers from -2 to 2

c)

rational numbers

d)

real numbers from -1 to 11

65.

The school is selling raffle tickets as a fundraiser. The profit from the tickets can be modeled by the equation P(x) = 3x - 35, where x is the number of tickets sold. Which best describes the possible domain?

a)

all real numbers greater than 0

b)

all whole numbers

c)

any rational number greater than 0

d)

all integers

66.

What is the range of the following graph?

a)

all real numbers

b)

all integers

c)

any real number greater than zero

d)

it can not be determined

67.

the set of all possible y-values

a)

Domain

b)

Range

c)

Interval Notation

d)

Inequality Notation

68.

the set of all possible x-values

a)

Domain

b)

Range

c)

Interval Notation

d)

Inequality Notation

69.

When identifying domain and range what symbol(s) is used when the value is not included?

a)

( )

b)

[ ]

c)

≤ ≥

d)

{ }

70.

What is the range in inequality notation?

a)

( -4 , 4 )

b)

[ 1 , -3 )

c)

-4 < x < 4

d)

1 ≥ y > -3

71.

What is the domain in inequality notation?

a)

( -4 , 4 )

b)

[ 1 , -3 )

c)

-4 < x < 4

d)

1 ≥ y > -3

72.

What is the range in inequality notation?

a)

[ -2 , 2 )

b)

( 5 , 1 ]

c)

-2 ≤ x < 2

d)

5 > y ≥ 1

73.

What is the domain in inequality notation?

a)

[ -2 , 2 )

b)

( 5 , 1 ]

c)

-2 ≤ x < 2

d)

5 > y ≥ 1

74.

What is the range in inequality notation?

a)

( -5 , 5 )

b)

[-2 , -4 )

c)

-5 < x < 5

d)

-2 ≥ y > -4

75.

What is the domain in inequality notation?

a)

( -5 , 5 )

b)

[-2 , -4 )

c)

-5 < x < 5

d)

-2 ≥ y > -4

76.

What is the range in inequality notation?

a)

[ -2 , 2 ]

b)

[ 4 , -4 ]

c)

-2 ≤ x ≤ 2

d)

4 ≥ y ≥ -4

77.

What is the domain in inequality notation?

a)

[ -2 , 2 ]

b)

[ 4 , -4 ]

c)

-2 ≤ x ≤ 2

d)

4 ≥ y ≥ -4

78.

What is the Domain?

a)

-3 < x ≤ 3

b)

-4 ≤ x < 5

c)

-4 ≤ y ≤ 5

d)

-3 < y ≤ 3

79.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

80.

What is the Domain of this linear function?

a)

-3 < x ≤ 5

b)

x = -1

c)

5 < x ≤ -3

d)

-2 < x ≤ 6

81.

What is the range?

a)

{-3, -1, 2, 4}

b)

{0, 4, 7}

c)

{0, 4, 4, 7}

d)

{7, 4, 0}

82.

Identify the domain of the following relation:

a)

{-6, 14, 2, 28}

b)

{(-6,14), (0,32), (2,38), (4,44)}

c)

{-6, 0, 2, 4}

d)

{14, 32, 38, 44}

83.

What is the range of the following relation:
(9, -2) (4, 3) ( 8, 10) ( -4, 8)

a)

{-4, 4, 8, 9}

b)

{-2, 3, 8, 10}

c)

{(9, -2) ( 4, 3)}

d)

{(8, 10) (-4, 8)}

84.

a)

{1, 2, 3, 4, 5}

b)

{-1, 1, 2, 3}

c)

{1, 2, 3, 5}

d)

[1, 5]

85.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D: {-4, 0, 1, 2}
R:{-4, -3, 1}

c)

D: {0, 1, 2, 3, 4}
R:{1, -3, -4}

d)

D: {0, 1, 2, -4}
R: {1, -3, -4, 1}

86.

Does this graph have a maximum or a minimum?

a)

Maximum

b)

Minimum

87.

Does this question have a maximum or a minimum?

a)

Maximum

b)

Minimum

88.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

89.

Which equation is in standard form?

a)

y=a(x-h)²+k

b)

y=ax²+bx+c

90.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

91.

What are the green points called?

a)

axis of symmetry

b)

vertex

c)

y-intercept

d)

x-intercepts

92.

How many solutions does the parabola have?

a)

none

b)

one

c)

two

93.

True or false: The y-intercept and vertex are the same

a)

True they are both at (0,-4)

b)

True they are both at (-2,0)

c)

False the y-intercept is at (-2,0)

d)

False the y-intercept is at (2,0)

94.

What are the x-intercepts (solutions)?

a)

(-2,0) and (2,0)

b)

(0,-4)

c)

(-2,-4) and (2,-4)

95.

What kind of Function is this?

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

96.

What type of Function is this?

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

97.

DOMAIN is found by reading the ends of a graph from ___ to ___.

a)

Right to left

b)

Left to right

c)

Bottom to top

d)

Top to bottom

98.

RANGE is found by reading the ends of a graph from ___ to ___.

a)

Right to left

b)

Left to right

c)

Bottom to top

d)

Top to bottom

99.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

100.

What is the common ratio of this sequence ? 5, 25, 125, ...

a)

4

b)

2

c)

5

d)

6

101.

Determine if the function graphed has a maximum or a minimum value and identify that value.

a)

maximum at -1

b)

minimum at -1

c)

maximum at 4

d)

minimum at 4

102.

What is the arrow pointing at? How can you use this value to determine the minimum/maximum values?

a)

The arrow is pointing at the y-intercept. The y value of this point is equivalent to the maximum/minimum

b)

The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum

c)

The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum

d)

The arrow is pointing at the vertex. The y value is equivalent to the minimum/maximum

103.

What's the axis of symmetry of y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

104.

Does
y = -4x²
have a maximum or minimum value?

a)

maximum

b)

minimum

105.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

106.

Does the equation have a max or min?
y = 2x² + 7x + 5

a)

max

b)

min

107.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

108.

The a value of this graph is

a)

negative

b)

positive

c)

impossible to tell

d)

0

109.

What is the minimum value of the quadratic function?

a)

-3

b)

-1

c)

All real numbers

d)

1

110.

Does this graph in the back have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

111.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

112.

What is the y intercept for the equation:
y = -8x² + 3x - 7

a)

(0, -8)

b)

(0, 3)

c)

(0, 7)

d)

(0, -7)

113.

Which of the following functions has a minimum value of -4?

a)

b)

c)

d)

Alg 1, Chapter 10 Review

Total questions: 113

Worksheet time: 4hrs 9mins

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