Free Printable Pre-Calculus 1st Semester Exam Review

1.

Factor

n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

2.

Factor Completely:

x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

3.

Factor by Grouping:

x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

4.

Factor the Trinomial:

5x² + 17x + 6

a)

(5x + 3)(x + 2)

b)

(5x + 2)(x + 3)

c)

(5x + 1)(x + 6)

d)

(5x + 6)(x + 1)

5.

Which is a zero of the graph?

a)

0

b)

-1

c)

1.5

d)

-3

6.

What are the zeros of x²+9x+14

a)

2, 7

b)

-2, -7

c)

2, -7

d)

-2, 7

7.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

8.

Find the zeroes of the quadratic equation

d² - 10d + 25 = 0

a)

d = -5 and d = +5

b)

d = 15 and d = -10

c)

d = -5 and d = 20

d)

d = 5

9.

Solve for the values of x:

(x - 5)(x - 1) = 0

a)

(5, 0) or (1, 0)

b)

(-5, 0) or (-1, 0)

c)

(0, -5) or (0, -1)

d)

(0, 5) or (0, 1)

10.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

11.

What is the slope?

a)

-1/3

b)

-3

c)

-4

d)

5

12.

Find the slope of the line that passes through
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

13.

Which graph represents the equation $y=4x-1$

a)

b)

c)

d)

14.

Write a linear equation in slope-intercept form give the point and slope. (-6, -11); slope = 1/2

a)

$y+6=\frac{1}{2}\left(x+6\right)$

b)

$x-2y=16$

c)

$y=\frac{1}{2}x-8$

d)

$y=\frac{1}{2}x-11$

15.

Write an equation in slope-intercept form given the point and slope: (-4, -7); slope = 1

a)

$y+7=x+4$

b)

$y=x-3$

c)

$y=x-7$

d)

$x-y=3$

16.

What slope is parallel to:
m = 3/4

a)

4/3

b)

3/4

c)

-3/4

d)

-4/3

17.

y = 6x + 2
y = -6x + 2
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

18.

Line a passes through (2, 4) and (4, 7)

Line b passes through (-5, 3) and (-3, 6)

Lines a and b are ?

a)

Parallel

b)

Perpendicular

c)

Neither

19.

Select ALL of the lines that are PERPENDICULAR to y = 3/4x + 9

a)

y = 3/4x - 3

b)

y = -3/4x + 9

c)

y = -4/3x + 8

d)

3y = -4x + 5

e)

4y = -3x + 7

20.

Write the equation of a line PERPENDICULAR to the line y = 3x + 2 that passes through the point (9, -2)

a)

y = -1/3x - 5

b)

y = 3x-29

c)

y = 1/3x -5

d)

y = -1/3x +1

21.

Find the midpoint of (-3, 2) and (5, -2).

a)

(1, 0)

b)

(0, 1)

c)

(-1, 0)

d)

(0, -1)

22.

Find the distance between the points (-3, 8) and (1, 5).

(a)

23.

$\left(x-h\right)^2+\left(y-k\right)^2=r^2$ is the form of what graph?

a)

quadratic (parabola)

b)

circle

c)

linear

d)

sin wave

24.

In the form of the circle, (h, k) is the (a) of the circle.

25.

What is the radius of the circle?
$x^2+y^2=49$

(a)

26.

What is the radius of the circle which has (0, 0) and (0, 6) on the circle?

(a)

27.

$y=2x^2-8$ is an example of a ___________________ function.

a)

quadratic

b)

circle

c)

linear

d)

sin

28.

What kind of function is shown in the graphs above?

a)

quadratic

b)

circle

c)

absolute value

d)

sin

29.

Which of the following points is a solution to the function: $y=3x^2-2x$ ?

a)

(2, 8)

b)

(0, -1)

c)

(1, -1)

d)

(8, 2)

30.

Is point (0, 2) a solution of the function:
$y=\sqrt{x+4}$ ?

a)

Yes

b)

No

31.

Find the distance between (4, 5) and (7, 14)

a)

$3\sqrt{10}$

b)

$\sqrt{90}$

c)

$3\sqrt{30}$

d)

$15$

32.

Find the distance between (-3, 8) and (2, -2)

a)

$\sqrt{125}$

b)

$5\sqrt{5}$

c)

$5\sqrt{25}$

d)

$25$

33.

Find the distance between (-3, 8) and (2, -4)

a)

13

b)

$\sqrt{169}$

c)

$13\sqrt{3}$

d)

$\sqrt{13}$

34.

Given a triangle with leg measurements of 9 and 5, what is the length of the hypotenuse?

a)

$\sqrt{106}$

b)

$2\sqrt{53}$

c)

$106$

d)

$14$

35.

Given a right triangle with leg measurements of 6 and 3, what is the length of the hypotenuse?

a)

$\sqrt{45}$

b)

$3\sqrt{5}$

c)

$5\sqrt{3}$

d)

$15$

36.

Given a right triangle with leg measurement 12 and a hypotenuse measurement of 13, what is the length of the other leg?

a)

5

b)

$\sqrt{12}$

c)

$13$

d)

$\sqrt{196}$

37.

Given an isosceles triangle with leg measurements 12 and 9, what is the length of the hypotenuse?

a)

$\sqrt{225}$

b)

$15$

c)

$5\sqrt{5}$

d)

Uhh... There isn't a hypotenuse?

38.

(2, 3) is in Quadrant...

a)

I

b)

II

c)

III

d)

IV

39.

(0, 0) is called the...

a)

origin

b)

center

c)

null

d)

empty

40.

Find the midpoint of (0, 2) and (8, 8)

a)

(4, 5)

b)

(5, 4)

c)

(-5, 4)

d)

(-4, -5)

41.

a)

Function

b)

Not a Function

42.

If f(x)=2x+25, find f(5).

a)

f(5) = 60

b)

f(5) = 40

c)

f(5) = -15

d)

f(5) = 35

43.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

44.

Solve the equation 4x + 5 = 3x + 9

a)

2

b)

4

c)

7

d)

14

45.

The point where the line crosses the y-axis is called the:

a)

origin

b)

x-intercept

c)

y-intercept

d)

slope

46.

Which graph represents the equation $y=4x-1$

a)

b)

c)

d)

47.

Give the equation for the graph

a)

y = 5x - 3

b)

y = 4x + 2

c)

y =-2x + 5

d)

y = - 2x + 4

48.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

49.

Would a triangle with these side lengths be a right triangle?
4, 5, 6

a)

Yes

b)

No

50.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

51.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

52.

True or False:
3 is a range value in the relation graphed.

a)

True

b)

False

53.

What is the RANGE?

a)

(-∞, ∞)

b)

(-2, ∞)

c)

[-2, ∞)

d)

(-∞, 0) U (0, ∞)

54.

What is the domain of the graph?

a)

[-7, 5)

b)

(-7, 5]

c)

[-3, 1)

d)

(-3, 1]

55.

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)

56.

Which is the interval of decrease in the function?

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,\ -1\right)$

c)

$\left(-\infty,\ 4\right)$

d)

$\left(4,\ \infty\right)$

e)

$\left(-1,\ \infty\right)$

57.

Which is an interval of increase in the function?

a)

$\left(-\infty,\ -3\right)$

b)

$\left(-3,\ 4\right)$

c)

$\left(-11,\ -6\right)$

d)

$\left(-6,\ -3\right)$

58.

Which best describes point R?

a)

Relative Minimum

b)

Relative Maximum

c)

Absolute Minimum

d)

Absolute Maximum

59.

Find the zero of the following function.

f\left(x\right)\ =\ 2x^2\ -\ 7x\ -\ 30

a)

$\frac{-5}{2}$ , 6

b)

$\frac{-5}{2}$ , -6

c)

$\frac{5}{2}$ , 6

d)

$\frac{5}{2}$ , -6

60.

Find the zero of the following function.

f\left(x\right)\ =\ x^2\ -\ 2x\ -80

a)

8, 10

b)

8, -10

c)

-8, 10

d)

-8, -10

61.

What is the ordered pair for point K?

a)

(-3, -3)

b)

(3, -3)

c)

(-4, -4)

d)

(5, 8)

62.

What are the coordinates of Point D?

a)

(-4,2)

b)

(2,-4)

63.

Which letter matches the coordinate (0, -6)?

a)

O

b)

L

c)

i

d)

Z

64.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

65.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

66.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

67.

Find the distance between (-5, -8) and (-1, -16).

a)

8.9

b)

9.8

c)

10.3

d)

11

68.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

69.

What is the midpoint between (3, -1) and (7, -5)

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

70.

What is the midpoint between (-4,4) and (-2,2)?

a)

(3,2)

b)

(-3,3)

c)

(4,5)

d)

(6,7)

71.

Find the midpoint: $\left(3,9\right),\left(-1,-5\right)$

a)

$\left(-1,-2\right)$

b)

$\left(2,7\right)$

c)

$\left(-2,-7\right)$

d)

$\left(1,2\right)$

72.

What rule would apply to the following description? Translate the triangle to the right eight units and up two units?

a)

(x, y) ---> (x + 8, y + 2)

b)

(x, y) ---> (x + 8, y - 2)

c)

(x, y) ---> (x - 8, y + 2)

d)

(x, y) ---> (x - 8, y - 2)

73.

If given the rule (x, y) ----->(x - 4, y - 1), how would you move your points?

a)

Horizontally 4 units and vertically 1 unit

b)

Horizontally -4 units, vertically -1 units

c)

Horizontally -4 units, vertically 1 unit

d)

Horizontally 4 units, vertically -1 unit

74.

A cylinder has a volume of 375π cm³ and has a height of 15 cm. What is the diameter of the cylinder?

a)

5 cm

b)

10 cm

c)

20 cm

d)

25 cm

75.

Sketch the graph of the function

a)

b)

c)

d)

76.

Sketch the graph of each function

a)

b)

c)

d)

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.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

79.

Write the standard equation of the circle with the given center and radius; center (0,0) and radius: 3

a)

x²+y²=3

b)

x²+y²=6

c)

x²+y²=9

80.

What is the domain?

a)

x = 2

b)

−∞ < x < ∞

c)

y = 2

d)

none of these

81.

Graph. y = -4

a)

a

b)

b

c)

c

d)

d

82.

Which graph represents the equation $y=4x-1$

a)

b)

c)

d)

83.

What is the slope of the line?

a)

Zero

b)

Undefined

c)

1

d)

-1

84.

Find the slope of the table.

(a)

85.

Find the equation of the line in slope-intercept form.

a)

y = - 1/4x - 3

b)

y = 1/3x + 3

c)

y = - 1/4x + 2

d)

y = 1/3x -3

86.

Which of these represents point-slope form of a linear equation?

a)

y - y₁ = m(x - x₁)

b)

Ax + By = C

c)

y = mx + b

87.

y = 3x +2
y = 3x - 3
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

88.

Which is the equation of the line that is parallel to the graph of y = 5x + 7 and has a y-intercept at (0, -2)?

a)

y = 5x - 2

b)

y = -2x + 7

c)

y = 5(x - 2)

d)

y = -1/5x - 2

89.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

90.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

91.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

92.

f(x)=4x+5
f(4)=

a)

21

b)

-11

c)

-31

d)

25

93.

f(x)=2x+2

for x = 4

a)

6

b)

-8

c)

10

d)

0

94.

Evaluate f(t)=-2t²+ 1 for f(2)

a)

9

b)

17

c)

-17

d)

-7

95.

State the domain:

a)

(-oo, 4)

b)

(-oo, 2]

c)

[2, oo)

d)

[4, oo)

96.

What is the ordered pair for point K?

a)

(-3, -3)

b)

(3, -3)

c)

(-4, -4)

d)

(5, 8)

97.

Which letter matches the coordinate (0, -6)?

a)

O

b)

L

c)

i

d)

Z

98.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

99.

Find the distance between (-5, -8) and (-1, -16).

a)

8.9

b)

9.8

c)

10.3

d)

11

100.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

101.

What is the midpoint between (3, -1) and (7, -5)

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

102.

What rule would apply to the following description? Translate the triangle to the right eight units and up two units?

a)

(x, y) ---> (x + 8, y + 2)

b)

(x, y) ---> (x + 8, y - 2)

c)

(x, y) ---> (x - 8, y + 2)

d)

(x, y) ---> (x - 8, y - 2)

103.

A cylinder has a volume of 375π cm³ and has a height of 15 cm. What is the diameter of the cylinder?

a)

5 cm

b)

10 cm

c)

20 cm

d)

25 cm

104.

Sketch the graph of the function

a)

b)

c)

d)

105.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

106.

What is the domain?

a)

x = 2

b)

−∞ < x < ∞

c)

y = 2

d)

none of these

107.

Which graph represents the equation $y=4x-1$

a)

b)

c)

d)

108.

What is the slope of the line?

a)

Zero

b)

Undefined

c)

1

d)

-1

109.

Find the equation of the line in slope-intercept form.

a)

y = - 1/4x - 3

b)

y = 1/3x + 3

c)

y = - 1/4x + 2

d)

y = 1/3x -3

110.

Which of these represents point-slope form of a linear equation?

a)

y - y₁ = m(x - x₁)

b)

Ax + By = C

c)

y = mx + b

111.

y = 3x +2
y = 3x - 3
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

112.

Which is the equation of the line that is parallel to the graph of y = 5x + 7 and has a y-intercept at (0, -2)?

a)

y = 5x - 2

b)

y = -2x + 7

c)

y = 5(x - 2)

d)

y = -1/5x - 2

113.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

114.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

115.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

116.

f(x)=4x+5
f(4)=

a)

21

b)

-11

c)

-31

d)

25

117.

f(x)=2x+2

for x = 4

a)

6

b)

-8

c)

10

d)

0

118.

Evaluate f(t)=-2t²+ 1 for f(2)

a)

9

b)

17

c)

-17

d)

-7

119.

State the domain:

a)

(-oo, 4)

b)

(-oo, 2]

c)

[2, oo)

d)

[4, oo)

120.

Find the distance between (-3, 8) and (2, -4)

a)

13

b)

$\sqrt{169}$

c)

$13\sqrt{3}$

d)

$\sqrt{13}$

121.

Given a triangle with leg measurements of 9 and 5, what is the length of the hypotenuse?

a)

$\sqrt{106}$

b)

$2\sqrt{53}$

c)

$106$

d)

$14$

122.

Given a right triangle with leg measurement 12 and a hypotenuse measurement of 13, what is the length of the other leg?

a)

5

b)

$\sqrt{12}$

c)

$13$

d)

$\sqrt{196}$

123.

Given an isosceles triangle with leg measurements 12 and 9, what is the length of the hypotenuse?

a)

$\sqrt{225}$

b)

$15$

c)

$5\sqrt{5}$

d)

Uhh... There isn't a hypotenuse?

124.

(0, 0) is called the...

a)

origin

b)

center

c)

null

d)

empty

125.

Find the midpoint of (0, 2) and (8, 8)

a)

(4, 5)

b)

(5, 4)

c)

(-5, 4)

d)

(-4, -5)

126.

If f(x)=2x+25, find f(5).

a)

f(5) = 60

b)

f(5) = 40

c)

f(5) = -15

d)

f(5) = 35

127.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

128.

The point where the line crosses the y-axis is called the:

a)

origin

b)

x-intercept

c)

y-intercept

d)

slope

129.

Give the equation for the graph

a)

y = 5x - 3

b)

y = 4x + 2

c)

y =-2x + 5

d)

y = - 2x + 4

130.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

131.

Would a triangle with these side lengths be a right triangle?
4, 5, 6

a)

Yes

b)

No

132.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

133.

Find the midpoint of (-3, 2) and (5, -2).

a)

(1, 0)

b)

(0, 1)

c)

(-1, 0)

d)

(0, -1)

134.

$\left(x-h\right)^2+\left(y-k\right)^2=r^2$ is the form of what graph?

a)

quadratic (parabola)

b)

circle

c)

linear

d)

sin wave

135.

What is the radius of the circle?
$x^2+y^2=49$

(a)

136.

What is the radius of the circle which has (0, 0) and (0, 6) on the circle?

(a)

137.

$y=2x^2-8$ is an example of a ___________________ function.

a)

quadratic

b)

circle

c)

linear

d)

sin

138.

What kind of function is shown in the graphs above?

a)

quadratic

b)

circle

c)

absolute value

d)

sin

139.

Is point (0, 2) a solution of the function:
$y=\sqrt{x+4}$ ?

a)

Yes

b)

No

140.

Find the slope of the line that passes through
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

141.

Write a linear equation in slope-intercept form give the point and slope. (-6, -11); slope = 1/2

a)

$y+6=\frac{1}{2}\left(x+6\right)$

b)

$x-2y=16$

c)

$y=\frac{1}{2}x-8$

d)

$y=\frac{1}{2}x-11$

142.

What slope is parallel to:
m = 3/4

a)

4/3

b)

3/4

c)

-3/4

d)

-4/3

143.

Line a passes through (2, 4) and (4, 7)

Line b passes through (-5, 3) and (-3, 6)

Lines a and b are ?

a)

Parallel

b)

Perpendicular

c)

Neither

144.

Select ALL of the lines that are PERPENDICULAR to y = 3/4x + 9

a)

y = 3/4x - 3

b)

y = -3/4x + 9

c)

y = -4/3x + 8

d)

3y = -4x + 5

e)

4y = -3x + 7

145.

Write the equation of a line PERPENDICULAR to the line y = 3x + 2 that passes through the point (9, -2)

a)

y = -1/3x - 5

b)

y = 3x-29

c)

y = 1/3x -5

d)

y = -1/3x +1

146.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

147.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

148.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x) = x²

c)

f(x) =√(x)

d)

f(x) =∛(x)

149.

Which parent function matches the graph?

a)

f(x) = √(x)

b)

f(x) = ∛(x)

c)

f(x) = |x|

d)

f(x) = a⋅b^x

150.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

151.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

152.

Name the parent function.

a)

cube root

b)

square root

c)

quadratic

d)

linear

153.

Which of the following parent functions does not have a Domain of all Real numbers?

a)

b)

c)

d)

154.

Give the name of the parent function of

y=4^x

a)

Exponential

b)

Logarithmic

c)

Absolute Value

d)

Sine

155.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

156.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

157.

Match the equation to its description.

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

158.

Describe the transformation from dotted to solid.

a)

f(x + 4)

b)

f(x - 4)

c)

f(x) + 4

d)

f(x) - 4

159.

Describe the transformation from dotted to solid.

a)

-f(x)

b)

f(x - 4)

c)

f(x) - 4

d)

f(-x)

160.

Describe the transformation from dotted to solid.

a)

f(x + 5) + 3

b)

f(x +3) + 5

c)

f(x - 5) + 3

d)

f(x - 3) + 5

161.

If the blue function is f(x)=x², then the red function must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

162.

What is the range to this graph?

a)

y> 1

b)

y>= 1

c)

y< 1

d)

y<= 1

163.

a)

b)

c)

d)

164.

The graph of the function p(x) is represented below. On the same set of axes, sketch the function p(x + 2).

a)

b)

c)

d)

165.

If the blue graph is
f(x) = x²the red must be...

a)

g(x) = (x + 3)²

b)

g(x) = (x - 3)²

c)

g(x) = x²+ 3

d)

g(x) = x²- 2

Pre-Calculus 1st Semester Exam Review

Total questions: 165

Worksheet time: 9hrs 5mins

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