Free Printable Final Exam Review

1.

What is the y-intercept shown on the graph?

a)

(0, -2)

b)

(3, 0)

c)

(0, 3)

d)

None of these.

2.

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

a)

(1, 0)

b)

(2, 0)

c)

( -1, 0)

d)

(-2, 0)

3.

Give the y-interecept
3x + y = 5

a)

(-3, 0)

b)

(0,5)

c)

(5, 0)

d)

(0, -3)

4.

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

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

5.

What is the equation for the line that passes through the points (4,2) and (0,6)?

a)

y = x + 6

b)

y = -2x + 2

c)

y = -x - 6

d)

y = -x + 6

6.

Write the equation of the line that passes through the point (1, -1) and has a slope of -4.

a)

y = -4x + 3

b)

y = -4x - 3

c)

y = -4x + 5

d)

y = -4x - 5

7.

Are the lines given by the equations parallel, perpendicular, or neither?

$y=-\frac{7}{4}x+8$

y=\frac{7}{4}x-9

a)

Parallel

b)

Perpendicular

c)

Neither

8.

Are the lines given by the equations parallel, perpendicular, or neither?

$y=-\frac{3}{4}x+13$

y=\frac{4}{3}x-8

a)

Parallel

b)

Perpendicular

c)

Neither

9.

Are the lines given by the equations parallel, perpendicular, or neither?

$y=\frac{3}{8}x+12$

y=\frac{8}{3}x+4

a)

Parallel

b)

Perpendicular

c)

Neither

10.

If a line has a slope of 3/4 a line that is parallel has a slope of what?

a)

3/4

b)

4/3

c)

-3/4

d)

-4/3

11.

If a line has a slope of 2/3 a line that is perpendicular has a slope of what?

a)

-3/2

b)

3/2

c)

2/3

d)

-2/3

12.

How is the distance formula correctly written:

a)

$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$

b)

$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)^2}$

c)

$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)^2}$

d)

d = $\sqrt{\left(x\right)^2-\ \left(y\right)^2}$

13.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

14.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

15.

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

a)

b)

c)

d)

16.

Find the midpoint of the line segment with the given endpoints (1,1) and (9,9)

a)

(5,5)

b)

(1,9)

c)

(17,17)

d)

(-4,-4)

17.

Find the midpoint: $\left(2,-7\right),\left(10,1\right)$

a)

(-3,6)

b)

(6,-3)

c)

(4,4)

d)

none

18.

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

a)

8.9

b)

9.8

c)

10.3

d)

11

19.

Find the midpoint of the segment with the endpoints: (-4, 5) and (7, -9)

a)

(-3/2, 2)

b)

(11/2, -7)

c)

(-2, 3/2)

d)

(3/2, -2)

20.

What does (h,k) stand for in the standard circle equation?

a)

(h,k) is the center of the circle

b)

(h,k) is a point on the circle.

c)

(h,k) is a point that we guess and find

d)

(h,k) is the distance of the circle

21.

In the equation (x-3)²+(y+4)²=121, the radius of the circle is

a)

242

b)

11

c)

121

d)

22

22.

What is the equation of a circle with radius 2 and center (3, 4)?

a)

(x+3)² + (y+4)² = 2

b)

(x-3)² + (y-4)² = 2

c)

(x+3)² + (y+4)² = 4

d)

(x-3)² + (y-4)² = 4

23.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

24.

Write the following in interval notation.

x < 8

a)

(8, -∞)

b)

(-∞, 8]

c)

(-∞, 8)

25.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

26.

Write the following in interval notation.

x ≥ 100

a)

(0, 100]

b)

(∞, 100]

c)

[100, ∞)

27.

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

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

28.

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

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

29.

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]

30.

On which interval(s) is the given function increasing?

a)

(-∞, 2) U (-2, ∞)

b)

(-2, 2) U (-2, ∞)

c)

(-∞, -2) U (0.5, ∞)

d)

(0, 2) U (0.5, ∞)

31.

Describe the intervals over which the given function is decreasing.

a)

(-∞, 0) U (2, ∞)

b)

(5, -4) U (2, -3)

c)

(-3, 0) U (2, 3)

d)

(5, -4) U (0, -3)

32.

Describe the range of the given function using interval notation.

a)

(-∞, ∞)

b)

(-4, 5)

c)

[-3, 5]

d)

[-4, 5]

33.

Determine the domain of the function.

a)

(5, -∞)

b)

(-∞, 5]

c)

[5, ∞)

d)

[5, -∞)

34.

What is the range of the given function?

a)

[-1, 1]

b)

(-1, 1)

c)

(∞, -∞)

d)

(-∞, ∞)

35.

a)

A

b)

B

c)

C

d)

D

36.

a)

A

b)

B

c)

C

d)

D

37.

a)

A

b)

B

c)

C

d)

D

38.

Simplify:
√45

a)

9√5

b)

3√5

c)

5√9

d)

3√15

39.

Simplify:
√200

a)

10√2

b)

2√10

c)

50√2

d)

2√50

40.

Simplify √75x²

a)

5x²√3

b)

5x

c)

5x√3x

d)

5x√3

41.

Simplify √121v

a)

11v

b)

11√v

c)

11v√v

d)

√11v

42.

Simplify √45x⁴y⁷

a)

3x²y³√5

b)

9x²y³√5y

c)

3x²y³√5y

d)

3x⁴y⁷

43.

Simplify

a)

x²y√xy

b)

xy

c)

x²y²

d)

Can't Simplify

44.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

45.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

46.

Match the graph with the correct equation.

a)

b)

c)

d)

47.

Evaluate f(3)=

a)

-1

b)

-7

c)

4

d)

5

48.

Evaluate f(-3)=

a)

-1

b)

-7

c)

4

d)

5

49.

What is the RANGE of the function?

a)

(-∞, +∞)

b)

(-∞, 4]

c)

(-∞, 4)

d)

[0, 4]

50.

What is the DOMAIN of the function?

a)

(-∞, +∞)

b)

(-∞, 4]

c)

(-∞, 4)

d)

[0, 4]

51.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

52.

Select the correct graph for the following piecewise function.

a)

b)

c)

d)

53.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

54.

Simplify

a)

A.(x+7)/(x-4)

b)

B.-3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

55.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

56.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

57.

Simplify:
$\frac{x^2+10x+24}{x^2-x-20}$

a)

$\frac{x+6}{x+4}$

b)

$\left(x+6\right)\left(x+4\right)$

c)

$x+6$

d)

$\frac{x+6}{x-5}$

58.

$\frac{\left(x+9\right)\left(x+8\right)}{8}\cdot\frac{\left(x-1\right)}{\left(x+8\right)\left(x-1\right)}$

a)

$\frac{\left(x+9\right)}{8}$

b)

$\frac{\left(x-1\right)}{8}$

c)

$\frac{1}{8}$

d)

$\frac{\left(x+9\right)\left(x+8\right)}{8}$

59.

$\frac{x^2-x-6}{x-3}\cdot\frac{x+9}{x+2}$

a)

$x+9$

b)

$\frac{x-3}{x-2}$

c)

$\frac{x+9}{x+2}$

d)

$x-3$

60.

Simplify:
$\frac{a-8}{7\left(a+2\right)}\cdot\frac{7\left(a+2\right)}{a+2}$

a)

$\frac{7\left(a+2\right)}{a+2}$

b)

$\frac{a-8}{a+2}$

c)

$\frac{a+2}{7}$

d)

$\frac{a-8}{7}$

61.

Simplify the expression.

$\frac{2}{x-1}+\frac{4}{x+1}$

a)

$\frac{6x+6}{\left(x-1\right)\left(x+1\right)}$

b)

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

c)

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

d)

$\frac{3x-1}{x}$

62.

Simplify the expression.

a)

b)

c)

d)

63.

Simplify the expression.

a)

b)

c)

d)

64.

If f(x) = x - 1 and g(x) = 5x - 2, then (f + g) (x) =

a)

5x²+ 1

b)

5x³ - 3

c)

6x + 1

d)

6x - 3

65.

f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

66.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

67.

a)

A

b)

B

c)

C

d)

D

68.

Solve for x
l x−6 l + 4= 10

a)

x = 12 and x = 0

b)

x = 3 and x = -3

c)

x = -12 and x = 0

d)

No Solution

69.

Evaluate each expression.
| x + 9 | = -5

a)

-14

b)

-4

c)

{-14, -4}

d)

no solution

70.

Solve. Select BOTH solutions.

$\left|x-1\right|=3$

a)

-2

b)

2

c)

4

d)

-3

71.

Solve. Select BOTH solutions.
$\left|3x\right|+2=8$

a)

$\frac{10}{3}$

b)

$2$

c)

$-2$

d)

$-\frac{4}{3}$

72.

Solve for x
l 4x−3 l = 17

a)

x = 5 and x =-3.5

b)

x = 0 and x = -5

c)

x = 10 and x = -10

d)

No Solution

73.

a)

- 1/2 ≤ z ≤ 5/2

b)

1/2 ≤ z ≤ 5/2

c)

z ≥ 1/2 or z ≤ 5/2

d)

z ≤ 1/2 or z ≥ 5/2

74.

a)

x > 11 or x < 5

b)

x > - 11 or x > 5

c)

5 < x < 11

d)

- 5 < x < 11

75.

Solve:
|x + 4| - 8 > 2

a)

x > 6 and x < 10

b)

x > 6 or x < -14

c)

all real numbers

d)

no solution

76.

Solve.
|p + 3| ≥ 10

a)

-13 ≤ p ≤ 7

b)

p ≤ -13 or p ≥ 7

c)

-7 ≤ p ≤ 13

d)

p ≤ -7 or p ≥ 13

77.

What is i?

a)

1

b)

-1

c)

√-1

d)

√1

78.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

79.

Find the Sum

3i + 2i

a)

5i

b)

5i²

c)

6i

d)

-5

80.

Find the sum.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

81.

Simplify:

(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

82.

(3+8i)(-2-i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

83.

$\left(1-7i\right)^2$

(a)

84.

even functions are symmetric with respect to the

a)

y-axis

b)

x-axis

c)

origin

d)

none of the above

85.

odd functions are symmetric with respect to the

a)

y- axis

b)

x - axis

c)

origin

d)

none of the above

86.

Is the graph an even, odd, or neither function
f(x) = x⁴ + x²

a)

Even

b)

Odd

c)

Neither

87.

Is the graph an even, odd, or neither function
f(x)=x³-x²

a)

even

b)

odd

c)

neither

88.

Is the graph an even, odd, or neither function
f(x) = x² + 2

a)

Even

b)

Odd

c)

Neither

89.

$y=x^2+3x+9$

a)

Even Function

b)

Odd Function

c)

Neither even nor odd

d)

Not a function

90.

Solve by the Quadratic Formula:

$-12q^2+3q+7=0$

a)

$\frac{-3\pm\sqrt{345}}{24}$

b)

$\frac{3\pm\sqrt{345}}{-24}$

c)

$\frac{3\pm\sqrt{345}}{24}$

d)

$\frac{3\pm i\sqrt{39}}{24}$

91.

What are the zeros of the function f(x) = x² + 64?

a)

-8 and 8

b)

-8i and 8i

c)

(-√8) i and (√8) i

d)

-√8 and √8

92.

Solve x² - 5x + 10 = 0

a)

(5 - i√15)/2 , (5 + i√15)/2

b)

(5 - √15)/2 , (5 + √15)/2

c)

(5 - i√65)/2 , (5 + i√65)/2

d)

(5 - √65)/2 , (5 + √65)/2

93.

Solve -2x² + 4x = 9

a)

(2 - i√14)/2 , (2 + i√14)/2

b)

(2 - i√-56)/2 , (2 + i√-56)/2

c)

(2 - i√-14)/2 , (2 + i√-14)/2

d)

(2 - √14)/2 , (2 + √14)/2

94.

$2m^2=-2m+12$
Solve using the quadratic formula.

a)

$x=2,-3$

b)

$x=3,-2$

c)

$x=1\pm\sqrt{13}$

d)

No Solution

95.

Describe the transformation from the parent absolute value function:

$y=\left|x\right|-5$

a)

Shift up 5 units

b)

Shift down 5 units

c)

Shift right 5 units

d)

Shift left 5 units

96.

Describe the transformation from the parent quadratic function:

$y=\left(x-2\right)^2$

a)

Shift up 2 units

b)

Shift down 2 units

c)

Shift right 2 units

d)

Shift left 2 units

97.

Describe the transformation from the parent square root function:

$y=\sqrt[]{x+4}$

a)

Shift up 4 units

b)

Shift down 4 units

c)

Shift right 4 units

d)

Shift left 4 units

98.

Describe the transformation from the parent cubic function:

$y=-x^3+3$

* Select TWO answers *

a)

Shift up 3 units

b)

Shift down 3 units

c)

Reflection over the y-axis

d)

Reflection over the x-axis

99.

Describe the transformation from the parent absolute value function:

$y=-\left|x+4\right|-3$

* Select THREE answers *

a)

Reflection over the x-axis

b)

Translation 4 units left

c)

Translation 4 units up

d)

Translation 3 units left

e)

Translation 3 units down

100.

Describe the transformation from the parent graph

a)

Reflect over x, right 3, down 4

b)

Reflect over y, right 3, down 4

c)

Reflect over x, right 3, up 4

d)

Reflect over y, left 3, down 4

Final Exam Review - Math 1000

Total questions: 100

Worksheet time: 7hrs 10mins

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