Free Printable SEMESTER REVIEW- Pre-Calculus

1.

What is the range of the graph?

a)

-2 < y < 10

b)

-3 < x < 3

c)

-2 ≤ y ≤ 10

d)

-3≤ x ≤ 3

2.

a)

Inverse Functions

b)

Not Inverse Functions

3.

What is/are the increasing interval(s) for the function shown?

a)

$\left(-3,\ 1\right)$

b)

$\left(4,\ 8\right)$

c)

$\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$

4.

What is the decreasing interval(s) on the function shown?

a)

$\left(-7,\ -6\right)\ and\ \left(-2,\ 4\right)$

b)

$\left(-7,\ 0\right)\ and\ \left(-2,\ 4\right)$

c)

$\left(-7,\ -6\right)\ and\ \left(-2,\ 0\right)$

d)

$\left(-7,\ 0\right)\ and\ \left(4,\ 5\right)$

5.

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

6.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

7.

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)

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

8.

Find the value of "c" that completes the square.

x_{ }^2+8x+c

a)

-4

b)

4

c)

8

d)

16

9.

Solve $x^2-4x+18=0$ .

a)

$x=-2\pm i\sqrt{14}$

b)

$x=-2\pm\sqrt{14}$

c)

$x=2\pm i\sqrt{14}$

d)

$x=2\pm\sqrt{14}$

10.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

11.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

12.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

13.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

14.

Simplify using your exponent rule(s) (-2)³⋅(-2)⁶

a)

(-2)⁹

b)

(-2)¹⁸

c)

(-2)⁻³

d)

(-2)

15.

Simplify using your exponent rule(s) x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

16.

Simplify using your exponent rule(s) x⁵⁄x³

a)

x²

b)

x

c)

1

d)

x⁸

17.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

18.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

19.

Factor using GCF or monomial factoring:

2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

20.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

21.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

22.

Factor
x² - 5x - 36

a)

(x - 4)(x + 9)

b)

(x - 6)(x + 6)

c)

(x + 4)(x - 9)

d)

(x -12)(x + 3)

23.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

24.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

25.

Solve
4m² - 100 = 0

a)

m=25 or m=-25

b)

m=96

c)

m=5 or m = -5

d)

m=-96

26.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

27.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

28.

Solve
x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

29.

Solve for the values of x:

(2x - 1)(x + 4) = 0

a)

x=1/2, x= -4

b)

x=1/2, x= 4

c)

x= 1, x=-4

d)

x=-2.5, x=4

30.

Rewrite the following

∛x⁵

a)

x^3/5

b)

x^5/3

c)

x²

d)

x³⋅x⁵

31.

Write in exponential form
∜(3x)³

a)

3x³⁄ ⁴

b)

(3x)³∕ ⁴

c)

(3x)⁴⁄ ³

d)

3x⁴⁄ ³

32.

∜m³ is the same as which answer?

a)

m^3/4

b)

m¹²

c)

m^4/3

d)

m⁷

33.

Simplify:

a)

2

b)

8

c)

16

d)

32

34.

Simplify the following expression:

a)

16

b)

32

c)

40

d)

64

35.

Simplify the following radical: √150

a)

5√15

b)

5√2

c)

5√6

d)

15√5

36.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

37.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

38.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

39.

$\sqrt{\frac{25}{64}}$

a)

1

b)

40

c)

$\frac{8}{5}$

d)

$\frac{5}{8}$

40.

$\sqrt{64}+\sqrt{81}$

a)

$\sqrt{17}$

b)

$17$

c)

$\sqrt{145}$

d)

8.5

41.

$\sqrt{49}-\sqrt{100}$

a)

$-\sqrt{51}$

b)

$-3$

c)

$-1.5$

d)

$-\sqrt{3}$

42.

Solve.

a)

-1/2

b)

2

c)

7

d)

no solution

43.

What is the domain?

a)

{-4, -1, 0, 2, 7}

b)

{-5, -4, -1, 0, 1, 2, 4, 7}

c)

{-5, 0, 1, 2, 4}

d)

{5}

44.

What is the Range?

a)

y ≥ 6

b)

y ≤ 6

c)

-10 ≤ y ≤ 6

d)

-10 ≤ x ≤ 6

45.

Identify all of the functions

a)

b)

c)

d)

e)

46.

What is the domain of the function graphed on the grid?

a)

-4 ≤ x < 5

b)

-4 ≤ x ≤ 5

c)

-3 ≤ x < 3

d)

-3 < x ≤ 3

47.

What is the range of the function graphed?

a)

x = 2

b)

All real numbers

c)

y = 2

d)

-6 < x < 6

48.

What is the decreasing interval on the function shown?

a)

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

b)

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

c)

$\left(2,\ \infty\right)$

d)

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

49.

What is the increasing interval on the function shown?

a)

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

b)

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

c)

$\left(2,\ \infty\right)$

d)

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

50.

Where is the function decreasing?

a)

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

b)

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

c)

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

d)

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

51.

Over what interval is this function constant?

a)

-5 < x < ∞

b)

-3 < x < 4

c)

4 < x < ∞

d)

-5

52.

What is/are the decreasing interval(s) for the function shown?

a)

$\left(2,\ 4\right)\ and\ \left(8,\ \infty\right)$

b)

$\left(-\infty,\ 1\right)\ and\ \left(8,\ \infty\right)$

c)

$\left(-\infty,1\right),\ \left(-3,\ 1\right)\ and\ \left(8,\ \infty\right)$

d)

$\left(-\infty,\ 1\right),\ \left(2,\ 4\right)\ and\ \left(8,\ \infty\right)$

53.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

54.

What is the domain interval for the green piece of this function?

a)

-2 < x ≤ 1

b)

-1 < x ≤ 0.5

c)

x > -2

d)

x ≤ 1

55.

Write the following in interval notation
x < 8

a)

(8, ∞)

b)

(8, -∞)

c)

(-∞, 8)

d)

[-∞, 8]

56.

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

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

57.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

58.

Would you use a closed or open circle to graph x < 3?

a)

Closed

b)

Open

59.

When writing a solution in interval notation, what brackets do i use for:

> or <

a)

[ ]

b)

( )

60.

√-20

a)

4i

b)

2i√5

c)

5√2

d)

10i

61.

Question 4

a)

x = 2

b)

x = 4

c)

x = 7

d)

x = 9

62.

Solve the equation.

a)

n = 27

b)

n = 18

c)

n = -18

d)

n = 36

63.

Solve.

a)

8

b)

-8

c)

0

d)

no solution

64.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

65.

f\left(x\right)=x+2\ \ \ and\ \ \ \ g\left(x\right)=2x^2-2x

Find\ \left(f-g\right)\left(x\right)

a)

$3x^3+2$

b)

$2x^2+3x+2$

c)

$2x^3+x^2+2x$

d)

$-2x^2+3x+2$

66.

$g\left(x\right)=3x+3$ $h\left(x\right)=4x+5$

$Find\ g\left(3\right)-h\left(3\right)$

a)

9

b)

-5

c)

-9

d)

5

67.

g\left(n\right)=n^2+4+2n

and

h\left(n\right)=-3n+2

Find\ \left(g\cdot h\right)\left(1\right)

a)

-7

b)

-5

c)

0

d)

35

68.

$If\ f\left(x\right)=x^2-1\ and\ g\left(x\right)=x^3$ $Find\ \left(f\ \circ\ g\right)\left(2\right)$

a)

72

b)

80

c)

63

d)

97

69.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(f\circ g\right)\left(2\right)$

a)

$\frac{1}{4}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

70.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

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

d)

$\frac{1}{3x+2}$

71.

Find\ g\left(f\left(4\right)\right).

a)

$4$

b)

$6$

c)

$8$

d)

$10$

72.

f(g(3)) =

a)

2

b)

1

c)

0

d)

-2

73.

f(h(-4)) =

(a)

74.

What is the equation of the following line?

a)

x=2

b)

y=2

75.

What is the equation of this line?

a)

y = 2x +2

b)

y = 2x -2

c)

y = -x + 2

d)

Cannot be Determined

76.

Write the equation of the line.

a)

y = -1/3x - 2

b)

y = 1/3x - 2

c)

y = 3x - 2

d)

y = -3x - 2

77.

Name the slope

a)

7/1

b)

3/4

c)

-3/4

d)

-7/1

78.

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

a)

Nothing in particular

b)

The y-intercept

c)

The x-intercept

d)

Slope

79.

Name the slope.

a)

Zero slope

b)

1

c)

Undefined

d)

-1

80.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

81.

Which parent function matches the graph?

a)

f(x) = √(x)

b)

f(x) = ∛(x)

c)

f(x) = |x|

d)

f(x) = a⋅b^x

82.

Name the parent function.

a)

constant

b)

quadratic

c)

linear

d)

exponential

83.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

84.

Name the parent function.

a)

quadratic

b)

cubic

c)

square root

d)

logarithmic

SEMESTER REVIEW- Pre-Calculus

Total questions: 84

Worksheet time: 3hrs 29mins

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