Free Printable Pre-Calc Exam Review

1.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

2.

What does the transformation $f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$ do to the graph of $f\left(x\right)$ ?

a)

translates it left one unit and down 9 units

b)

translates it right one unit and down 9 units

c)

translates it up one unit and right 9 units

d)

translates it down one unit and left 9 units

3.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

4.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

5.

Given the function $y=\left(x+4\right)^2+2$ , what is the parent function?

a)

$y=x^2$

b)

$y=a\left(x-h\right)^2+k$

c)

$y=mx+b$

d)

$y=0\left(x-0\right)^2+0$

6.

What does the transformation $f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$ do to the graph of $f\left(x\right)$ ?

a)

translates it left one unit and down 9 units

b)

translates it right one unit and down 9 units

c)

translates it up one unit and right 9 units

d)

translates it down one unit and left 9 units

7.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

a)

A

b)

B

c)

C

d)

D

8.

Use the Rational Root Theorem to list the possible rational zeros.

a)

A

b)

B

c)

C

d)

D

9.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

a)

-3+5i

b)

-3-5i

c)

-5i

d)

3-5i

10.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that -7i is a root.

a)

7i

b)

-7i+1

c)

1-7i

d)

1+7i

11.

Use the factored form of the function to find the zeros. (hint: set each factor = 0)

a)

A

b)

B

c)

C

d)

D

12.

Find the zeros of polynomial given one zero.

a)

A

b)

B

c)

C

d)

D

13.

Find the zeros of the polynomial given one zero

a)

A

b)

B

c)

C

d)

D

14.

Find ALL zeros

a)

A

b)

B

c)

C

d)

D

15.

Find all zeros of the polynomial

a)

A

b)

B

c)

C

d)

D

16.

One zero of 3x³-4x²-28x-16 is 4.
What is another zero?

a)

8

b)

-2

c)

6

d)

1

17.

Simplify:
(3 + 2i) + (4i + 6)

a)

9 + 6i

b)

7i + 8

c)

9 + 6i²

d)

9 - 6i

18.

(-7+6i)²

a)

49+36i

b)

85

c)

13-84i

d)

13+84i

19.

Simplify 2√-32

a)

2i√32

b)

4i√2

c)

8i√2

d)

-16i√2

20.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

21.

Evaluate.
3 log₂4

a)

3

b)

6

c)

2

d)

4

22.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

23.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

24.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

25.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

26.

Solve: $3^x=18$

a)

x = 6

b)

x = 2.5

c)

x = 2.63

d)

2.47

27.

Solve: $6^x\ +\ 3\ =\ 129$

a)

x = 21

b)

x = 2.69

c)

x = 2.43

d)

x = 3.5

28.

Solve $\log\left(1000\right)=x$

a)

x = 10

b)

x = 3

c)

x = 4

d)

x = 100

29.

Solve:
log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

30.

Solve

a)

5

b)

13

c)

84

d)

-20

31.

Paul deposits $4000 in a bank which pays a compound interest rate of 4% per year. How much will he have in 5 years.

a)

$4866.61

b)

$5628.40

c)

$6077.53

d)

$6326.60

32.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

33.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

34.

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually,what will be the balance after 18 years?

a)

$6,273.50 frustrated

b)

$6,314.08 bewildered

c)

$6,385.72 pleased

d)

$6,427.94 tickled pink

35.

What is the domain of the graph?

a)

(-∞,∞)

b)

(-2, ∞)

c)

(0,∞)

d)

(-∞,2)

36.

What is the range of the graph?

a)

(-∞,∞)

b)

(-2, ∞)

c)

(0,∞)

d)

(-∞,-2)

37.

f(x)=log₅(x+4) - 2

Describe the asymptote

a)

Horizontal Asymptote x = -4

b)

Vertical Asymptote x = -4

c)

Horizontal Asymptote x = 4

d)

Vertical Asymptote x = 4

38.

f(x)=log₅(x+4) - 2

Describe the transformation

a)

translation 4 units to the right, 2 units down

b)

translation 4 units to the left, 2 units down

c)

translation 4 units to the up, 2 units right

d)

translation 4 units to the up, 2 units left

39.

What is the DOMAIN of the above graph?

a)

$-5<x<4$

b)

$-5<y<-2$

c)

$-5\le x\le4$

d)

$-5\le y\le-2$

40.

What is the RANGE of the above graph?

a)

$-5<x<4$

b)

$-5<y<-2$

c)

$-5\le x\le4$

d)

$-5\le y\le-2$

41.

What is the domain in Interval notation?

a)

[ -2 , 2 ]

b)

[ 4 , -4 ]

c)

(-2 , 2 )

d)

(4 , -4 )

42.

What is the range of the graph?

a)

[-7, 5)

b)

(-3, 1]

c)

[-3, 1)

d)

(-7, 5]

43.

$f\left(x\right)=\frac{1}{x-5}$ Find the domain of

a)

$\left(-\infty,5\right)\left(5,\infty\right)$

b)

$\left[5,\infty\right)$

c)

$\left(-\infty,5\right]$

d)

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

44.

Find the domain of $f\left(x\right)=\frac{x^2}{\sqrt{7-x}}$

a)

$\left(-\infty,0\right)\left(0,7\right]$

b)

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

c)

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

d)

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

45.

Write the domain of $f\left(x\right)=\frac{x}{x^2-16}$

a)

$\left(-\infty,0\right)\left(4,\infty\right)$

b)

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

c)

$\left(-\infty,0\right)\left(0,4\right]$

d)

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

46.

Find the domain of $g\left(x\right)=\sqrt{2x-4}$

a)

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

b)

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

c)

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

d)

$\left(-\infty,\frac{1}{2}\right)\left(\frac{1}{2},\infty\right)$

47.

Find the domain of $f\left(x\right)=\frac{1}{\sqrt{x-5}}$

a)

$\left(-\infty,5\right]$

b)

$\left(-\infty,5\right)\left(5,\infty\right)$

c)

$\left(5,\infty\right)$

d)

$\left[5,\infty\right)$

48.

a)

All real numbers except for c=5

b)

(-∞, 5]

c)

[5, ∞)

d)

All real numbers except for c=0

49.

$What\ is\ the\ domain\ of\ \ f\left(x\right)=x^2+3x-10$

a)

$\left[5,\infty\right)$

b)

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

c)

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

d)

[-2,5]

50.

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

51.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

52.

g(n) = n² + 5n

f(n) = n + 4

Find g(f(n))

a)

n² + 3n + 36

b)

n² + 13n + 16

c)

n² + 13n + 36

d)

n² + 3n + 20

53.

f(a) = a² + a - 3

g(a) = 3a

Find f(g(a))

a)

9a² - 3a + 3

b)

9a² + 3a - 3

c)

3a² - 3a + 3

d)

3a² + 3a - 3

54.

$If\ f\left(x\right)=2x+1\ \ and\ \ g\left(x\right)=3x+2$

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

a)

f(g(x)) = 6x + 4

b)

f(g(x)) = 6x + 5

c)

f(g(x)) = 5x + 8

d)

f(g(x)) = 5x + 5

55.

$If\ f\left(x\right)=x^2-5\ \ and\ \ g\left(x\right)=2x-3$

Find\ \left(g\circ f\right)\left(2\right)

a)

-5

b)

-3

c)

0

d)

2

56.

FInd the inverse of the function.
$f\left(x\right)=\frac{3x-15}{2}$

a)

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

b)

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

c)

$f^{-1}\left(x\right)=\frac{15+2x}{3}$

d)

$f^{-1}\left(x\right)=\frac{2}{3}x-\frac{19}{3}$

57.

Find the inverse of the function.
$f\left(n\right)=-4-\frac{2}{5}n$

a)

$f^{-1}\left(n\right)=\frac{-6-5n}{2}$

b)

$f^{-1}\left(n\right)=3n-4$

c)

$f^{-1}\left(n\right)=-\frac{5}{2}n-10$

d)

$f^{-1}\left(n\right)=\frac{-2n-4}{5}$

58.

$h\left(x\right)=-\frac{2}{x-1}-3$
Find the inverse of the function.

a)

$h^{-1}\left(x\right)=\frac{2}{-x-3}+1$

b)

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

c)

$h^{-1}\left(x\right)=\frac{2}{-x+3}$

d)

$h^{-1}\left(x\right)=\frac{3}{-x-3}-2$

59.

$f\left(n\right)=-n^3+2$
Find the inverse of the function.

a)

$f^{-1}\left(n\right)=\left(n+1\right)^5$

b)

$f^{-1}\left(n\right)=^3\sqrt{-n+2}$

c)

$f^{-1}\left(n\right)=2n^5$

d)

$f^{-1}\left(n\right)=\left(n+3\right)^5$

60.

A graph and its inverse are always symmetrical about the line...

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

61.

Are these the graphs of two inverse functions?

a)

Yes

b)

No

c)

No way to tell

62.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

63.

What are the asymptotes?

a)

x = -1 y = -3

b)

x = 1 y = -3

c)

x = -1 y = 3

d)

x = 1 y = 3

64.

a)

All Reals Except 0

b)

All Reals

c)

All Reals Except -3

d)

All Reals Except 0 and -3

65.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

66.

$w^2+7w+4=0$

a)

$\frac{-7\pm\sqrt{33}}{2}$

b)

$\frac{-7\pm\sqrt{65}}{2}$

c)

$\frac{7\pm\sqrt{33}}{2}$

d)

$\frac{-7\pm3\sqrt{11}}{2}$

67.

$x^2-6x+4=0$

a)

$3\pm\sqrt{5}$

b)

$\frac{6\pm\sqrt{20}}{2}$

c)

$3\pm\sqrt{20}$

d)

$3\pm i\sqrt{13}$

68.

$y^2=-9-9y$

a)

$\frac{-9\pm\sqrt{117}}{2}$

b)

$\frac{9\pm\sqrt{45}}{2}$

c)

$\frac{-9\pm3\sqrt{5}}{2}$

d)

$\frac{9\pm5\sqrt{3}}{2}$

69.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

70.

Let f(x) = 4x² -33x -27. Is k = 9 a zero of the function?

a)

yes

b)

no

71.

Solve using long division. $\left(8x^2+6x-20\right)\div\left(4x-5\right)$

a)

$2x-4$

b)

$2x+4$

c)

$2x-1-\frac{16}{4x-5}$

d)

$2x-4-\frac{40}{4x-5}$

72.

Use long division algorithm.

a)

4x - 2

b)

4x + 2

c)

2x - 4

d)

2x + 4

73.

If $\sin\theta=\frac{4}{5}$ , then $\csc\theta=$

a)

$\frac{4}{5}$

b)

$-\frac{4}{5}$

c)

$-\frac{5}{4}$

d)

$\frac{5}{4}$

74.

Find a coterminal angle to 45°.

a)

360°

b)

405°

c)

315°

d)

295°

75.

Convert 150⁰ to Radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

76.

Convert 210^o to Radians

a)

7π / 6

b)

21π / 10

c)

5π / 6

d)

9π / 4

77.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

78.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

79.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

80.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

81.

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

a)

-9x+11

b)

4x²+4x

c)

9x²+9x - 4

d)

9x+11

82.

What is the range of the following function in interval notation?

a)

(1, ∞)

b)

[1, ∞)

c)

(2, ∞)

d)

[2, ∞)

83.

What is the domain of the following function?

a)

(-∞, ∞)

b)

(-4, ∞)

c)

[-1.5, 1.5]

d)

(-∞, -4]

84.

Classify the function as continuous or classify its discontinuity.

a)

Continuous! The left and right limits match the function value.

b)

Discontinuous with a removable discontinuity

c)

Discontinuous with a jump discontinuity

d)

Discontinuous with an infinite discontinuity

85.

Classify the function as continuous or classify its discontinuity.

a)

Continuous! The left and right limits match the function value.

b)

Discontinuous with a removable discontinuity

c)

Discontinuous with a jump discontinuity

d)

Discontinuous with an infinite discontinuity

86.

For some function c(x), the limit of c(x) as x approaches -7 does not exist and c(-7) does not exist. Which is a true statement about the function?

a)

There is infinite discontinuity at x = -7

b)

There is removable discontinuity at x = -7

c)

There is jump discontinuity at x = -7

d)

The function is continuous

87.

Identify the parent function of:

a)

quadratic

b)

cubic

c)

logarithmic

d)

reciprocal

88.

What is one of the transformations taking place in the following function?

a)

horizontal compression

b)

horizontal translation

c)

vertical compression

d)

reflection with respect to the x-axis

89.

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

a)

1/5

b)

-1/5

c)

5

d)

-5

90.

Write the equation of a line in point slope form that passes through (3,8) and has a slope of 5.

a)

y-8=5(x-3)

b)

y=5x+8

c)

y-3=5(x-8)

d)

y-y₁₌ m(x-x₁₎

91.

What is the equation of the line y + 5 = -3(x - 6) in slope intercept form?

a)

y = -3x - 23

b)

y = -3x -13

c)

y = -3x - 11

d)

y = -3x+13

92.

Write an equation
m = 5/4 through (-4, -3)

a)

y = 5/4x +2

b)

y = -5/4x + 2

c)

y = 2x - 5/4

d)

y = 3/4x + 2

93.

$\frac{\left(x^6y\right)^{-4}}{\left(x^2y^3\right)^{-3}}$

a)

$\frac{y}{x^5}$

b)

$x^{18}y^5$

c)

$\frac{y^5}{x^{18}}$

d)

$x^5y$

94.

$y=x^4-6x^3+5$

Is the function even, odd or neither?

a)

even

b)

neither

c)

odd

95.

$y=\frac{4x^5}{9x^5-6x}$

Is the function even, odd or neither?

a)

even

b)

neither

c)

odd

96.

$y=\frac{x^2-9}{4x+8}$ Find the horizontal asymptote.

a)

none

b)

y=1/4

c)

y=1

d)

y=0

97.

$y=\frac{x^2-9}{4x+8}$

Find the vertical asymptote(s).

a)

x = -2

b)

x = 1/4

c)

x = -3

d)

x = 3

98.

$f\left(x\right)=\frac{1}{x-9}\ \ \ \ \ \ \ \ g\left(x\right)=\sqrt{x+13}$

Find the domain of f(g(x)).

a)

[-13, 94) U (94, oo)

b)

[-13, 68) U (68, oo)

c)

[-13, oo)

d)

(-13, oo)

99.

$f\left(x\right)=x^2-9\ \ \ \ \ \ \ \ g\left(x\right)=\sqrt{x+3}$

Are f and g inverses? Find this using composition.

a)

no

b)

yes

100.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

101.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

102.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

103.

$y=-2x^4\left(x+3\right)\left(x-2\right)$
Select the zeros and their multiplicities.

a)

x=0, mult. 4

b)

x=2, mult. 4

c)

x=2, mult. 1

d)

x=-3, mult. 1

e)

x=-2, mult. 4

104.

$y=-2x^4\left(x+3\right)\left(x-2\right)$
Select the degree and leading coefficient.

a)

Degree = even, LC = negative

b)

Degree = odd, LC = negative

c)

Degree = even, LC = positive

d)

Degree = odd, LC = positive

105.

a)

A

b)

B

c)

C

d)

D

106.

a)

A

b)

B

c)

C

d)

D

107.

a)

A

b)

B

c)

C

d)

D

108.

Expand the following: $\log_7\left(4x\right)$

a)

$\log_7\left(4\right)+\log_7\left(x\right)$

b)

$\log_7\left(4\right)-\log_7\left(x\right)$

c)

$\log_7\left(x^4\right)$

d)

$4\log_7\left(x\right)$

109.

$\log_nn=$ (a)

110.

Expand the following: $\log_5\left(z^8\right)$

a)

$5\log_8\left(z\right)$

b)

$8\log_5\left(z\right)$

c)

$\log_5\left(8z\right)$

d)

$8+\log_5\left(z\right)$

111.

Simplify the following: $\log_324-\log_36$

a)

$\log_318$

b)

$\log_3144$

c)

$\log_34$

d)

$\log12$

e)

$18\log3$

112.

Expand the following: $\log\left(j^4k^7\right)$

a)

$\log\left(4j\right)+\log\left(7k\right)$

b)

$11\log\left(j+k\right)$

c)

$28\log\left(jk\right)$

d)

$4\log\left(j\right)+7\log\left(k\right)$

113.

Simplify the following: $\log_4x+\log_4x$

a)

$\log_4\left(x^2\right)$

b)

$\log_4\left(2x\right)$

c)

$\log_{16}\left(x^2\right)$

d)

$\log_8\left(2x\right)$

e)

$\log_4x$

114.

Simplify the following: $\log_5\left(3\right)+\log_5\left(r\right)-\log_5\left(w\right)$

a)

$\log_5\left(3rw\right)$

b)

$\log_5\left(3+r-w\right)$

c)

$\log_5\left(\frac{3r}{w}\right)$

d)

$\frac{\log_5\left(3r\right)}{\log_5\left(w\right)}$

115.

Expand the following: $\log_2\left(5a^{10}\right)$
hint: $5a^{10}=5\cdot a^{10}$

a)

$\log_25+10\log_2a$

b)

$10\log_25+\log_2a$

c)

$\log_2\left(50a\right)$

d)

$\log_250+\log_2a$

e)

$10\log_25-10\log_2a$

116.

Is the following true or false? Explain your answer!!
$\log_6\left(10\right)+\log\left(4\right)=\log_6\left(40\right)$

4 lines

117.

Solve the equation for x: $\frac{2}{x+2}+\frac{5}{x\ -2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

118.

Solve for x: $\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}$

a)

x = 5

b)

x = $\frac{4}{5}$

c)

x = 1

d)

x = - 4

119.

$\frac{2n+16}{n-8}=\frac{1}{2n-16}-\frac{1}{2}$

a)

$-\frac{23}{5}$

b)

$7$

c)

$-4$

d)

$\frac{4}{3}$

120.

\lim_{x\rightarrow0}\ f\left(x\right)\ =\

(a)

121.

$\lim_{x\rightarrow1\ }f\left(x\right)=$

(a)

122.

$\lim_{x\rightarrow1}\ g\left(x\right)$

(a)

Pre-Calc Exam Review

Total questions: 122

Worksheet time: 6hrs 28mins

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