Free Printable PreCalc Semester One Exam Review

1.

Which is the domain of the function

g\left(x\right)=9^x

?

a)

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

b)

$\left[0,\ \infty\right)$

c)

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

d)

$\left[-\infty,0\right]$

2.

Which function is a transformation of

f\left(x\right)=3^x

two units down?

a)

$g\left(x\right)=3^{x+2}$

b)

$g\left(x\right)=3^{x-2}$

c)

$g\left(x\right)=3^x-2$

d)

$g\left(x\right)=3^x+2$

3.

Which of the following correctly describes the end behavior of f(x) as x approaches zero?

a)

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

b)

$\lim_{x\rightarrow0}f\left(x\right)=0$

c)

$\lim_{x\rightarrow0}f\left(x\right)=8$

d)

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

4.

Evaluate $\log_3\left(\frac{1}{81}\right)$

a)

$-4$

b)

$4$

c)

$27$

d)

$-3$

5.

Use the Change of Base formula to evaluate $\log_310$ . Round your answer to the nearest hundredth.

a)

$0.52$

b)

$048$

c)

$2.10$

d)

$-0.52$

6.

Expand $\ln\frac{x-6}{\sqrt{x+4}}$

a)

$\ln\left(x\ -6\right)+\frac{1}{2}\ln\left(x+4\right)$

b)

$\frac{1}{2}\ln\left(x+4\right)-\ln\left(x\ -6\right)$

c)

$\ln\left(x\ -6\right)-\frac{1}{2}\ln\left(x+4\right)$

d)

$\ln\left(x\ -6\right)-\ln\sqrt{x+4}$

7.

Condense $4\log_2\left(3x\right)-3\log_2y-\log_2z$

a)

$\log_2\ \frac{3x^4}{y^3z}$

b)

$\log_2\ \frac{64x^4}{y^3z}$

c)

$\log_2\ \frac{81x^4}{y^3z}$

d)

$\log_2\ \frac{81x^4z}{y^3}$

8.

The number of seniors at Freedmont High School was 386 in 2008. If the number of seniors increases exponentially at a rate of 2.3% per year, how many seniors will be in the class of 2021? Use $N\left(t\right)=N_0\left(1+r\right)^t$

(a)

9.

Jasmine invests $2500 in an account that earns an interest rate of 3% compounded continuously. How much will her account have in 6 years?

(a)

10.

Charlie deposits $2400 into an account for his daughter when she is born. If the account has a 2.5% interest rate and is compounded monthly, how much will be in her account after 18 years?

(a)

11.

A city's population can be modeled by the equation $y=29,760e^{-0.021t}$ , where t is the number of years since 2008. Find the projected population in 2042. Round to the nearest whole number.

(a)

12.

State the range for the function

f\left(x\right)=4^{x-2}

a)

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

b)

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

c)

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

d)

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

13.

In 2008, the bird population in a certain area was 10,000. The number of birds increases exponentially at a rate of 9% per year. Predict the population in 2013.

a)

15,386

b)

15,683

c)

30,658

d)

54,709

14.

A scientist has 86 grams of a radioactive substance that decays continuously at an exponential rate. Assuming

k=-0.4

, how many grams of radioactive substance remains after 10 days?

a)

21.5 g

b)

15.8 g

c)

3.7 g

d)

1.6 g

15.

Write

3^{-2}=\frac{1}{9}

in logarithmic form.

a)

$\log_3\left(-2\right)=\frac{1}{9}$

b)

$\log_3\ \frac{1}{9}=-2$

c)

$\log_{-2}\ \frac{1}{9}=3$

d)

$\log_{-2}3=\frac{1}{9}$

16.

Evaluate

\log_9\ \frac{1}{27}

.

a)

$-3$

b)

$-\frac{2}{3}$

c)

$-\frac{3}{2}$

d)

$\frac{3}{2}$

17.

Solve

\log_4x+\log_4\left(x-2\right)=\log_415

a)

$x=-3$

b)

$x=5$

c)

$x=-3$ or $x=5$

d)

$x=3$

18.

Evaluate

\log_627.5

using the Change of Base Formula.

a)

1.120

b)

0.240

c)

1.850

d)

0.541

19.

Solve

5^x=3^{x+2}

.

a)

0.811

b)

3.109

c)

4.117

d)

4.301

20.

Solve

e^{0.2x}=21.2

a)

$-13.17$

b)

$106$

c)

$0.065$

d)

$15.27$

21.

Condense

3\log x+\log7-2\log y

a)

$\log\ \frac{7x^3}{y^2}$

b)

$\log\ \frac{x^3}{7y^2}$

c)

$\log\ \frac{21x}{y^2}$

d)

$\log7x^3y^2$

22.

Expand

\ln\ \frac{5x^6}{11y^7}

completely.

a)

$6\ln5x-7\ln11y$

b)

$\ln6+\ln5x-\ln7-\ln11y$

c)

$\ln5+6\ln x-\ln11-7\ln y$

d)

$\ln11+7\ln y-\ln5-6\ln x$

23.

Solve

\ln x+\ln\left(x-4\right)=\ln12

a)

$x=6$

b)

$x=6$ or $x=-2$

c)

$x=-6$ or $x=2$

d)

$x=2$

24.

Given

f\left(x\right)=\log x

and

g\left(x\right)=\log\left(x-2\right)+1

, how does the graph of g compare to the graph of f ?

a)

g is shifted 2 units left and 1 unit up

b)

g is shifted 2 units right and 1 unit up

c)

g is shifted 2 units down and 1 unit left

d)

g is shifted 2 units up and 1 unit right

25.

If Katie invests $1000. Find the amount of time required for her investment to double at a rate of 12.3% if the interest is compounded continuously.

a)

5.64 years

b)

5.98 years

c)

61.8 years

d)

16.26 years

26.

The table above shows the population of a given bacteria colony. Assuming the data is exponential, linearize the data and find the linear regression equation for the linearized data.

a)

$y=0.37x+4.47$

b)

$y=0.08x+4.55$

c)

$y=56.07x+77.11$

d)

$y=0.5x+9.56$

27.

Simplify

$4\log_3x^2-3\log_3x^3$

a)

$\log_x3$

b)

$\log_3x$

c)

$\log_3\left(-x\right)$

d)

$-\log_3x$

28.

Based on the end behavior which option best describes the leading term?

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

29.

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

30.

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

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

31.

Describe the end behavior of the graph.

a)

x →∞, y→∞ and x→∞, y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→0 and x→∞, y→⁻∞

32.

Determine the end behavior of the graph of
f(x) = 3x⁴ + 2x - 5

a)

As x →∞, f(x) →∞.
As x→-∞, f(x) →-∞.

b)

As x →∞, f(x) →∞.
As x→-∞, f(x) →∞.

c)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →∞.

d)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →-∞.

33.

Solve

a)

x = -5

b)

x = 1/5

c)

No Solution

d)

x = -1

34.

Solve

a)

v = -14

b)

v = 14

c)

No Solution

d)

v = 28

35.

Solve

a)

x= -9

b)

x= -2 and 3

c)

x= 5

d)

x= 0

36.

a)

x=4

b)

x=7

c)

x=12

d)

No Solution

37.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect, and error occurs on the 2nd line!

c)

This is incorrect, and the error occurs on the 4th line!

d)

This is incorrect, and the error occurs on the 3rd line!

38.

Divide using long division. $\left(9x^3-18x^2-x+2\right)\div\left(3x+1\right)$

a)

$3x^2+7x-14$

b)

$3x^2-7x-2$

c)

$3x^2-7x+14$

d)

$3x^2-7x+2$

39.

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

40.

State if the given binomial is a factor of the given polynomial.

p^5+4p^4-17p^3+18p^2-64p+40\ ;\ p+7

a)

Yes

b)

No

41.

State if the given binomial is a factor of the given polynomial.

2n^3+13n^2+29n+36\ ;\ n+4

a)

Yes

b)

No

42.

Use synthetic substitution to evaluate the given value and determine the remainder.

f\left(x\right)=-4x^4+9x^3+8x^2+9x-13\ at\ x=3

a)

-11

b)

10

c)

11

d)

5

43.

a)

(-∞, ∞)

b)

[-2, 2]

c)

(-2, 2)

d)

[-5, 5]

44.

What is the DOMAIN for the following graph?

a)

(-∞, ∞)

b)

(-∞, 0]

c)

[-12, 12]

d)

[-4, 0]

45.

Write the factored form of the polynomial with roots x=-2. x=5, x=2/3

a)

y=(x-2)(x+5)(3x+2)

b)

y=(x-2)(x+5)(2x+3)

c)

y=(x+2)(x-5)(2x-3)

d)

y=(x+2)(x-5)(3x-2)

46.

Find all zeros of the polynomial function P(x) = x³+6x²+9x+54

a)

6, 3, -3

b)

-6, 3, -3

c)

-6, 3i, -3i

d)

6, 3i, -3i

47.

Find all zeros for the polynomial function P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

48.

Find a polynomial function of degree 3 with zeros 3i and -2.

a)

P(x) = x³+2x²+9x+11

b)

P(x) = x³-2x²+9x+18

c)

P(x) = x³+2x²+9x+18

d)

P(x) = x²-3ix+2x-6i

49.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

50.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

51.

What is the equation of the horizontal asymptote?

a)

y = 0

b)

y = -2

c)

y = 2

d)

There isn't one

52.

Find the x-intercept(s), if one exists.

a)

(1, 0)

b)

(-1, 0)

c)

(1, 0), (-1, 0)

d)

(0, 0), (1, 0)

53.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

54.

What are the coordinates of the hole, if one exists.

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

55.

Find the y-intercept.

a)

(0, -2)

b)

(0, 2)

c)

(0, 4)

d)

it is undefined

56.

What is the domain of this function?

The dashed blue lines represent asymptotes

a)

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

b)

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

c)

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

d)

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

57.

What is the range of this function?

a)

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

b)

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

c)

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

d)

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

58.

Solve for x: $-4x^2+2x\le-20$

a)

no solution

b)

$\left(-\infty,-2\right]\cup\left[\frac{5}{2},\infty\right)$

c)

$\left[-2,\frac{5}{2}\right]$

d)

all real numbers

59.

Solve the inequality in interval notation

x^2-9\le0

a)

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

b)

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

c)

$\left[-\infty,-3\right]\cup\left[3,\infty\right]$

d)

$\left[-3,3\right]$

60.

Solve the inequality in interval notation

\frac{x+2}{x-4}\ge3

a)

$\left(-\infty,4\right)\cup\left(7,\infty\right)$

b)

$\left(4,7\right]$

c)

$\left[-\infty,4\right]\cup\left[7,\infty\right]$

d)

$\left[4,7\right)$

61.

Solve the inequality in interval notation

\frac{3x^2}{x^2+4}\ge1.5

a)

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

b)

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

c)

$\left(-\infty,-2\right]\cup\left[2,\infty\right)$

d)

$\left[-2,2\right]$

62.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

63.

What is the domain?

a)

[-2, 3]

b)

[-2, 3)

c)

(-2, 3]

d)

[-3, 4]

e)

(-3, 4]

64.

What is the range?

a)

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

b)

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

c)

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

d)

None of the answer choices

e)

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

65.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

66.

Is this table a function or not a function?

a)

Function

b)

Not a Function

67.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

68.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

69.

Evaluate f(-2) if f(x) = x²+ 3

a)

-1

b)

1

c)

7

d)

-7

70.

If h(a) = 3 - 2x²
Find h(-3).

a)

33

b)

21

c)

39

d)

-15

71.

Find the domain of

f\left(x\right)\ =\ \frac{x-3}{x+4}

.

a)

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

b)

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

c)

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

d)

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

72.

Find the domain of each function.

f\left(x\right)=\sqrt{3x-21}

a)

$\left[7,\infty\right]$

b)

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

c)

$\left[7,\infty\right)$

d)

$\left[21,\infty\right)$

73.

What are the local maxima of this graph?

a)

local maximum at (2.2, 3.9)

b)

local maximum at (-8, 5)

c)

local maximum at
(5, -8) and (3.9, 2.2)

d)

local maximum at
(-8, 5) and (2.2, 3.9)

74.

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)

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

75.

Where is the function increasing?

a)

\left(1,\infty\right)

b)

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

c)

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

d)

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

76.

a)

The end behavior of the graph is x →∞, y→⁻∞ and x →⁻∞,y→⁻∞

b)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

c)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→2

d)

The end behavior of the graph is x →∞,y→2 and x→⁻∞, y→∞

77.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

78.

Whats is the average rate of change of the function $f\left(x\right)\ =\ 2x^2+\ 1\ at\ the\ interval\ x\ =\ 0\ and\ x\ =\ 1?$

(a)

79.

Which of the following is the end behavior of the following graph?

a)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty\$ and

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty\$

b)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty\$ and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\$

c)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty\$

and $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty\$

d)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty\$

and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\$

80.

Describe the end behavior of the graph.

a)

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

and

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

b)

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

and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

c)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$ and

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

d)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$ and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

81.

$f\left(x\right)=x^3+x^2-24x+36$ has a minimum at which point

a)

(2.5, -2.1)

b)

(2.5, -3.1)

c)

(3.1, -2.1)

d)

(3.1, -2.5)

82.

$f\left(x\right)=x^3+x^2-24x+36$ has a maximum at which of the following?

a)

( -3.2, 90.3)

b)

(-4.2, 97.5)

c)

(-3.7, 97.5)

d)

(-3.9, 88.6)

83.

The given polynomial is decreasing over what interval?

a)

-3.2 < x < 2.5

b)

90.3 < x < -2.1

c)

2.5 < x < -3.2

d)

-2.1 < x < 90.3

84.

Use the graph to determine the zeros of this function.

a)

x = -6

b)

x = 1, x = -2

c)

x = 2, x = -3

d)

x = 1, x = -3

85.

A survey of 976 American households found that 32% of the households own two cars. Identify the the sample. {hint: a survey of what __)

a)

All American households

b)

976 American households

c)

32% of Americans own two cars

d)

two cars

86.

A survey of 976 American households found that 32% of the households own two cars. Identify the the population. {hint: which group was targeted... used for the survey}

a)

All American households

b)

976 American households

c)

32% of Americans own two cars

d)

two cars

87.

A survey of 1000 patients at Emory hospital found that 40% cases are heart disease treatment. Identify the population

a)

All Emory hospital patients

b)

1000 Emory hospital patients

c)

40% cases

d)

40 hear disease cases.

88.

A survey of 1000 patients at Emory hospital found that 40% cases are heart disease treatment. Identify the sample.

a)

All Emory hospital patients

b)

1000 Emory hospital patients

c)

40% cases

d)

40 hear disease cases.

89.

Like or dislike of math

a)

categorical

b)

numerical

c)

data that changes over time

90.

Number of teeth lost

a)

categorical

b)

numerical

c)

data that changes over time

91.

How many chemical engineers chose Science as their favorite subject?

a)

80

b)

91

c)

171

d)

262

92.

Of the mechanical engineers, what is the probability that math is their favorite subject?

a)

1.91

b)

52%

c)

17%

d)

35%

93.

True or false:

The most popular season among 8th graders was summer.

a)

true

b)

false

94.

Find the class grade for a student with grades: Test 89%, Quiz 92, Homework 86%, and Classwork 95%.
Tests are 60% of the grade, Quiz 15%, Homework is 10% of the grade, and Classwork is 15% of the grade.

a)

89.25

b)

91.55

c)

90.05

d)

i don't know

95.

Roger bowled 7 games last weekend. His scores are: 155, 165, 138, 172, 127, 193, 142. What is Roger's median score?

a)

127

b)

155

c)

156

d)

193

96.

What is the the 1st Quartile of the data set: 2, 7, 8, 3, 9, 8, 12

a)

3

b)

8

c)

2

d)

12

97.

What is the 3rd Quartile of the data set: 2, 7, 8, 3, 9, 8, 12

a)

3

b)

7

c)

9

d)

12

98.

What data value is the upper quartile (Q3)?

a)

64

b)

62

c)

66

d)

58

99.

33, 25, 42, 25, 31, 37, 46, 29, 38
What is the third quartile (UQ) of the data?

a)

37

b)

38

c)

40

d)

46

100.

Find the interquartile range using the following.
Minimum: 1
Q1: 3
Median: 5
Q3: 7
Maximum: 9

a)

8

b)

4

c)

5

d)

10

101.

Find the IQR (interquartile range) using the following information.
Minimum: 77
Q1: 79.5
Median: 86.5
Q3: 90.5
Maximum: 99

a)

86.5

b)

22

c)

90.5

d)

11

102.

Find the median, first quartile, third quartile, and interquartile range of the data.

203, 183, 212, 181, 157, 204, 189, 190

a)

Median: 189

First Quartile: 182

Third Quartile: 203

IQR: 21

b)

Median: 189.5

First Quartile: 182

Third Quartile: 203

IQR: 21

c)

Median: 189

First Quartile: 182

Third Quartile: 203.5

IQR: 21.5

d)

Median: 189.5

First Quartile: 182

Third Quartile: 203.5

IQR: 21.5

103.

Use the interquartile range to identify any outliers in the following data.

23, 22, 25, 16, 27, 43, 29, 40, 35

a)

No outliers.

b)

43 is an outlier.

104.

Use the interquartile range to identify any outliers in the following data.

52, 63, 55, 56, 62, 54, 59, 60, 53, 61, 88

a)

No outliers.

b)

88 is an outlier.

105.

Given the data set {1, 3, 5, 6, 8, 9, 11, 13, 15, 18, 20, 23}.

Evaluate $\sum_{x=2}^5-\sum_{x=7}^{10}$

a)

17

b)

-35

c)

-17

d)

35

106.

How many students have more than 1,000 songs on their MP3 player?

a)

5

b)

16

c)

10

d)

4

107.

21. How many students are represented by the histogram?

a)

Cannot be determined

b)

9

c)

31

d)

35

PreCalc Semester One Exam Review

Total questions: 107

Worksheet time: 4hrs 39mins

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