Free Printable Math 4 - Practice Final Exam

1.

Describe how the graph of

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

translates to

f\left(x\right)=\left(x-5\right)^{2\ }+8

a)

down 5, right 8

b)

up 5, down 8

c)

left 5, up 8

d)

right 5, up 8

2.

Find the domain of the given graph

a)

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

b)

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

c)

$\left(-\infty,6\right]$

d)

$\left[-2,6\right]$

3.

Which of the following graphs shows a linear function?

a)

b)

c)

d)

4.

Which of the following is a graph of a quadratic function?

a)

b)

c)

5.

Match the parent function shown with its equation.

LINEAR

a)

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

b)

$f\left(x\right)=x^2$

c)

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

d)

$f\left(x\right)=\left|x\right|$

e)

$f\left(x\right)=\sqrt{x}$

6.

Match the parent function shown with its equation.

SQUARE ROOT

a)

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

b)

$f\left(x\right)=x^2$

c)

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

d)

$f\left(x\right)=\left|x\right|$

e)

$f\left(x\right)=\sqrt{x}$

7.

Match the parent function shown with its equation.

CUBIC

a)

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

b)

$f\left(x\right)=x^2$

c)

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

d)

$f\left(x\right)=\left|x\right|$

e)

$f\left(x\right)=\sqrt{x}$

8.

Match the parent function shown with its equation.

CONSTANT

a)

$f\left(x\right)=c$

b)

$f\left(x\right)=x^2$

c)

$f\left(x\right)=a^x$

d)

$f\left(x\right)=\left|x\right|$

e)

$f\left(x\right)=\sqrt{x}$

9.

Match the parent function shown with its equation.

QUADRATIC

a)

$f\left(x\right)=c$

b)

$f\left(x\right)=x^2$

c)

$f\left(x\right)=a^x$

d)

$f\left(x\right)=\left|x\right|$

e)

$f\left(x\right)=\sqrt{x}$

10.

Match the parent function shown with its equation.

ABSOLUTE VALUE

a)

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

b)

$f\left(x\right)=x^2$

c)

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

d)

$f\left(x\right)=\left|x\right|$

e)

$f\left(x\right)=\sqrt{x}$

11.

Match the parent function shown with its equation.

EXPONENTIAL

a)

$f\left(x\right)=c$

b)

$f\left(x\right)=x^2$

c)

$f\left(x\right)=a^x$

d)

$f\left(x\right)=\left|x\right|$

e)

$f\left(x\right)=\sqrt{x}$

12.

Find $g\left[f\left(1\right)\right]$

from the given graphs

a)

1

b)

-1

c)

0

d)

5

13.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

14.

What is f when x equals 4?

a)

-5

b)

0

c)

3

d)

6

15.

A piecewise function (f(x)) is shown in the graph. What is f when x equals -4?

a)

-4

b)

-2

c)

0

d)

Does not exist

16.

A piecewise function (f(x)) is shown in the graph. What is f when x equals 0?

a)

-4

b)

0

c)

1

d)

Does not exist

17.

$f\left(x\right)=2x+5$ and $g\left(x\right)=x-7$
Find $f\left(g\left(5\right)\right)$

a)

-1

b)

1

c)

8

d)

9

18.

$f\left(x\right)=x-3$ and $g\left(x\right)=2x+6$
Find $g\left(f\left(-1\right)\right)$

a)

-2

b)

-1

c)

1

d)

16

19.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

20.

Solve log(x) + log(x+3) = 1

a)

5

b)

-2

c)

-5

d)

2

21.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

22.

log₂(x²- 6) = log₂(2x+2)

a)

4, -2

b)

No Solution

c)

4

d)

-2

23.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

24.

log(4x) - log(4) = log(12)

a)

12

b)

4

c)

10

d)

100

25.

Simplify

$\cot\theta\tan\theta$

a)

sin²θ/cos²θ

b)

1

c)

0

d)

cos²θ/sin²θ

26.

Simplify

$\cot^2\theta\left(1+\tan^2\theta\right)$

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

27.

Simplify

$\tan x\csc x\cos x$

a)

1/cos x

b)

1

c)

cot x

d)

-1

28.

Find AB

a)

10

b)

8

c)

6.1

d)

4.9

29.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

30.

Use the Law of Sines to solve for BC

a)

33

b)

24

c)

12

d)

29

31.

Find angle Z

a)

20.15°

b)

71.23°

c)

51.06°

d)

57.71°

32.

The amplitude of $y=5\sin\left(2\theta\right)$ is ________.

a)

$-5$

b)

$5$

c)

$2\pi$

d)

$\frac{\pi}{2}$

33.

The period of $y=5\sin\left(2\theta\right)$ is ________.

a)

$2$

b)

$\pi$

c)

$2\pi$

d)

$\frac{\pi}{2}$

34.

Find the interquartile range?

a)

8

b)

6

c)

5

d)

4

35.

What is the standard deviation for the data given:

5, 10, 7, 12, 0, 20, 15, 22, 8, 2

a)

6.89

b)

10.1

c)

7.26

d)

9

36.

Find the mean of these numbers:
5,11,2,12,4,2

a)

4.1

b)

6

c)

4.5

d)

4

37.

Find the median of these numbers:
4, 2, 7, 4, 3

a)

2

b)

5

c)

7

d)

4

38.

The lifespan of radios is normally distributed with a mean of 15.2 years and a standard deviation of 5 years. 5% of the radios last longer than k years. Find the value of k.

a)

≈23.4 years

b)

≈19.8 years

c)

≈36.1 years

d)

≈15.2 years

39.

In the city of Longskank, the mean adult weight is 62kg and the standard deviation is 10kg. Assuming that the weight of adult males is normally distributed, find the probability that an adult chosen at random weighs between 62kg and 85kg?

a)

0.489

b)

0.511

c)

0.326

d)

0.296

40.

Clara discovers that the height of sunflowers in a farmer's field is normally distributed with mean 130 cm and standard deviation 15 cm.

Using the familiar portions of 1, 2, 3 standard deviations, approximately what proportion of the sunflowers will be taller than 160 cm?

a)

10%

b)

5%

c)

2.5%

d)

25%

41.

The average cost for a gallon of gasoline is $2.51 (source AAA.org) with a standard deviation of $0.42. Find the mean and standard error of the sampling distribution if n = 49

a)

μ_x-bar = 2.51, σ_x-bar = 0.06

b)

μ_x-bar = 0.358, σ_x-bar = 0.06

c)

μ_x-bar = 2.51, σ_x-bar = 0.857

42.

The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees. What is the z-score for a temperature of 17 degrees?

a)

1

b)

1.43

c)

-1.43

d)

11.5

43.

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p-hat be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. Suppose this claim is true.
What is the mean of the sampling distribution of p-hat?

a)

0.4

b)

0.44

c)

0.56

d)

0.6

44.

30% of all dogs in a city are micro-chipped. In a sample of 500 dogs, what is the probability that less than 140 dogs are micro-chipped? Select the closest option.

a)

0.25

b)

0.21

c)

0.17

d)

0.13

45.

A test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions.
What is the probability of getting exactly 6 questions correct on this test?

a)

0.6%

b)

0.00001%

c)

0.0064%

d)

0.0002%

46.

A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000?

a)

0.001 < p < 0.005

b)

0.566 < p < 0.693

c)

0.148 < p < 0.252

d)

0.023 < p < 0.045

47.

A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet?

a)

0.321 < p < 0.379

b)

0.316 < p < 0.384

c)

0.309 < p < 0.391

d)

0.305 < p < 0.395

48.

A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse?

a)

0.148 < p < 0.192

b)

0.136 < p < 0.204

c)

0.144 < p < 0.196

d)

0.139 < p < 0.201

49.

A researcher at a major hospital wishes to estimate the proportion of the adult population of the U.S. that has high blood pressure. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%?

a)

9

b)

271

c)

164

d)

542

50.

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?

a)

(0.621, 0.780)

b)

(0.591, 0.812)

c)

(0.584, 0.830)

d)

(0.615, 0.805)

Math 4 - Practice Final Exam

Total questions: 50

Worksheet time: 2hrs 25mins

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