Free Printable Math 3 Spring Practice Final

1.

Which correctly describes the transformations as the parent function f(x) = sinx is changed to g(x) = 3sin(2x)?

a)

Translated 3 units up and the new period is twice as long

b)

Translated 3 units up and the new period is half as long

c)

The distance between the midline and relative maximums changes from 1 to 3; the new period is twice as long

d)

The distance between the midline and relative maximums changes from 1 to 3; the new period is half as long

2.

Theresa wants to know what type of calculator she should get to replace her off-brand one. She asks 30 different people around campus over the course of a week what type of calculator they prefer. This is an example of what type of statistical study?

a)

Survey

b)

Observational study

c)

Experiment

d)

None of these

3.

Amy is trying to argue for more points by claiming a test was too difficult. The scores on a recent test followed the normal distribution with a mean of 80 and standard deviation of 5. According to the empirical rule, what percent of students got an A (90% or above)?

a)

2.5%

b)

5%

c)

10%

d)

16%

e)

95%

4.

Amir conducted a survey in which a sample of 36 HS students said they get an average of 6 hours of sleep. The population standard deviation is known to be 1 hour of sleep. Construct the 95% confidence interval for the population mean.

a)

(5.67, 6.33)

b)

(5, 7)

c)

(5.83, 6.17)

d)

(5.84, 6.16)

5.

Which of the following are equivalent to this? Select all that apply.

a)

b)

c)

d)

e)

6.

Which of the following are correct solutions to 4^x= 3? Select all that apply.

a)

b)

c)

d)

e)

7.

Which of the following are coterminal with 45°? Select all that apply.

a)

225°

b)

-315°

c)

5π/4

d)

9π/4

8.

Which function creates this graph?

a)

2cos(4x)+1

b)

3cos(x/4)

c)

2cos(x/4)+1

d)

3cos(4x)+1

9.

Which of the following could simulate an event with 20% probability of success? Select all that apply.

a)

Roll a die: 1 is success, 2-5 are failure, 6 is re-roll.

b)

Draw a card: Ace and 2 are success, 3-10 are failure, J/Q/K are re-draw

c)

Use a random number generator: 0-2 are success, 3-9 are failure

d)

Flip 10 coins: if 2 are heads it is a success, anything else is failure.

10.

Find all the solutions 0 < x < 2π for this equation:

tan x = -1

a)

3π/4

b)

π/4

c)

5π/4

d)

π

e)

7π/4

11.

Solve

a)

A

b)

B

c)

C

d)

D

12.

A sample of 40 people owned an average of 1.35 apple products. It is known from a previous study that the population standard deviation of apple product ownership is 0.63 products. Construct a 95% confidence interval.

a)

(1.11, 1.58)

b)

(1.15, 1.55)

c)

(1.19, 1.51)

d)

(1.09, 1.61)

13.

Evaluate: $\cos\left(\frac{4\pi}{3}\right)$

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

14.

Evaluate:

\tan\left(\frac{5\pi}{3}\right)

a)

$\sqrt{3}$

b)

$-\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

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

15.

Which of the graphs below could be the graph of the first period for the function?
$f\left(x\right)=3\cos x-2$

a)

b)

c)

d)

16.

Which of the graphs below could be the graph of the first period for the function?
$f\left(x\right)=2\sin\left(x-\frac{\pi}{2}\right)$

a)

b)

c)

d)

17.

Which of the following are equivalent? Select all that apply.

a)

b)

c)

d)

18.

Abiha gets a $100 gift for her birthday which she responsibly deposits in a savings account that gives 3% interest compounded quarterly. To the nearest cent, what is the balance after 5 years?

a)

$1.64

b)

$116.12

c)

$116.18

d)

$180.61

19.

Garrett takes out a loan in order to buy tickets and airfare to see Game 5 of the Stanley Cup Finals. He borrows $1000 at a 15% interest rate compounded continuously. After how many years will it take the balance to double?

a)

0.10 years

b)

4.62 years

c)

6.67 years

d)

18.34 years

20.

Ariana heard that a new brand of baking soda causes cakes to become even fluffier. She makes two cakes, one with the old brand of baking soda and one with the new brand of baking soda and compares the fluffiness of the resulting cakes. What type of statistical study is this?

a)

Survey

b)

Observational study

c)

Experiment

d)

None of the above

21.

$\log_3\left(\frac{1}{9}\right)$ Evaluate:

a)

1/2

b)

2

c)

-2

d)

3

22.

condense into one logarithm $2\log_5\ a+\log_5\ b-4\log_5\ c$

a)

$\log_5\left(\frac{a^2b}{c^4}\right)$

b)

$\log_5\left(\frac{ab}{c}\right)$

c)

$\log_5\left(a^2+b-c^4\right)$

d)

$-2\log_5\left(a+b-c\right)$

23.

Write an equation for the cosine function with amplitude 3, period 2pi, phase shift of pi, and vertical shift of 5.

a)

y = 5cos(x - pi) + 3

b)

y = 3cos(x - pi) + 5

c)

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

d)

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

24.

Solve for x:

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

25.

Solve the equation such that $0\degree\le\theta<360\degree$

$2\sinθ+\sqrt{3}=0$

a)

$60\degree,240\degree$

b)

$30\degree,150\degree$

c)

$240\degree,300\degree$

d)

$210\degree,330\degree$

26.

a)

-1

b)

sin θ

c)

csc θ

d)

1

27.

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

28.

Solve: $2\sqrt{3}\sec\theta\ +\ 4\ =\ 0$
State all solutions in the interval [0, 2π)

a)

π /3, 2π/3

b)

2π /3, 4π/3

c)

π /6, 5π/6

d)

5π /6, 7π/6

29.

Solve: 4sinθ + 1 = 3

State all solutions in the interval [0, 2π)

a)

π/ 6, 7π/6

b)

π/6, 5π/ 6

c)

5π/6, 7π/6

d)

7π/6, 11π/6

30.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

31.

Match the graph with its equation

a)

y = log₆(-x) + 1

b)

y = log₆(x − 2) + 1

c)

y = log₆(x + 2) - 1

d)

y = log(x-8) + 1

32.

$\log_7\ \left(x\ +\ 4\right)\ -\ \log_{7\ }x\ =\ \log_{7\ }33$

a)

$\frac{1}{8}$

b)

$-\frac{60}{7}$

c)

No solution

d)

$\frac{68}{7}$

33.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

34.

Find the inverse of the function f(x)=5^(x+2)

a)

f^-1(x)=log₅(x-2)

b)

f^-1(x)=log₅(x)-2

c)

f^-1(x)=log₅(x)+2

d)

f^-1(x)=log₅(x+2)

Math 3 Spring Practice Final

Total questions: 34

Worksheet time: 2hrs 14mins

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