Free Printable Overall Final Exam Review

1.

What is the simplifies form of (11 – 7i) – (–3 + 12i)

a)

8 – 19i

b)

8 + 5i

c)

13 – 19i

d)

14 –19i

2.

Multiply:

(4 – 3i)(–7 – 2i)

FYI - your calculator can do this one :)

a)

–23 + 13i

b)

–23 – 29i

c)

–34 + 13i

d)

–34 – 29i

3.

Find the product.

a)

b)

c)

d)

No Product Exists

4.

Find the product.

a)

Not possible.

b)

-3 16

17 12

8 -10

c)

3 12

-15 -8

-1 -3

5.

Subtract

a)

-5
-8
3
10

b)

-9
8
3
2

c)

5
-8
3
10

d)

-5
8
3
2

6.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

7.

What is the RANGE of the function?

a)

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

b)

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

c)

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

d)

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

8.

Which graph matches:

-x+4 if x < 2

2x-6 if x ≥ 2

a)

A

b)

B

c)

C

d)

D

9.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

10.

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

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

11.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\sqrt{x}$ find $g\left(f\left(x\right)\right)$

a)

$x^4$

b)

$x$

c)

$\sqrt[]{x}$

d)

$x^2$

12.

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

a)

2

b)

15

c)

7

d)

-9

13.

What is the equation of this table?

a)

y=512(1/4)^x

b)

y=32(4)^x

c)

y=32(1/4)^x

d)

y=512(4)^x

14.

find the asymptote: y = log₁₀ (x+3)

a)

x=-3

b)

x=3

c)

y=-3

d)

y=3

15.

Find the asymptote of the following: y = log₁₀x - 6

a)

x=6

b)

x=-6

c)

x= 0

d)

y=0

16.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

17.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

18.

Rewrite the equation into logarithmic form:
6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

19.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

20.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

21.

Write in logarithmic form

2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

22.

log₅25 = ?

a)

2

b)

5

c)

125

23.

$Evaluate\ \log_5\sqrt{5}$

(a)

24.

What is the x-intercept of log₇(x)?

a)

(2, 0)

b)

(-1, 0)

c)

(0, 1)

d)

(1, 0)

25.

Identify the Law of Sines

a)

$\sin^2x+\cos^2x=1$

b)

$\frac{\sin\left(A\right)}{a}=\frac{\sin\left(B\right)}{b}=\frac{\sin\left(C\right)}{c}$

c)

$\sin\left(A\right)\sin\left(B\right)\sin\left(C\right)=1$

d)

Soh Cah Toa

26.

Calculate the length of AC

a)

30

b)

24

c)

27

d)

35

27.

x² - 9

a)

(x + 3) (x - 3)

b)

(x - 3) (x - 3)

c)

(x + 3) (x - 6)

d)

Can't factor using Diff. of Squares

28.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

2secθ

b)

cot²θ

c)

tan²θ

d)

sec²θ + 1

29.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

30.

What is the domain and range of y=sinx?

a)

D: (-∞, ∞)
R: [-1, 1]

b)

D: (-∞, ∞)
R: [-π, π]

c)

D: (∞, -∞)
R: [-1, 1]

d)

D: (-∞, ∞)
R: [-∞, ∞]

31.

what is the amplitude of y=3sin(7x)-2

a)

7

b)

-2

c)

3

d)

6

32.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

33.

What is the phase shift for the function

f(x) = -2sin(4x + π) - 1

a)

π right

b)

π/4 left

c)

2π right

d)

π left

34.

What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

35.

Find angle Z

a)

20.15°

b)

71.23°

c)

51.06°

d)

57.71°

36.

Find XZ

a)

16.004 meters

b)

544.165 meters

c)

34.7 meters

d)

1204.165 meters

37.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

38.

(a)

39.

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

a)

(114.5, 125.6)

b)

(113.8, 127.4)

c)

(112.52, 127.68)

d)

(114.56, 125.64)

40.

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, 0.192)

b)

(0.136, 0.204)

c)

(0.144, 0.196)

d)

(0.139, 0.201)

41.

The questions on a multiple choice test each have 6 answer choices. Which model can be used to simulate randomly selecting the correct answer on a 20 question multiple choice test?

a)

rolling a six-sided number cube 6 times

b)

rolling a six-sided number cube 20 times

c)

spinning a spinner with 4 equal sized sections 4 times

d)

choosing 1 marble in a bag of 20 different colored marbles

42.

What shape is a normal distribution curve?

a)

Half curve

b)

Round curve

c)

Bell curve

d)

Square curve

43.

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What proportion of weeks would you expect to have more than 7 accidents? Assume the data is a normal distribution.

a)

0.3446

b)

0.2856

c)

0.4

d)

0.6554

44.

Barry Bonds has a career batting average of .298. What is the probability that he will get on base 6 times in 10 at bats?

a)

3.57%

b)

5.46%

c)

22.67%

d)

100%

45.

The student who makes the morning announcements has the bad habit of saying “like” all the time. The chance that they say “like” in a sentence is 60%. You decide to keep a tally of how many times they say like. If they say 350 sentences this week, what is the probability that they will say “like” at least 200 times?

a)

0.87

b)

0.13

c)

0.85

d)

0.15

46.

Find the mean (expected value) of the probability distribution.

a)

85

b)

83.2

c)

87.1

d)

84.4

47.

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household?

a)

2.00

b)

2.13

c)

1.97

d)

1.27

Overall Final Exam Review

Total questions: 47

Worksheet time: 8hrs 50mins

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