Free Printable Math 4 - Mid-Term Review

1.

Which of the following is NOT a maximum of the graph?

a)

(-5, 1)

b)

(4, 1)

c)

(0, 3)

d)

(-3, -2)

2.

Convert to logarithmic form: $3^x=27$

a)

$\log_x27=3$

b)

$\log_3x=27$

c)

$\log_327=x$

d)

$\log_{27}x=3$

3.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

4.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

5.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

6.

Convert to exponential form: $\log_8\left(\frac{1}{64}\right)=-2$

a)

$-2^8=\frac{1}{64}$

b)

$\left(\frac{1}{64}\right)^{-2}=8$

c)

$8^{-2}=\frac{1}{64}$

d)

$\left(\frac{1}{64}\right)^8=-2$

7.

Condense

\log5-\log4

a)

$\log\left(5-4\right)$

b)

$\log\left(\frac{4}{5}\right)$

c)

$\log\left(\frac{5}{4}\right)$

d)

$\log\left(5^{-4}\right)$

8.

Condense

\log_3x+2\log_3y

a)

$\log_3\left(x+2y\right)$

b)

$\log_3\left(xy^2\right)$

c)

$\log_3\left(x\cdot2y\right)$

d)

$2\log_3xy$

9.

$\log_6\ \left(x\ +\ 8\right)\ +\ \log_{6\ }\left(x\ +\ 9\right)\ =\ 1$

a)

-11, -17

b)

-6, -17

c)

-6

d)

-11

10.

$\log_3\ \left(4x^2\ -\ 8\right)\ -\ \log_3\ 4\ =\ \log_{3\ }47$

a)

7, -7

b)

-2, 2

c)

16

d)

-1, 1

11.

Middletown High School has student elections every year. Lately, the school has seen a 5% decrease in voting from election to election. If 910 students voted this year, how many will be expected to vote 8 years from now? (Round to the nearest whole number if necessary).

a)

604

b)

777

c)

29

d)

198

12.

A publishing industry report predicts that magazine subscriptions will drop by 10% each year. If this prediction is correct, then how many subscribers will a magazine with 98,000 subscribers have in 10 years? (Round to the nearest whole number if necessary).

a)

34,170

b)

16,348

c)

7690

d)

76,023

13.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

14.

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

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

15.

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

a)

19

b)

23

c)

-10

d)

None of these.

16.

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

a)

16

b)

4

c)

-4

d)

None of these.

17.

a)

6

b)

8

c)

15

d)

None of the Above

18.

a)

7

b)

6

c)

11

d)

None of the Above

19.

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

a)

y=1400(1.09)^x

b)

y=1.09(1400)^x

c)

y=1400(.91)^x

d)

y=1.09^x

20.

The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?

a)

29 to 30 years

b)

23 to 24years

c)

15 to 16 years

d)

19 to 20 years

21.

Which graph matches:

-x+4 if x < 2

2x-6 if x ≥ 2

a)

A

b)

B

c)

C

d)

D

22.

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

23.

(3 + 2i) + (4 - 5i)

a)

7 + 7i

b)

1 - 3i

c)

1 - 7i

d)

7 - 3i

24.

Simplify
3i - (4 + 7i)

a)

-4 + 10i

b)

21 - 12i

c)

4 - 10i

d)

-4 - 4i

25.

Choose the correct answer for the operation pictured.

a)

7-13i

b)

7-i

c)

1-13i

d)

1-i

26.

(3 + 8i)(-2 - i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

27.

The expression (2 + 3i)² is equal to

a)

-5

b)

-5 + 12i

c)

13

d)

13 + 12i

28.

Simplify:
(10+ 15i)-(48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

29.

(3 + 8i)(-2 - i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

30.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

31.

Find A+B

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

32.

What do w, x, y and z equal in this matrix subtraction?

a)

w = 13, x = 4, y = 7, z = 23

b)

w = 13, x = -4, y = 11, z = 23

c)

w = 13, x = 4, y = 11, z = 23

d)

w = 13, x = 4, y = 11, z = 17

33.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

34.

find: B*A

a)

47 30
9 5

b)

17 15
42 35

c)

10 25
7 1

d)

not possible because rows do not match columns

35.

What do a, b, c and d equal in this matrix addition?

a)

a = -1, b = 10, c = 7, d = -11

b)

a = -1, b = 10, c = -11, d = 7

c)

a = 10, b = -1, c = 7 , d = -11

d)

a = 10, b = -1, c = -11, d = 7

36.

Which equation would you use to find

f\left(29\right)

a)

Top

b)

Middle

c)

Bottom

37.

Which equation would you use to find

f\left(-5\right)

a)

Top

b)

Middle

c)

Bottom

38.

Please find

f\left(-6\right)

a)

5

b)

22

c)

-9

d)

undefined

39.

Please find

f\left(0\right)

a)

0

b)

-4

c)

-9

d)

-8

40.

Given f(x) = 2x and
g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

41.

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

a)

-42

b)

-26

c)

-18

d)

None of these.

42.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

Math 4 - Mid-Term Review

Total questions: 42

Worksheet time: 4hrs 30mins

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