Free Printable Review for CIA # 2 Advanced Algebra

1.

Solve for x.

3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

2.

Solve for x.

2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

3.

What is the original amount?

$y=1200\left(1+0.03\right)^t$

a)

Growth

b)

1200

c)

0.03

d)

Decay

4.

What is the rate of growth?

$y=1200\left(1+0.03\right)^t$

a)

Growth

b)

1200

c)

0.03

d)

Decay

5.

Marburn has 80 total students in our High School. It is projected to grow at rate of 2% every year. How many students will be in the High School in 5 years from now?

a)

72.3 students

b)

88.3 students

c)

199.1 students

d)

80 students

6.

The population of a town is decreasing at a rate of 5% per year. This year there are 10,000 people in this town, how many people will be left in 20 years from now? (round to the nearest whole number)

a)

26,533 people

b)

358 people

c)

1 person

d)

3,585 people

7.

The value of a book is $58 and depreciates at a rate of 7% per year. Write an exponential function to find the value of the book after 8 years. (Verbal Question: How do we know this is growth or decay?)

a)

f(t) = 58(0.93)^t; $32.46

b)

f(t) = 58(1.07)^t; $76.32

c)

f(t) = 58(0.93)^t; $34.26

d)

f(t) = 58(1.07)^t; $73.62

8.

The population of a small town is 1600 and is increasing at a rate of 3% per year. Write an exponential function to model this situation. Then find the population of the town after 10 years. (Verbal Question: How do we know this is growth or decay?)

a)

f(t) = 1600(1.03)^t; 2,150 people

b)

f(t) = 1600(0.97)^t; 1,738 people

c)

f(t) = 1600(1.03)^t; 2,128 people

d)

f(t) = 1600(0.97)^t; 1,819 people

9.

The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams would be left after 7.2 minutes has elapsed?

a)

100.0g

b)

50.0g

c)

12.5g

d)

8.5g

10.

A new online bank is offering customers a savings account that will compound interest continuously at a rate of 2.5%. Nick wants to deposit $20000 into this account. What amount should Nick expect to have after 4 years?

a)

$22103.42

b)

$31844.12

c)

$23456.09

d)

$2455.99

11.

Damara invests $3500 at 2% compounded continuously for 5 years. How much will she have in her account after 5 years?

a)

$3868.10

b)

$3886.10

c)

$3688.10

d)

$3286.10

12.

Match the graph with its equation

a)

y = log₅ (x + 1) + 1

b)

y = log₅ (x - 1) + 1

c)

y = log₅ (x²) + 1

d)

y = log₅ (x)-1

13.

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

14.

What is the x-intercept of log₇(x)?

a)

(0.5, 0)

b)

(-1, 0)

c)

(0, 0)

d)

(1, 0)

15.

Evaluate log₇ 343

a)

3

b)

49

c)

7

d)

1

16.

Condense into a single logarithm.

a)

A

b)

B

c)

C

d)

D

17.

Which type of function has a vertical asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

18.

Where is the asymptote?

a)

x=1

b)

x=-1

c)

y=1

d)

y=-1

19.

What is the domain?

a)

(-∞,∞)

b)

(0,∞)

c)

(1,∞)

d)

(-∞, 1)

20.

What is the range?

a)

(-∞,∞)

b)

(0.∞)

c)

(1,∞)

d)

(-∞, 1)

21.

Describe the transformation on $g\left(x\right)=\log_2\left(x-3\right)$

from the parent function $f\left(x\right)=\log_2\left(x\right)$

a)

The graph has been shifted 3 units up

b)

The graph has been shifted 3 units right

c)

The graph has been shifted 2 units right

d)

The graph has been shifted up units left

22.

Which graph corresponds to the exponential function $y=4^x$ ?

a)

b)

c)

d)

23.

For $f\left(x\right)=\left(\frac{1}{2}\right)^x$ , find the correct graph, asymptote, domain and range.

a)

b)

24.

What is the Range of this function?

a)

y> 0

b)

x> 0

c)

All Real Numbers

d)

y= 1

25.

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

26.

log₂(2) + log₂(8x) = 6

a)

x = 3

b)

x = 2

c)

x = 6

d)

x = 4

27.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

28.

Solve the equation. $\log_{11}\left(x^2-22\right)=\log_{11}\left(-x-2\right)$

a)

4,-5

b)

2,-5

c)

-7,-5

d)

-5

29.

Solve the equation $\log_4\left(8n-3\right)=\log_4\left(n^2+12\right)$

a)

4,3

b)

5,3

c)

5

d)

3

30.

Solve for x: $\log\left(x+9\right)+\log x=\log22$

a)

2, -11

b)

2

c)

-11

d)

11

31.

ln(9x-2)=ln(x+14)

a)

x=2

b)

x=.156

c)

x=-3

d)

x=0

32.

$y=\log_{ }\left(x-5\right)+2$

Write the inverse to the function above

a)

$y=\log\left(x-5\right)+2$

b)

$y=10^x+3$

c)

$y=10^{x-2}+5$

d)

$y=10^{x-2}-5$

33.

Graph

a)

A

b)

B

c)

C

d)

D

34.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

35.

Describe domain of the function shown: y=log₂(x+1)

36.

Match the following graphs with their domains

a)

1.

Domian: x > -2

b)

2.

Domian: x > 3

c)

3.

Domian: x > 0

d)

4.

Domian: x > 2

37.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

38.

To prove two functions are inverses of each other, both f(g(x)) and g(f(x)) should equal...

a)

1

b)

x

c)

0

d)

y

39.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

40.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

41.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

Review for CIA # 2 Advanced Algebra

Total questions: 41

Worksheet time: 3hrs 29mins

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