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Chapter 1
1. Here are the first three figures of a pattern.
a.
List the numbers of line segments in Figures 1–7.
b.
Write a recursive formula that generates the sequence you found in
c.
How many line segments are in Figure 21?
d.
Which figure has 211 line segments?
part a.
2. Consider the sequence 0.01, 0.03, 0.09, 0.27, 0.81, ….
a.
Is the sequence arithmetic or geometric? Justify your answer.
b.
Write a recursive formula for the sequence. Use u1 to represent the
starting term.
c.
What is the 9th term of the sequence?
d.
Which term of the sequence is the first to be greater than 10,000?
3. A small country has a population of 2.5 million people. Each year about 4% of
the previous year’s population dies or leaves the country and about 120,000
people are born or immigrate to the country. If this pattern continues, what will
the population be in 5 years?
Chapter 3
1. Graph each linear equation
2
a. y  x  3
5
b. 2 y  6 x  4
2. Write the equation for each line.
a.
b.
3. Solve each system of equations (all answers are whole numbers, no
decimals)
a)
ì y = 3x +15
í
î y = -2x + 5
b)
ì3x + 2 y = 23
í
î-6 x + 8 y = 2
c)
ì-4 x = y +1
í
î12 x + 3 y = 3
Chapter 4
1. For each relation representation, say whether it is a function or not and
explain your answer.
d.
e.
f.
2 Use g(x) = (x – 4)2 -11 to find:
a. g(0)
b. g(5)
3. (4 points each) If f ( x)  3x  2 , g(x) = –2x2, and h(x) = (x– 2)2, find each
value.
a.
f(g(–2))
b.
h(g(5))
c.
h(f(9))
4. (3 points each) Answer each question for the graph of f(x) on the right.
a. What is the domain of the function?
b. What is the range of the function?
c. What is f(3)?
d. For what values of x does f(x) = 1?
5. Each of the graphs below represents a transformation of one of the
parents functions, y = x2 Write the equation for each graph.
a.
b.
c.
d.
Chapter 5
1. Simplify each radical expression. You can not use decimal answers.
20
a. 40
b. 8  2
c.
5
2.
Rewrite each expression as a fraction with positive exponents or as an
integer. Show work. Do not just give the answer.
a. 2
3
b.  
5
5
3
d. 4
3
c.  33
Rewrite each expression in the form b n in which n is a rational exponent.
(Put it in exponential form)
c. (5 x ) 3
a. b
b. 12 b8
3.
4.
Match all expressions that are equivalent. Every letter matches with only
one other letter.
4
a. y 4 / 7
b. y1 / 4
d. y 4
c. 1y
e.
4
y
f.

 y
4
g. y1.75
7
a. and ________ are equivalent
equivalent
h.
y
7
4
c. and _______ are
b. and ___________ are equivalent
equivalent
f. and _________ are
5.
Simplify each expression. Make sure there are no negative exponents.
2
b. a 3a 9
x
c. m3
a.  2
y
 
0

d. 3x 4  5 x 2
 28 x 3 

g. 
14
x



e.  8 x 2  6 x5
2
x   3x
3 4
h.

y 3  2 y 3
2 x  2 y 1
54 y 8
f.
6 y2
2
i.
9 y 2
x4
6.
Solve for x. Round all answers to the nearest hundredth.
5 x  5  5  30
1
a. 2 x 
b.
c. 6  2 x  6
8
x 7  50
d.
g.
4
x 3  27
e. x 5  5230
h.
x2 9
x 5  65
f.
i.
 x
5
3
 2523
j. 7 4 x  8  11  17
7. Rewrite each logarithmic equation in exponential form using the definition of
a logarithm. Then solve each equation.
a. log 100 = x
b. log71 = x
c. logx36 = 2
d. log2x = -3
e. log4
1
=x
16
8.
Rewrite each exponential equation in logarithmic form using the definition
of a logarithm.
a. 4x = 200
b. 0.6x = 20
c. 30x = 0.8
9.
Use the properties of logarithms to rewrite each expression in another
logarithmic form.
a. 4logb
b. log712
c. log10 – log3
d. log 6 12  log 6 3
Chapter 6
1. Simplify.
1 3  0 5 0  5
a. 



4 0  1 2 1  2
3 4    3 1 
b. 36  2  5 2  4

 

1 0    1 5 
 3 4 1 0 
c. 


 5 2 2  3
 3
d.  3 5 
5
 5  3 6 
e.   

 6   2  4
0
1
 1 0 

f.  1  5 
0  1

 0

3
2. Solve.
 2 0
 10 5 
a. 3
 2X  


  1 5
 0 17
4b  2  3 4d   11 2c  1 0
b.   4a
2
3    8
2
3

2 f  1 14 1   0 3g  2 1
Chapter 7
1. Determine whether each expression is a polynomial or not. If the
expression is a polynomial, state the leading coefficient and classify by
degree and number of terms.
4
5
a.  3  4 x  3.5 x 2  x 3
b. 5 p 4  3.5 p  2  16
9
p
c. 4 x 3  12
d. x 2 15  x  4 2
2. Simplify.
a. (5y2 + 7y) – (3y2 + 9y – 8)
b. (y2 + 9y)– (3y2 – 4y + 5)
c. 4x2 – 3(5x2 – 2x + 6)
d. (4x2 – 3)(5x2 – 2x + 6)
e. -3(x + 2)2
3. Factor.
a. 3r2 – 48
b. a2 – 8a + 12
c. 2x2 + 5x – 12
d. 4w2 – 9
4. Solve each equation.
a. x2 + 25 = 0
b. x2 + 5x = 24
c. 3x2- 21x + 3 = 0
d. 6x2 = 9x
e. 4x2 + 4x + 4 = 0
f. 5x2 + x + 2 = 0
g. -3x2 – 2x + 7 = 0
h. 2x2 + 6x + 12 = 0
i. x2 = -6x + 7
j. 0 = 3x2 – x + 3
k. -2x2 - 4x + 1 = 0
l. 6x = x2 + 9
5. Simplify each expression.
a.  16
b. 4  9  2
c. (4 – i) + (5 – 9i)
d. (2 + 3i)(8 – 5i)
e. (-3 + 2i) – (6 + i)
6. Graph each number on the complex
plane.
a. 7 – 2i
b. 8i
c. 4 + 8i
d. 5
e. 6 – 4i
f. -2 + 3i
f.
7  4i
10  2i
Chapter 10
1. Suppose you select a number at random from the sample space {1, 2, 3, 4, 5,
6, 7, 8, 9}. Find each theoretical probability.
a. P(a number that is a multiple of 5)
b. P(a number that is an integer)
c. P(a number that is a factor of twelve)
d. P(a number that is less than or equal to 4)
e. P(a number that is greater than 6)
f. (a number that is a composite number)
2. How many different orders can you choose to read six of the nine books on
your summer reading list?
3. How many ways are there to choose five shirts out of seven to take to camp?
4. How many ways can you choose two out of four kinds of flowers for a
bouquet?
5. How many different outfits can you make from 4 shirts, 3 ties, and 6 pants?
6. A bag contains 8 black marbles, 10 white marbles, and 2 red marbles.
Without replacement, you choose three marbles. Find the following probabilities.
a. P(3 black)
b. P(2 black, then 1 white)
c. P(1 of each)
d. P(2 red)
Chapter 12
Solve for each variable.
1.
3.
2.