Name
Class
Date
Chapter 1 Test
Form K
Do you know HOW?
Identify a pattern and find the next three numbers in the pattern.
1. 25, 21, 3, 7, c
Each term is 4 more than the previous
term; 11, 15, 19
2. 64, 32, 16, 8, c
Each term is half of the previous
term; 4, 2, 1
3. What properties of real numbers are illustrated by each equation below?
a. 28 1 3 5 3 1 (28) Commutative Property of Addition
b. 4 1 (24) 5 0 Inverse Property of Addition
c. 2(8 1 t) 5 2 ? 8 1 2 ? t Distributive Property
7
8
d. 8 ? 7 5 1 Inverse Property of Multiplication
Evaluate the expression for the given value of the variable.
4. a2 2 2(a 1 1); a 5 3 1
5. 5(2s 2 1) 2 3(s 1 2); s 5 4 17
6. The expression 15 1 5x models the daily cost in dollars of renting scuba gear
from the water sports store. In the expression, x represents the number of
hours the scuba gear is used. What is the cost of renting scuba gear for a day
when the gear is used for 3 hours? $30
Solve each equation.
7. 2r 1 2 5 3r 2 5 7
8. 8(t 1 1) 5 64 7
Solve each equation for x. State any restrictions on the variables.
9.
xt 2 1
135a
8
10.
x 5 8a 2t 23 ; t u 0
6x 2 1
5y
5
x5
5y 1 1
6
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Chapter 1 Test (continued)
Form K
Write an equation and solve the problem.
11. Two buses leave Columbus, Ohio at the same time and travel in opposite
directions. One bus averages 55 mi/h and the other bus averages 48 mi/h.
When will they be 618 mi apart? 6 h
Solve each inequality. Graph the solution.
13. 2a 1 5 , 6a 1 1 a S 1
12. 2n 1 1 $ 7 n L 3
0
1
2
3
4
5
6
0
1
2
3
4
5
6
Solve each compound inequality. Graph the solutions.
14. 3x # 26 or 2x 1 1 $ 3 x K 22 or x L 115. 22t 1 2 , 4 and 2t , 6 21 R t R 3
⫺3 ⫺2 ⫺1
0
1
2
⫺3 ⫺2 ⫺1
3
0
1
2
3
Solve each equation. Check for extraneous solutions.
16. u 3x 1 3 u 5 18 x 5 5 or x 5 27
17. u b 1 2 u 5 2b b 5 2
18. The weatherman announced that the temperature T over the next few weeks
will be at least 648F and at most 788F. Write an absolute value inequality for the
temperature over the next few weeks. »T 2 71… K 7
Do you UNDERSTAND?
19. What is another name for the multiplicative inverse? reciprocal
20. Reasoning Explain in words why 2 u x u , 24 has no solution.
Answers may vary. Sample: Dividing both sides by 2 gives |x| R 22. The absolute value
of any number must be nonnegative, so the inequality has no solution.
21. Open-Ended What is the difference between simplifying an expression and
evaluating an expression?
Answers may vary. Sample: Simplifying an expression is rewriting it using the
properties of real numbers and combining like terms, resulting in a simpler expression.
Evaluating an expression is substituting values for the variables, resulting in a
numerical value.
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Chapter 2 Test
Form K
Do you know HOW?
Determine whether each relation is a function.
1. 5(0, 2), (4, 3), (5, 5), (4, 7)6
no
2. 5(21, 0), (25, 2), (0, 4), (2, 28)6
yes
Evaluate each function for the given value of x, and write the input x and output
f(x) as an ordered pair.
1
3. f (x) 5 7x 1 5 for x 5 22 (22, 29)
4. f (x) 5 4 x 2 6 for x 5 8 (8, 24)
For each function, determine whether y varies directly with x. If so, find the
constant of variation, and write the function rule.
5.
x
y
3
12
20
32
5
8
6.
yes; k 5 4; y 5 4x
x
y
6
11
14
20
9
15
no
Graph each equation.
7. 4x 2 3y 5 22
8. 3 1 x 1 y 5 0
y
y
2
2
O
2
x
2
x
2
4
Write in point-slope form an equation of the line through each pair of points.
9. (5, 8) and (0, 22)
y 2 8 5 2(x 2 5) or
y 1 2 5 2(x 2 0)
10. (1, 3) and (6, 22)
y 2 3 5 2(x 2 1) or
y 1 2 5 2(x 2 6)
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Chapter 2 Test (continued)
Form K
Write the function rule g(x) for the given transformations applied to the graph
of f (x) 5 x2.
11. 4 units down,
12. 7 units up,
1 unit left
3 units right
g( x) 5 (x 1 1)2 2 4
g( x) 5 (x 2 3)2 1 7
Graph each equation. Then describe the transformation from the parent
function f (x) 5 |x|.
13. y 5 |x 2 2|
14. y 5 2|x|
y
y
translation 2 units right
x
4
4 2
2
4
2
2
2 O
O
reflection in the x-axis
2
4
4x
Graph each absolute-value inequality.
15. y , u 3x u 1 1
y
16. y 2 3 $ u x 1 5 u
y
4
6
4
2
2 O
2
2
x
x
6 4 2 O
Do you UNDERSTAND?
17. If y varies directly with x and y 5 18 when x 5 6, what is the constant of
variation? Find the value of y when x 5 10.
k 5 3; y 5 30
18. Open-Ended Graph a line that has a slope that is undefined.
Answers may vary. Sample: a graph of any vertical line
Size (ft2)
Price
35
48
80
120
192
200
320
$1.39
$1.99
$3.19
$4.79
$7.69
$7.99
$12.79
19. Suppose you manufacture and sell tarps. The table at the right
displays your current sizes and prices.
a. Draw a scatter plot showing the relationship between the area
of a tarp and its price. Use area as the independent variable.
b. Draw a trend line and write the equation.
c. Reasoning Is this an accurate model? Explain.
d. Using your model, predict the price of a 250 ft2 tarp.
b. Equations should be close to y 5 0.04x 1 0.02
c. Yes; all the points are very close to the line, so the
linear model is accurate.
d. about $10.02
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14
12
8
4
y
x
100 200 300
Name
Class
Date
Chapter 3 Test
Form K
Do you know HOW?
Solve each system by substitution or elimination.
1. e
2x 2 y 5 7
6x 2 3y 5 14
2. e
no solution
5x 1 2y 5 12
26x 2 2y 5 214
(2, 1)
3. e
5x 1 2y 5 28
4x 1 3y 5 2
(24, 6)
Graph the solution of each system.
4. e
y $ 22x 1 3
y,x
5. e
y 2 1 # 3x
y11#x
y
y . 2x 1 4
y # 2x 1 1
y
2
⫺4 ⫺2
⫺2
6. e
y
6
2
x
⫺4 ⫺2
4
⫺4
2
x
4
4
2
⫺4
⫺2
x
2
4
7. You have 13 bills in your wallet in $1, $5, and $10 bills. There are twice as
many $1 bills as $5 bills. The number of $10 bills is one more than the number
of $5 bills. How many of each bill do you have? How much money do
you have? six $1 bills, three $5 bills, four $10 bills; $61
Graph the system of constraints. Identify all vertices. Find the values of x and y
that maximize or minimize the objective function. Then find the maximum or
minimum value.
y
6
y # 2x 1 7
8. • 4y # x 1 8
x $ 0, y $ 0
C(4, 3)
4
B(0, 2)
Maximize for P 5 5x 1 2y
A(0, 0)
x
2
4
6 D(7, 0)
max P at (7, 0) 5 35
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Chapter 3 Test (continued)
Form K
2 21
2 12
9. What is the solution of the system represented by the matrix? C 3
2 21 † 0 S
21 23
2 11
(24, 1, 3)
(1, 24, 3)
(3, 24, 1)
C
(1, 3, 24)
Do you UNDERSTAND?
10. Writing Explain how you determine whether a system of linear equations is
independent, dependent, or inconsistent without graphing the lines.
Rewrite both equations in slope-intercept form. If the lines have the same slope
and same y-intercept, then they are equations of the same line, and the system is
dependent. If the lines have the same slope but different y-intercepts, they are parallel
lines, and the system is inconsistent. If the lines have different slopes, then the system
is independent.
11. Mechanic A charges $45 for car repairs and $80 for each hour spent on your car.
Mechanic B charges $60 for repairs and $60 for each hour spent on your car.
a. If your car takes 5 hours to repair, which mechanic charges the least
money? Mechanic B
b. How much will it cost you to have the work done by the less expensive
mechanic? $360
12. At a bookstore, you spend $76 on 11 books and magazines. Books cost $8 each
and magazines cost $5 each. Write a matrix that represents this system. How
many books and how many magazines did you buy?
B
1 1 11
`
R ; 7 books, 4 magazines
8 5 76
13. Reasoning The sum of three numbers is 15. The second number is twice
the third number. Do you have enough information to determine the three
numbers? If so, what are the three numbers? If not, what information do you
still need? No; you need a third equation that defines another relationship
between two or three of the numbers.
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Date
Chapter 4 Test
Form K
Do you know HOW?
Identify the vertex, the axis of symmetry, the maximum or minimum value, and
the domain and the range of each function.
1. y 5 3(x 2 2)2 1 6
vertex 5 (2, 6); axis of symmetry x 5 2; minimum 5 6; domain 5 all real numbers;
range 5 all real numbers L 6
2. y 5 2(x 1 4)2 23
vertex 5 (24, 23); axis of symmetry x 5 2 4; maximum 5 23; domain 5 all real
numbers; range = all real numbers K 23]
y
3. y 5 2 x2 2 2x 1 3
4. y 5 3x2 2 4x 1 1
y
6
4
4
O
⫺10 ⫺4
⫺4
2
Factor each expression.
⫺4 ⫺2 O
⫺8
2 x
5. 4c2 1 4c 1 1
6. g2 2 49
(2c 1 1)2
(g 1 7)(g 27)
Use a graphing calculator to solve each equation. Give each answer to at most
two decimal places.
7. 5x2 1 9x 1 4 5 0
x 5 2 1 and x 5 2 0.8
8. 23x2 2 2x 1 7 5 0
x 5 1.2 and x 5 21.9
Complete the square.
9. x2 1 14x 1 j
49
10. x2 2 18x 1 j
81
Evaluate the discriminant for each equation. Determine the number of real
solutions.
11. 5x2 1 x 1 6 5 0
2119; 0 real solutions
12. 23x2 2 4x 1 1 5 0
28; 2 real solutions
Plot each complex number and find its absolute value.
13. 7 2 2i !53
8i imaginary axis
4i
14. 8i 8
8i imaginary axis
4i
real axis
⫺8 ⫺4 O
⫺4i
4
⫺8 ⫺4 O
⫺4i
7 ⫺ 2i
⫺8i
real axis
4
⫺8i
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x
Name
Class
Date
Chapter 4 Test (continued)
Form K
Find all solutions to each quadratic equation.
15. y 5 2x2 2 2x 1 5
3 1
3
1
1 i, 2 i
2
2 2
2
16. y 5 3x2 1 2x 1 4
2
Solve each system by graphing.
17. y . x2
d
6
y
18. y . x2 1 3x
d
4
y , 2 x2 1 4
2
4
2O
2
"11
"11
1
1
1
i, 2 2
i
3
3
3
3
x
2
6
4
y . x2 2 2
2
4
4
y
2O
2
x
2
Do you UNDERSTAND?
19. The parabolic path of a hit tennis ball can be modeled by the table at
the right. The top of the net is at (4, 10).
a. Find a quadratic model for the data. y 5 20.5x2 1 3x 1 4.5
b. Will the ball go over the net? If not, will it hit the net on the way up
or the way down? No; it will hit the net on the way down.
4
x
y
1
2
7
7
8.5
1
20. Writing Explain the relationship between the x-intercepts of quadratic
function and the zeros of a quadratic function.
They are the same thing because the x-intercepts are the x-coordinates where the
quadratic function equals zero.
21. The period of a pendulum is the time the pendulum takes to swing back and
forth. The function l 5 0.81t2 relates the length l in feet of a pendulum to the
period t.
a. If a pendulum is 30 ft long, what is the period of the pendulum in seconds? t 5 6.1 s
b. Reasoning Why does only one of the solutions work for this problem?
The other solution is negative and you cannot have negative time.
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Chapter 5 Test
Form K
Do you know HOW?
Write each polynomial in standard form. Then classify it by degree and by
number of terms.
1. 6x5 2 2x2 1 1 2 2x5
4x5 2 2x2 1 1; quintic trinomial
2. x2 2 3x 1 6x3 2 5x 1 1
6x3 1 x2 2 8x 1 1; cubic, 4 terms
Determine the end behavior of the graph of each polynomial function.
3. y 5 3x 1 2x2 2 4
up and up
4. y 5 4x3 2 7x 1 2
down and up
Find the zeros of each function. State the multiplicity of multiple zeros.
5. y 5 (x 1 2)(x 2 3)2
22 multiplicity 1; 3 multiplicity 2
6. y 5 x3 1 4x2
0 multiplicity 2; 24 multiplicity 1
Find the real solutions of each equation using a graphing calculator. Where
necessary, round to the nearest hundredth.
7. 5x3 2 2x2 2 1 5 0
0.75
8. 2x4 1 4x2 5 4
20.86, 0.86
Divide using long division. Check your answers.
9. (x2 1 6x 1 24) 4 (x 1 4)
x 1 2, R 16
10. (x3 1 2x2 1 4x 1 10) 4 (x 1 1)
x2 1 x 1 3, R 7
Write a polynomial function with rational coefficients so that P(x) = 0 has the
given roots.
12. 2i, !2
P(x) 5 x4 2 x2 2 2
11. 21, 2, 6
P(x) 5 x3 2 7x2 1 4x 1 12
Find all the zeros of each function.
13. y 5 x3 1 2x2 1 4x 1 8
22, 22i, 2i
14. y 5 x4 2 14x2 1 45
23, 3, 2"5, "5
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Chapter 5 Test (continued)
Form K
Expand each binomial.
15. (x 1 2)6
16. (2x 1 3)5
x6 1 12x5 1 60x4 1 160x3
1 240x2 1 192x 1 64
32x5 1 240x4 1 720x3 1 1080x2 1 810x 1 243
17. Find a cubic function to model the data in the table. Let x represent years after 1990.
Births in the United States
y N 20.00073332x3 1 0.0202x2 2 0.1407x 1 4.18
Determine the cubic function that is obtained from
the parent function y = x3 after each sequence of
transformations.
18. a vertical stretch by a factor of 3;
a reflection across the y-axis;
and a horizontal translation 4 units right
Year
1990
Births
(millions)
4.16
1995
3.89
2000
4.06
2005
4.14
SOURCE: www.cdc.gov
y 5 23(x 2 4)3
19. a reflection across the x-axis; a horizontal translation 2 units left; and a vertical
translation 6 units down
y 5 2(x 1 2)3 2 6
Do you UNDERSTAND?
20. The product of three integers is 56. The second number is twice the first
number. The third number is five more than the first number. What are the
three numbers?
2, 4, 7
21. What is P(2) given that P(x) 5 3x4 2 x3 1 2x2 2 10? Use synthetic division and
the Remainder Theorem.
P(2) 5 38
22. Open-Ended Write a polynomial function of degree 3 with rational
coefficients and exactly one real zero. List all of the zeros of the function.
Answers will vary. Sample: y 5 x3 2 3x2 1 5x 2 15; zeros: 3, i "5, 2 i "5
21. A cubic box is 4 in. on each side. If each dimension is increased by 2x in., what
is the polynomial function modeling the new volume V?
V 5 8x3 1 48x2 1 96x 1 64 in.3
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Chapter 11 Test
Form K
Do you know HOW?
1. Your brother is ordering 5 pizzas for the family. There are 18 different kinds of
pizza. How many different ways could he order 5 different kinds of pizzas? 8568 ways
A box contains 8 blueberry muffins, 6 banana muffins, and 4 pumpkin muffins.
You pick one muffin from the box at random. Find each theoretical probability.
2. P(banana) 1
3
4. P(banana or pumpkin) 59
3. P(not pumpkin) 7
9
1
1
2
5. J and K are independent events. P(J) = 4 and P(K) = 3 . Find P(J and K). 6
6. A company is testing a new sunscreen to see if it is more likely to cause skin
irritation that the sunscreen it currently sells. The results of the test are shown in the
contingency table.
Used new sunscreen
Used current sunscreen
Totals
Skin irritation
2
3
5
No skin irritation
38
37
75
Totals
40
40
80
The company decides to make and sell the new sunscreen. Based on the results of the
test, did the company make a good decision? Explain.
Answers may vary. Sample: Yes; about 2 out of 40 people who use the new sunscreen
have skin irritation, compared to about 3 out of 40 people who use the current
sunscreen. Based on this study, the new sunscreen is no more likely to cause skin
irritation than the current sunscreen, so the company made a good decision.
For Exercises 7 and 8, use the following data set: 27 35 32 25 36.
7. Find the mean, variance, and standard deviation for the data set.
31; 18.8; ≈ 4.85
8. Within how many standard deviations of the mean do all of the data values fall?
All of the values fall within 2 standard deviations of the mean.
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Chapter 11 Test (continued)
Form K
9. A team of biologists is studying the foxes in a state forest. The team captures 4 foxes,
weighs them, and then releases them. Which type of study method is described in this
situation? Should the sample statistics be used to make a general conclusion about the
population? observational study; Answers may vary: Sample: The sample size may be
too small for the sample statistics to be reliable as a general conclusion.
Find the probability of x successes in n trials for the given probability of success p
on each trial.
10. x 5 4, n 5 9, p 5 0.3
N 0.17
11. x 5 7, n 5 12, p 5 0.6
N 0.23
12. x 5 2, n 5 7, p 5 0.5
N 0.16
13. A set of data has a normal distribution with a mean of 36 and a standard deviation of 4.
What percent of the data are within the interval from 32 to 40? about 68%
Do you UNDERSTAND?
14. An alumni association compiled the following information about its recent
graduates.
• 20% graduated with a B average or better
• 95% of those students who graduated with a B average or better were
employed within 6 months of graduation
• 50% of those that graduated with less than a B average were employed
within 6 months of graduation
a. What is the probability that someone is employed within 6 months of
graduation, given that he had less than a B average? 0.50 or 50%
b. What is the probability that someone is not employed within 6 months of
graduation, given that she had a B average or better? 0.05 or 5%
15. Make a box-and-whisker plot for this set of values: 10 7 12 8 18 12 10 16.
4
6
8
10
12
14
16
18
16. Reasoning On a history test, there were 12 As, 8 Bs, 6 Cs and 1 D. Are the
numerical scores on the test likely to be normally distributed? Explain.
No; there are more As than any other test grade, so there are more high scores than
low scores. The data are likely skewed rather than normally distributed.
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Chapter 12 Test
Form K
Do you know HOW?
Find each sum or difference.
6
3
1 27
1. c
d 1 c
d
21 24
5 22
c
7 24
d
4 26
9 4
4 1
2. c
d 2 c
d
23 6
22 6
c
5 3
d
21 0
7 23
£ 29
8§
10 23
Find the value of each variable.
3 x
21 24
2 23
4. c
d 1 c
d 5 c
d
6 7
y
z
9
5
5. c
x 5 1; y 5 3; z 5 22
Find each product.
4 7 25
4
6. c
dc
d
21 2
3 26
c
1 226
d
11 216
2
3
5 26
3. £ 24
1 § 1 £ 25
7§
8 26
2
3
2x 1 4 10
10 2z
d 5 c
d
24y 25
16 25
x 5 3; y 5 24; z 5 5
7. c
c
5 23
2 4
dc
d
0
1 21 5
8. f1 3g c
4 25 1
d
2
3 6
f10 4 19g
13 5
d
21 5
Do you UNDERSTAND?
9. Writing Describe the matrix operations that you must use to solve the following
matrix equation. Then find the value of X.
4
1
22 22
2c
d 1 2X 5 c
d
2 23
22
4
First, multiply by the scalar 2. Then, use the Subtraction Property of Equality to isolate
the variable matrix. Subtract corresponding elements. Finally, multiply each side by 12
7 22
and simplify; X 5 c
d
23
5
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Chapter 12 Test (continued)
Form K
Do you know HOW?
Determine whether the following matrices are multiplicative inverses.
25 2
1 23
10. c
d, c
d
3 7
3
8
no
2 5
3 25
11. c
d, c
d
1 3
21
2
yes
4 3
1 21 12
12. c
d, £
§
2 2
21
2
yes
Use inverse matrices to find the solution of each matrix equation.
5 1
54
23 1
25 217
4 23
14
13. c
dX 5 c d
14. c
dX 5 c
d 15. c
dX 5 c
d
23 8
2
5 4
14
51
1 28
211
X 5 c
10
d
4
X 5 c
2 7
d
1 4
5
X5 c d
2
Use matrices to solve the following systems of equations.
4x 1 3y 5 7
16. e
22x 1 4y 5 24
x 1 20 5 23y
17. e
5x 5 4 2 2y
x 5 22; y 5 5
x 5 4; y 5 28
4y 1 2z 5 2
18. • 5z 5 20 1 3x
2x 1 3z 5 7 2 8y
x 5 5; y 5 23; z 5 7
Do you UNDERSTAND?
19. Roger and Clarissa each sold boxes of cookies for a fundraiser. They sold large
and small boxes for different prices. Roger sold 12 large boxes and 8 small
boxes for a total of $56.00. Clarissa sold 16 large boxes and 11 small boxes for a
total of $75.50. Use a system of two equations and matrices to find the price of
a large box and a small box. large: $3.00; small: $2.50
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