Name: ________________________ Class: ___________________ Date: __________
Algebra II-H Test Review 1-4 to 1-6
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. An absolute value equation ____ has an extraneous solution.
a. always
b. sometimes
c.
never
2. The theoretical probability of an event is ____ a negative number.
a. always
b. sometimes
c. never
Short Answer
Solve the equation.
3. |3x + 5| = 1
4. 3 |3x + 4| − 7 = 5
Solve the inequality. Graph the solution set.
5. 2 + 2k ≤ 8
6. 2(2m – 5) – 6 > –36
7. 4(3b – 5) < –31 + 12b
8. 2r – 9 ≥ –6
1
ID: A
Name: ________________________
ID: A
Solve the problem by writing an inequality.
9. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts.
Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at
least $100.
10. If the perimeter of a rectangular picture frame must be less than 200 in., and the width is 36 in., what must
the height h of the frame be?
Solve the compound inequality. Graph the solution set.
11. 5x + 10 ≥ 10 and 7x – 7 ≤ 14
12. 4x – 5 < –17 or 5x + 6 > 31
13. The perimeter of a square garden is to be at least 22 feet but not more than 36 feet. Find all possible values
for the length of its sides.
Solve the equation. Check for extraneous solutions.
14. 4 |4 − 3x| = 4x + 6
2
Name: ________________________
ID: A
Solve the inequality. Graph the solution.
15. | 2x + 3 | ≥ 19
16. | 2x + 10 | < 26
17. When Spheres-R-Us ships bags of golf balls, the number of balls in each bag must be within 6 balls of 300.
Write an absolute value inequality and a compound inequality for an acceptable number of golf balls b in
each bag.
18. Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of
tossing heads using Lynn and Dawn’s results?
19. A biologist has determined that a particular osprey has a 70% chance of catching a fish on any given day.
Carry out a simulation of twenty trials using the random number table below to find the probability that the
osprey will actually catch a fish on all of the next three days. Explain your method.
945
106
832
793
025
746
180
726
354
981
250
864
793
105
871
496
236
012
835
947
3
Name: ________________________
ID: A
20. This is a spinner used in a board game. What is the probability that the spinner will land on a multiple of 3
and 4?
21. A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability
of obtaining a number less than 2 or greater than 7 in a single spin?
22. A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P(red or blue).
23. If a dart hits the target at random, what is the probability that it will land in the shaded region?
4
Name: ________________________
ID: A
Essay
24. The manufacturing specification for a bolt calls for a tolerance of 0.2 cm and a length of 6 cm.
a.
b.
c.
Write the specification as an absolute value inequality.
Write the specification as a compound inequality.
An engineer selects two bolts to check the machine’s accuracy. One is 5.92 cm long and
the other is 6.21 cm long. Do these bolts fall within the specification?
25. Suppose 10 out of 25 students in your class have dogs for pets.
a.
b.
What is the theoretical probability that a student selected at random from your class has
a dog?
Using your result from part (a), predict how many dog-owning students you can expect
among the 200 students in your grade. Show your work.
5
ID: A
Algebra II-H Test Review 1-4 to 1-6
Answer Section
MULTIPLE CHOICE
1. B
2. C
SHORT ANSWER
1
3
3. x = −1 or x = −2
4. x = 0 or x = −2
2
3
5. k ≤ 3
6. m > –5
7. no solutions
8. r ≥ 1
1
2
9. 12x − (8x + 20) ≥ 100; x ≥ 30
10. h < 64 in.
11. x ≥ 0 and x ≤ 3
12. x < –3 or x > 5
13. 5.5 ≤ x ≤ 9
14. x =
5
8
or x =
11
4
1
ID: A
15. x ≤ −11 or x ≥ 8
16. –18 < x < 8
17. |b − 300| ≤ 6; 294 ≤ b ≤ 306
11
20
19. Using the digits 0–6 to represent a caught fish, the probability of catching a fish on each of the next three
days is 35%.
3
18.
20.
8
2
21.
5
5
22.
8
1
23.
16
ESSAY
24.
[4]
[3]
[2]
[1]
a. |L − 6| ≤ 0.2
b. 5.8 ≤ L ≤ 6.2
c. The 5.92-cm bolt falls within the specification, but the 6.21-cm bolt does not.
parts (a) and (b) correct but with incorrect or missing answer for (c)
parts (a) and (c) correct OR parts (b) and (c) correct
part (a) correct OR part (b) correct
[4]
a.
25.
10
2
, or
25
5
2
× 200 = 80
5
[3] part (a) correct, but minor computational error in part (b) or no work shown
[2] part (a) incorrect, but part (b) calculated using appropriate method
[1] part (a) correct
b.
2