PreCalculus Review sheet for Chapter 3 Test
____________________
Name
I. Solve the following
1. 8x + 6 > 30
2.
8  11x
 13
4
3.
4. 2x (6x  1)  (3x  2)(4x + 3)
5.
4
1 1
2
5
 x    x   2x  
3
2 2
3
2
6. | x |  5
7. | x | >  2
8. | x  7 | > 3
9. | x + 2 | <  1
10. | x + 3 | = 7
11. | 3x  9 |  9
12. | 6  3x | < 12
13. 2 < | x |  4
14. 1  | x  4 |  3
15. | x | + | x  6 | > 7
16. ( x + 7 ) ( x + 9 ) > 0
17. ( 2x  5 )2 ( x + 3 ) ( x + 2 )  0
18. 2 – x 
19. 3x3 + 7x2  6x  0
20. b4  16 < 2x 2 – x
21.
2x
3  2x

3
5
II. Solve these harder inequalities
x 1
( x  1)( x  3) 2
( x  5) 2
 0
III. Graph the following
22.
x 2
y < 7
23.
3x  4y  8
|x|2
2y + 3x  8
1
y  x2  9
2
IV. Solve the linear programming problems
24. Every day Rhonda Miller needs a dietary supplement of 4 mg of vitamin A, 11 mg of vitamin B, and 100 mg of vitamin C. Either
of two brands of vitamin pills can be used: Brand X at 6 cents a pill or Brand Y at 8 cents a pill. The chart below shows that Brand X
supplies 2 mg of A, 3 mg of B and 25 mg of C. Likewise, Brand Y supplies 1, 4, and 50 mg of vitamins A, B, C respectively. How
many pills of each brand should she take each day in order to satisfy the minimum daily need most economically?
Vitamin A
Vitamin B
Vitamin C
Cost per pill
Brand X
2 mg
3 mg
25 mg
6 cents
Brand Y
1 mg
4 mg
50 mg
8 cents
Min. Daily need
4 mg
11 mg
100 mg
25. A game company is developing two new games, a board game and a mechanical game. Each board game requires 1/2 hour to
manufacture, 1/2 hour to assemble, and 1/4 hour to inspect and package. Each mechanical game requires 1 hour to manufacture, 1/2
hour to assemble, and 1/2 hour to inspect and package. In a given week, there are 40 hours available for manufacturing, 32 hours for
assembly, and 18 hours for inspection and packaging. Suppose the profit on each board game is $10 and the profit on each mechanical
game is $15. How many of each game should be produced each week for maximum profit?