Download Supplemental Problems and Test Review Chapter 1

1.1 – 1.4 Homework Problems and Test Review
Order of Operations
I. Simplify the following by hand. All answers must be written as fractions (when necessary)
2
11
3
2
2 5
3
1.
2. 16  2
3. 14
11
6
3 2
4
16
7
17
7
3
1
1
3
2 3 5  3
92
4.  25 
5. 
6.     
3
5
2 4
5
4
3
3 8 6  5
5
6
7. (-5)2
8. -52
9. (-5)3
10. -42(-2)2
11. 4 32  3
12. 4  22 – 15  4
15. 112 – 2[16 + 2[14 – 2(7 + 1)]] – 42
13. 5  9  3  3  8
14. 4 + 49  7  8  2
16. 3  [8  (9  2(4))]
17. 5  8(3  6)  22  10
III. Evaluate each expression if a = -5, b = .25, c = ½ , and d = 4.
3a + 4c
18. a + 10  c
19.
20. (a + c)2 – bd
2c
IV. True or False
a
a a
= +
21. c + b c b
a+b b
=
22. a + c c
a+b
b
= 1+
a
23. a
a
1
=
24. a + b b
1.1 Sets of Numbers & 1.2 Algebraic Expressions
(Supplemental problems and Textbook p. 15-17 #38-53, 67-69)
To which sets of numbers does each number belong?
1. 4
2. 6
5. 0
6. 0.6
3. π
7. - 0.04
4. - 6
8. 0.4
Show that each statement is false by finding a counterexample (an example that makes the statement
false)
9. The reciprocal of each whole number is a whole number.
10. The opposite of each natural number is a natural number.
11. The product of two irrational numbers is an irrational number.
12. There is no integer that has a reciprocal that is an integer.
True or False. If false, give a counterexample.
13. If a > b, then a2 > b2.
14. If a2 > b2, then a > b.
15. If c > d, then c – a > d – a.
16. If a2 = b2, then a = b.
True or False.
17. The product of two rational numbers is a rational number.
18. The difference of two whole numbers is a whole number.
19. The sum of two whole numbers is a whole number.
Textbook p. 15-17 #40-45, 47-50, 67
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1.3 Solving Equations
Textbook p. 21-22: 28, 41, 42, 46, 55, 57, 60, 63, 64, 29, 32, 34, 35, 48, 53, supp. problems 1-4
Solve for x. State any restrictions if necessary.
x 3
 x  17
1.
2. 5(3 – x) = 2 – 5x
6
2
5
1
4. x  x  6  x  5
3
6
2
3. 6[x – (2x + 3)] = 8 – 5x
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1.4 Solving Inequalities
p 30-31: 38, 45-55, supplemental problems #1-11
Solve each compound inequality. Graph the solutions.
1.4 Solving Inequalities Supplemental
Solve and graph the solution set. Write answers in interval notation.
1
3 7 2
1. x    x
2. 2x < 6 and x + 2 >1
3. 3x + 7 < 10 or 2x – 1 > 5
2
2 6 3
4. -6 < 2x - 4 <12
5. 5y < 25 or 6y > 30
6. 4x  16 and 3x  12
7. 3 +5z > 2z – 15 and 3(1 – 3z) + 6 < 18
8. 5z – 4 + 3z > 6z – 24 and 14z – 3 < 25
9. 4w + 7  8 + 3w or 6(2w + 3) < 11w + 15
10. 4x – 5  16 – 3x and 7x – (5 – 2x)  31
11. 2x + 10 < 12 or 4x – 12 < 4
Test Review
I. Order of Operations
1.
5  3  7  
3
144  25
2. 10  2(14  2)  22  6
3.
(2)3  42  6  42  8
II. Subsets of Real Numbers
Name the sets of numbers to which each number belongs: Real, Rational, Irrational, Integer,
Whole, Natural
1
4. 16
5. 
6.
7. 7
8. 12
3
III. Linear Equations
9. 4x + 3(x - 2) = -(5x - 20) - x
10. 2d - 3(d + 1) = -(5d + 3) + d
3m 3 m 5
8x 1 2x 1
  
 

11.
12.
4 8 3 6
9 2
3
6
Write an equation, then solve
13. Find four consecutive even integers that the sum of the third and fourth is 114.
14. The sides of a triangle are in the ratio 3:4:5. What is the length of each side if the
perimeter of the triangle is 90 cm.
IV. Literal Equations.
Solve for the indicated variable and state any restrictions.
1
m
15. K  r3h , for h
16.
 5g  15 , for m
k
8
x 5
17. a(x  d)  2ad  b(c  x)  bc,for x
18.
 1  b, for x
a
V. Linear Inequalities.
Solve each of the following inequalities, write your answer in interval notation.
19. x  0 or x  2
20. x  4 and x  10
21. x  7 and x  4
22. x  5 or x  3
23. 3  2x or x - 4  2
24. 5  2x  1  11
25. 6y  2 and y  5  2y
26. 5  9  4x  13
Solve each of the following by writing an inequality.
27. Mrs. Johnson plans to buy art supplies for her art class. She plans to buy one kit for the
entire class that cost $22.50 and one quart of paint for each student that cost $8.75. If she
has a budget of $250, what is the maximum amount of students she can have in her class to
stay within her budget?
28. Mike earns $8.50 an hour plus 5% commission on the price of each item that he sells.
Mike can work 80 hours this month, and would like to make at least $1200. What must his total
sales be for the month if he wants to reach his goal?
29. A cab company charges $5.00 for the first mile and $2.50 for each additional mile. Connor
only has $70 on transportation, what is the maximum distance he can travel in the cab?
30. Robert wants to buy lunch for his coworkers. He plans to buy each person a “Bubba Joe’s
Lunch Special” which cost $6.50. There is a $4 delivery charge, and he has to $60 to spend.
How many coworkers can he provide lunch for?