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Math 090 Exam 3 Review – Chapter 4
Remember that material from earlier exams may be on this exam also – your exams will build on
each other!
Section 4.1 Integers: Opposites, Absolute Value, and Inequalities
Negative numbers are located to the left of 0 on the number line
Positive numbers are located to the right of 0 on the number line
Opposite – the opposite of a number is the number that is the same distance from the number and
zero on the number line but on the opposite side of 0
Absolute Value – the distance between zero and the number on the number line. The distance
is always positive or 0. To find the absolute value: if the number is positive or 0, write the
number. If the number is negative, write its opposite. The absolute value of 0 is 0.
Whole numbers are
0, 1, 2, 3, ….
Integers are the whole numbers and their opposites:
…  3,  2,  1, 0, 1, 2, 3…
When comparing two integers, remember that the number farthest to the right on the number line
is the greater number.
Simplify:
1.
 ( 196)
2.
 [ ( 47)]
3. Brad’s doctor recommended to him that he exercise for a certain period of time five days a
week. During the first week, on the first two days he exercised 18 minutes more than he
needed to. On the next two days he exercised 27 minutes less than he was supposed to, and
on the last day, he exercised 14 minutes more than he was supposed to. Looking at the week
as a whole, how many minutes more or less than the doctor recommended did he exercise?
Find the absolute value:
4.
5.
 467
 56  27  10
2
6. Evaluate:
46  32
7. True or False?  x  7 has one solution, x  7
True or False:
8.
26  15
9.
((11))  (((4)))
10.
57  168
11.
765  (258)
12.
25, 689  (25, 689)
13.
174  (506)  492
Section 4.3 Subtracting Integers
14. 65  14  (18)  5
15.
16  21 14  6  (5)
16. True of false, 42  76  42  76
3
Section 4.4 Adding and Subtracting Polynomials (Integers)
Simplify:
17.
35 x  45 x  (22 x)
18.
9x
19.
Subtract 8 x 2  9 x  12 from  4 x 2  3 x  9
20.
Find the difference between 8 x 2  9 x  12 and  4 x 2  3 x  9
2
 15 x  17    5 x 2  21  14 x 








Section 4.5 Multiplying and dividing Integers
Multiplication and Division:
+ times + = +
 times  = +
+ times  = 
 times + = 
Squaring a number means multiplying a number by itself (ex. 32 = 3·3=9)
32  (3) 2
2
*NOTE THAT: 3  (3  3)  9 (the opposite of 3  3 which is  9)
(3) 2  (3)  (3)  9 (here a negative times a negative equals a positive)
ALSO NOTE THAT A NEGATIVE TO AN EVEN POWER IS POSITIVE AND THAT A
NEGATIVE TO AN ODD POWER IS NEGATIVE.
4
Simplify:
21.
92  12  2
3


 3
 32
22. 5   3  110  3 6  22
2
23. True or false,
2
24. True or false, 5(6)  5  (6)
Section 4.6 Multiplying and dividing Polynomials (Integers)
Rules for variables with exponents:
Multiplying: add exponents ex. ( x 2 )  ( x3 )  x 23  x5
Dividing: subtract exponents ex.
x5
 x 5 2  x 3
2
x
Power to a power: multiply exponents ex.
x 
2 3
 x 23  x6
Remember that any number (other than 0) to the zero power = 1 ex. x 0  1 for x ≠ 0
Simplify:

25. 4 x 3 x 2  12 y


26. 12 x 2 y 3 3 y 8  5 x 4 y 4

5
27.  3x  512 x  8
28.  4 x 10 9 x  5
29. 2(6 x  4)  (3x  2)
30. ( x  5)  6(2 x  7)
Divide:
31.
45 x 2 y  20 x
5x
32.
27 x3 y 4  15 x 2 y 3  3x 2 y
3x 2 y
6
Section 4.7 Order of Operations and Average (Integers)
Reminder: You must calculate problems in this order to get the right answer:
Please Excuse My Dear Aunt Sally
Or:
Parentheses
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)
Simplify:


33. 3 42  6  2  7  (9)  3

34. 14  36   4  2   7  22
   3
2
2
35. 32  10  2  3  10   3 4
36. What is the result of the product of 12 and the difference of  23 and  45 ?
37. What is the result when 10 is subtracted from the quotient of  16 and 4?
Find the average:
38. Find the average of: 14,  6, 5,  3, and 15
39. Find the average of: 35,  10, 46, and 13
7
Section 4.8 Evaluating Algebraic Expressions and Formulas (Integers)
Evaluate:
40.
41.
x
y
 z 2  ( x) 2
2
3  x 2  (4) x
+ xy
y
for x  5, y  6, z  4
for x  5 y   4
Section 4.9 Solving Equations (Integers)
42.
5r  16  51
43.
( x  25)  3  x  5  6 x
44.
16x  20 14x 13  5x  34
45.
3p
 6  18
4
8
Answers to Math 090 Exam 3 Review
1.
196
24. False
2.
 47
25. 12 x3  48 xy
3.
 4 minutes (He exercised 4 minutes
26. 36 x 2 y11  60 x6 y 7
less than the doctor recommended.)
27. 36 x 2  36 x  40
4.
467
28.
36 x 2  110 x  50
5.
 19
29.
9x  6
6. 14
30. 13x  47
7. False, another solutions is x = 7
31. 9 xy  4
8. False
32. 9 xy 3  5 y 2  1
9. False
33.
10. 111
34. 7
11.  1023
35.
12. 0
36.  264
13.  188
37. 6
14.  66
38. 5
15. 8
39. 21
16. False
40.
17. 32x
41. 22
18. 4 x 2  x  4
42.
r=7
2
19. 12 x  6 x  3
43.
x = 10
20. 12 x 2  12 x  3
44.
x = 9
21.  19
45.
p = 16
22.  50
23. False
9
 22
11
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