1
091 Exam 1 Review (Sections 1.3 – 2.5, 2.7, Handouts A, B, C)
KNOW THE DEFINITIONS OF ALL KEY TERMS PRESENTED IN CLASS. ALSO KNOW
WHAT ALL SYMBOLS MEAN (EX. , , , ,
ETC.)
Adding/Subtracting Fractions
Reduce answers to lowest terms.
1.
2.
1 1
1
8
2
2
3
3
Multiplying/Dividing Fractions
Reduce answers to lowest terms.
3.
2 5
 
3 8
4.
2  4
 
3  3
5.
4  
  
5  
Comparing Fractions
6. True or False

11
1

36
4
________________
Review Definitions
Absolute Value – distance between a number and 0 on the number line
Equation – solving for a variable: has an = sign (ex. 2x - 4 = 8)
Expression- just simplify: no = sign (ex. 2x - 4)
Term – in expression, parts that are added (ex. in 2x – 4, 2x and -4 are terms)
Like Terms – have the same variables to the same power (ex. 3x 2 y and 5 x 2 y are like terms)
Factor – the numbers or variables that are multiplied (ex. in 2x-4, 2 and x are factors)
Expressions
For the expression:
x
4
6
List the:
7. Numerical coefficient________
8. Variable____________
9. Constant____________
10. 2 terms______________
11. 2 factors_____________
2
Match the equation with the corresponding property. (You can use them more than once.)
12.
3 3 9
 
4 3 12
_______________________________________
13.
6∙4∙2 = 6∙2∙4
_______________________________________
14.
4 + (3 + 2) = (4 + 3) + 2
_______________________________________
15.
24 
16.
8  0  8
17.
(2 +7) + 12 = (7 + 2) + 12 _________________________________________
18.
(3 + 2x) ∙2 = 6 + 4x
19.

20.
(2 + 7) + 12 = 12 + (2 + 7) __________________________________________
21.
4∙(3∙7) = (4∙3)∙7
1
1
24
12 12
 0
5 5
________________________________________
_________________________________________
_________________________________________
__________________________________________
__________________________________________
Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of
Addition, Associative Property of Multiplication, Identity Property of Addition, Identity Property of
Multiplication, Inverse Property of Addition, Inverse Property of Multiplication, Distributive Property
Remember:
Commutative Property (both addition and multiplication) – can change order
Associative Property (both addition and multiplication) – can change grouping
Identity Property for Addition – adding 0 doesn’t change the answer
7
Identity Property for Mult. – multiplying by 1 (in any form, ex. ) doesn’t change the answer
7
Inverse Property for Addition – a number added to its opposite equals 0
Inverse Property for Multiplication – a number multiplied by its reciprocal equals 1
Distributive Property – involves both multiplication and addition/subtraction
True or False:
22. 6.92 is a natural number
23.  7 is an irrational number
24. 0 is a whole number
25.  is a real number
26.  82   64
27.
 4  4
________________
________________
________________
________________
________________
________________
3
Subsets, Union, and Intersection
Let:
A = {1,2,3,4,5}
B = {1,2,3,5,8,10,11}
Place , ,, or  to fill in the blank.
28. A____B
29. 2____C
32. A____C
33. {6}____A
C = {1,2,3,4,5,6,7,8}
30.  ____A
34. 6____B
31.
D = {9, 12}
A____A
Using sets A, B, and C from above, complete:
35. A  B_______________________ 36. C   _________
37. B  D __________
38. B  C_______________________ 39. A  C___________
40. A  C __________
41. A  { } ____________
Remember:
0
0
any #
any #
 undefined
0
Signs: +∙+ = +
−∙−=+
+ ∙ − = − and − ∙ + = −
Perform the indicated operations and reduce all answers to lowest terms:
42.
2
5 4  1  
    
6  3  2  
43. 3  6 + [ (4−5) − (2−8)]
 20  18  9  2 
3 2
44.
10  2  3  5 
2
4
45.
3(5  2 ) (3  2  7)(5)

32
5  2  (1)
46.
2(5)  (3)(2) 2
6  10  2  1
2
2
Simplify:
47. 3 2  4( x  y)   4  2(2 y  2 x)
48.  y 2  2 x 2  (3x  2 y 2 )  4 x 2  2( x  y)
Solve: (Remember to check your answers!)
49.
5
 x  20
6
50.
3(2 x  4)  7  2( x  6)  1
51.
7( x  4)  2 x  5 x  ( x  28)
52.
2
3 5 1
x   x
3
4 12 2
53.
6x  2  x  4  4 x  6
54.
2  3(2  3x)  3(3 x  2)  2
55.
1
2
 x  2   3   x  5
4
3
5
6
Evaluate when x  
1
2
and y  
2
3
56.
 x2
5 x  2 y
57.
8x2   2 x  3 y 
Ratios and Proportions
Ratio: quotient of 2 quantities, written: a to b, a:b or
a
(Note: a & b must be in the same units)
b
Solve:
58. Write the ratio of 10 minutes to 1 hour.
Proportion: a statement of equality between two ratios
a c

a and c must have the same units
b d
b and d must have the same units
To solve a proportion, cross multiply: a∙d = b∙c
Solve:
59. Amy Smith earns $380 in 2 weeks. How much will she earn in 52 weeks?
Answers to Math 091 Exam 1 Review
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
13
5
1
8
8
7
1
  2
3
3
5

12
1

2
32
35
False
1
6
x
 4
x
, 4
6
1
,x
6
Identity – Multiplication
Commutative - Multiplication
Associative - Addition
Inverse - Multiplication
Identity - Addition
Commutative - Addition
Distributive
Inverse- Addition
Commutative - Addition
Associative – Multiplication
False
True
True
True
False
True






34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.

{1,2,3,4,5,8,10,11}
C

{1,2,3,5,8}
A
C

1

4
4
8
2
undefined
8 x  16 y  2
2 x 2  y 2  5x  2 y
x= 24
x2
x=0
x 1
no solution
all real numbers
x 2
3

14
3
1
6
$ 9880
7