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MATH 091 REVIEW FOR EXAM 2
KNOW THE DEFINITIONS OF ALL KEY TERMS AND ALSO KNOW WHAT ALL
SYMBOLS MEAN.
2.6 FORMULAS
Solve:
1. P = 2l + 2w
2. A=
5(m+n)
L
solve for w
solve for n
3. 2xy + 6 = 4xz – 5y
solve for x
1
If Betty invested $5000 at a simple interest rate of 5 % , how many years would it
2
take her to earn $825 in interest?
I=PRT
4.
2.8 INEQUALITIES IN ONE VARIABLE
Remember: multiplication and division by a negative number reverses the inequality.
Solve inequalities, graph, and write answer in interval notation
5. 6 x  2( x  4)  4
2
6. 4( x  5)  (3x  24) or  ( x  3)  4
3
7. 7x + 6 < 48 and  10x ≥ 3x  8  5x
8. (  5,∞)  (  ∞,3]
9. 2(5  x)  3( x  2)  4  8 x
10. 8( x  4)  2(5  x) or  9 x  6  48
3.1 – 3.3 STORY PROBLEM HINTS
a subtracted from b means b-a
The difference between a and b means a-b
A percent is always a percent of some number: ex. an increase of 6% means: x + .06x
Consecutive integers are x, x+1, x+2, …
Consecutive even integers OR consecutive odd integers are x, x+2, x+4,…
(If you can’t remember this, write down actual numbers, and then see what you do to
get from one to the next. Then apply this same principal to the variable.)
Perimeter is the distance around. Perimeter of a rectangle is 2L + 2W
Area of a rectangle is L · W
The sum of the angles in a triangle is 180º
The sum of the angles in a quadrilateral is 360º. (If you can’t remember this, think of a
square or rectangle. It has 4 right angles (90º each). 4· 90 =360
The sum of: complementary angles = 90º and supplementary angles = 180º
Vertical angles have equal measure
3.1 CHANGING APPLICATIONS PROBLEMS INTO EXPRESSIONS &
EQUATIONS
11.
10 less than 4 times a number
12. The difference between 7 and a number
13. 7 less than a number
14. The sum of three consecutive even numbers is 36
15. A salary increased by a 3% raise
3.2 SOLVING APPLICATION PROBLEMS/3.3 GEOMETRIC PROBLEMS
Solve the following problems: Be sure to include all 4 steps!
Step 1.
Create Legend: define variables including units
Step 2.
Set up equations
Step 3.
Solve for Variable
Step 4.
Answer the Question
“Step 5.”
Check your answer
16. The sum of two consecutive odd integers is  28 Find the integers.
17. Jane spent a total of $47,000 to start a business. She spent $12,000 on furniture and
supplies, and spent the remaining amount on 2 machines. If she spent $4,000 less than twice
the amount on one machine than on the other machine, how much did she pay for each
machine?
18. A coat is on sale for $92. If the coat is marked 20% off, what is the original price?
19. Joe wants to put a rectangular fence around his dog run. The length is 5 more than
twice the width. If the perimeter is 40 feet, what are the dimensions of the fence?
20. Susan’s salary for next year is going to be $31,650. This is a 5.5% increase from her
current salary. Find her current salary.
21. It cost Ben $8.75 a week to wash and dry his clothing at the corner laundromat. Ben
could reduce this cost to $1.25 a week (for water and electricity) if he purchased a washer
and dryer for $960. How many weeks would it take for Ben’s laundry cost at the corner
laundry to equal the laundry cost of his loads with purchasing a washer and dryer? If Ben is
planning on moving overseas in 2 years, which option should he choose?
22. Edward Brown left his estate of $210,000 to his two children and his favorite charity.
Each child received 3 times the amount left to his favorite charity. How much did each child
and the charity receive?
23. Chris is at a restaurant and is deciding what to order. He has $36 in his wallet. He
wants to leave a 15% tip and tax on the meal is 5%. What is the most expensive meal he can
order?
24. Jamie just started a cake decorating business. She currently makes 25 cakes a month, but
is hoping to increase her business. If she increases her business by 3 cakes a month, how
many months will it take her to reach a production level of 70 cakes a month?
4.1 EXPONENTS/ 4.2 NEGATIVE EXPONENTS
Simplify:
25.
4 x3 y 2 z
12 x 2 yz
26.
 25 x 2 y 


2
 5 xz 
27.
4 1  8 1
28.
32  22
23
Simplify:
(6  8) 2
29.
42  23
2
30.
4  32  3  22
31.
 3xy z  4 x y
32.
 2
33.
 53 x 3 y 2 z 7 

5 6 7 
 5x y z 
34.
 3x 
35.
 3 x y   3x y 
2 2
2
2
0
4
3
x 3 y 2 z 
2
3 4
z
 3x y
2


4 5 3
z
2
  2 y 0  1
2 2
4
4 3
4.3 SCIENTIFIC NOTATION
Change to scientific notation.
36. 450,000
37. 625,000,000
38. 0.000004
39. 0.0000000587
Multiply and express each answer without exponents.
40.
 3.4 10  2.110 
41.
 4.3 10  3.7 10 
5
7
3
4
Divide and express each answer without exponents.
42.
 6.8 106 

9 
 2.5 10 
43.
 1.6 105 

8 
 8.0 10 
Perform each indicated operation by first converting each number to scientific notation.
Write the answer in scientific notation.
44.
1, 470, 000
0.007
Answers to Math 091 Review for Exam 2
Section 4.1, 4.2
25.
Section 2.6
1.
2.
3.
4.
P-2l
2
AL+5m
n= 
5
5 y  6
x
2 y  4z
w=
3 years
26.
27.
28.
29.
30.
Section 2.8
[3, )
5.
(, 4]  (9, )
6.
( , 4]
7.
( 5,3]
8.
9.
10.
 0,  
 ,  
Section 3.1
11.
4x – 10
12.
7–x
13.
x–7
14.
x + (x + 2) + (x + 4) = 36
15.
x + .03x
Section 3.2/3.3
16.
The first odd integer is  15, and the
next odd integer is  13
17.
One machine cost $13,000 and the
other machine cost $22,000
18.
The original price of the coat is
$115
19.
The width of the fence is 5 ft. and
the length of the fence is 15 ft.
20.
Susan’s current salary is $30,000
21.
It would take 128 weeks for the cost
of washing and drying Ben’s
clothes at the corner laundromat to
equal the cost with purchasing a
washer and dryer. If Ben is moving
overseas in 2 years (104 weeks), he
should continue to use the corner
laundromat.
22.
Charity would receive $30,000 and
and each child would receive
$90,000
23.
The most expensive meal that
Chris can order is $30
24.
It will take Jamie 15 months to
reach a production level of 70
cakes.
31.
32.
33.
 xy
3
25x 2 y 2
z4
3
8
26
9
4
11
36
12x 4 z 2
y
16 y 8
27 z17
x4
54 y16
34.
4
35.
3y16
x4
Section 4.3
36. 4.5  105
37. 6.25  108
38. 4.0  10 -6
39. 5.87  10-8
40. 714
41. 0.01591
42. 0.00272
43. 200
44. 2.1 108