Math 086, Introductory Algebra
Math 086, Introductory Algebra, covers the mathematical
content listed below. In order to place
out of Math 086 or to prepare for the final examination in this course, one
should be extremely
comfortable with all of these items.
NOTE: Calculators are not permitted in this course. The content listed
below is covered
in chapters 1 through 8 in the first half of Pre and Introductory Algebra, A
Combined Text by
Aufman, Barker and Lockwood (published by Houghton Mifflin Company), the current
textbook
used in Math 086.
• Adding, subtracting , multiplying, dividing, and exponentiating numbers
(integers, fractions
and decimals); reducing fractions to lowest terms (simplest form); converting
between
fractions, decimals, and percents.
• Simplifying arithmetic expressions by following the order of operations.
• Simplifying complex fractions.
• Converting between fractions, mixed numbers, decimals, and percents.
• Evaluating algebraic expressions for given values of the variable (s).
• Adding and subtracting polynomials; multiplying monomials by polynomials;
exponentiating
and dividing monomials .
• Translating words into numbers, verbal expressions into variable expressions
and sentences
into algebraic equations.
• Solving algebraic equations involving integers, fractions, decimals,
proportions and/or
parentheses.
• Solving application problems (including, but not limited to,
determine-the-number problems,
distance-rate-time, perimeters and areas, money/salary problems, percents,
ratios/rates
and markup and discount problems)
Review Problem Set
At Essex County College you should be prepared to show all work clearly and in
order, ending
your work by boxing the answer. Furthermore, justify your answers
algebraically whenever
possible. These questions are for review only, and placement tests are not
limited to these
problems alone. Solutions and work are provided for each question.
1. Simplify. 2 + (−5) − 7 + 6 − (−3)
Solution:
2. Simplify. 5.41 − 2.683
Solution:
3. Simplify and reduce final answer to lowest terms .
Solution: The LCD is 12.
4. Simplify and reduce final answer to lowest terms.
Solution: Rewrite as improper fractions first. The
LCD is 10.
5. Simplify and reduce final answer to lowest terms.
Solution:
6. Simplify and reduce final answer to lowest terms.
Solution:
7. Simplify. 1.334 ÷ 2.3
Solution: Long division.
8. Simplify. (−2)3
Solution:
9. Simplify. 3-2
Solution:
10. Simplify. 2 (3 − 5) − 12 ÷ 2
Solution:
11. Simplify. 
Solution: The minor LCD is 28.
12. Convert 
to a mixed number.
Solution:
13. Convert 
to a decimal.
Solution: You may have to resort to long division.
14. Convert 
to a percent.
Solution:
15. Convert 
to
an improper fraction.
Solution:
16. Convert 
to a
decimal.
Solution: You may have to resort to long division.
17. Convert 
to a
percent.
Solution: Rewrite as an improper fraction first.
18. Convert 4.54 to a fraction, reduce your final answer
to lowest terms.
Solution:
19. Convert 3.124 to a mixed number, reduce your final
answer to lowest terms.
Solution:
20. Convert 1.8 to a percent.
Solution:
21. Convert 6% to a fraction, reduce your final answer to
lowest terms.
Solution:
22. Convert 132% to a mixed number, reduce your final
answer to lowest terms.
Solution:
23. Convert 9% to a decimal.
Solution:
24. Evaluate 3x − 2y for x = −2 and y = −4.
Solution:
25. Evaluate x2 − 3x − 5 for x = −1.
Solution:
26. Evaluate ab for a = 3.58 and b = −1.026.
Solution:
27. Evaluate 
for 
and 
.
Solution:
28. Simplify. 
Solution:
29. Simplify. (−4t2 + 3t − 6) −(t2 +
5t − 1)
Solution:
30. Simplify. 5 (3t − 2w) + 2 (t + 4w)
Solution:
31. Simplify. 
Solution:
32. Simplify.
Solution:
33. Simplify. 
Solution:
34. Simplify.
Solution:
35. Write 4, 302, 007 in words.
Solution: Four million, three hundred and two thousand , and seven.
36. Translate “fifteen less than twice the sum of a number and three” into a
variable expression
and simplify.
Solution: Let n represent the number.
37. Translate “the quotient of a number and negative four ”
into a variable expression.
Solution: Let n represent the number.
38. Translate “the difference between twice a number and
five is thirty” into an equation and
solve.
Solution: Let n represent the number.
39. Solve for x. 5x − 2 − 3x = 10
Solution:
40. Solve for x. 3x − 4 = 4x + 9
Solution:
41. Solve for x. 2 (x − 1) = −10
Solution:
42. Solve for 
Solution:
43. Solve for x. 4.1x − 2.52 = −2.233
Solution:
44. Solve for 
Solution:
45. If James drives for 
hours at a rate of 60 miles per hour (mph), how far will he have
driven?
Solution: Note, distance equals rate times time.
The distance is 195 miles .
46. A rectangle has an area of 24 square inches. If the length of the rectangle
is 8 inches, what
is its width? (Note: Area of a rectangle is equal to length times width.)
Solution: Let w represent the measure of the rectangle’s width.
The rectangle’s width measures 3 inches .
47. Alex has $340.56 in his checking account. If he
deposits $92.18 and then writes checks for
$36.07 and $142.50, what will his balance be?
Solution:
48. If you are paid $8.75 per hour and work for 38 hours,
how much have you earned (before
taxes are taken out)?
Solution:
49. What is 12% of 60?
Solution:
50. What percent of 84 is 21?
Solution: Let x represent the percent.
The answer is 25% .
51. 42 is 60% of what number?
Solution: Let x represent the number.
The answer is 70 .
52. If there are 280 calories in a serving size of 4 cookies, then how many
calories are there in
one cookie?
Solution:
There are 70 calories in each cookie.
53. If the landlord increases your current rent of $750 by 5.6%, how much will
your new rent
be?
Solution:
The new rent is $792 .
54. A graphing calculator that costs $48 is marked up $60. What is the markup
rate and what
is the selling price of the graphing calculator?
Solution: Let x be the markup rate.
The markup rate is
and the selling price is $108 .
55. A television that regularly sells for $560 is on sale
at 40% off the regular price. What is
the sale price of the television?
Solution:
The sale price of the television is $336 .
