MTH 086 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 20, 2006

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1 MTH 06 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 0, 006 Math 06, Introductory Algebra, covers the mathematical content listed below. In order to place out of Math 06 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 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 06. 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) 1 This document was prepared by Ron Bannon using L A TEX ε and is a slight modification of Susan Gaulden s MTH 06 Content worksheet. 1

2 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. Please feel free to with questions or comments pertaining to this document. 1. Simplify. + ( ) ( 3) + ( ) ( 3) = + ( ) + ( 7) = ( ) + ( 7) = 11 + ( 1) = 1. Simplify = Simplify and reduce final answer to lowest terms The LCD is = = = = 16 1 = 3 = 11 3 These are sample problems and you should not limit your study to just these problems.

3 . Simplify and reduce final answer to lowest terms Rewrite as improper fractions first. The LCD is = = = = 10 = = Simplify and reduce final answer to lowest terms = 9 7 = 7 9 = 1 3 = 3 = Simplify and reduce final answer to lowest terms. ( ) ( ) 9 = 7 9 = 9 7 = = 1 1 3

4 7. Simplify Long division = = = 3 3 = = 0.. Simplify. ( ) 3 ( ) 3 = ( ) ( ) ( ) = 9. Simplify. 3 3 = 1 3 = Simplify. (3 ) 1 (3 ) 1 = ( ) 1 = ( ) + ( 6) = 10

5 11. Simplify The minor LCD is = = = = 9 1. Convert 31 to a mixed number. 31 = Convert to a decimal. You may have to resort to long division. = Convert 9 to a percent. 9 = 9 % = 36%

6 1. Convert 3 7 to an improper fraction. 3 7 = = Convert 3 to a decimal. You may have to resort to long division. 3 = Convert 3 to a percent. Rewrite as an improper fraction first. 3 = 17 % = 17 0% = 30% 1. Convert. to a fraction, reduce your final answer to lowest terms.. = = 7 0 = Convert 3.1 to a mixed number, reduce your final answer to lowest terms. 3.1 = = =

7 0. Convert 1. to a percent. 1. = 1. % = 10% 1. Convert 6% to a fraction, reduce your final answer to lowest terms. 6% = 6 3 = 0. Convert 13% to a mixed number, reduce your final answer to lowest terms. 13% = 13 = 1 3 = 1 3. Convert 9% to a decimal. 9% = 9 = Evaluate 3x y for x = and y =. 3x y = 3 ( ) ( ) = ( 6) ( ) = ( 6) + = 7

8 . Evaluate x 3x for x = 1. x 3x = ( 1) 3 ( 1) = 1 3 ( 1) = 1 ( 3) = = 1 6. Evaluate ab for a = 3. and b = ab = (3.) ( 1.06) = (3.) (1.06) = Evaluate c + d cd for c = 3 and d = 1. c + d cd /3 + 1/ = (/3) (1/) = 11/1 1/3 = = = 11 = 3. Simplify. t + 3t 6 + t + t 1 t + 3t 6 + t + t 1 = ( t ) + t + 3t + t + ( 6) + ( 1) = ( 3t ) + t + ( 7) = 3t + t 7

9 9. Simplify. ( t + 3t 6 ) ( t + t 1 ) ( t + 3t 6 ) ( t + t 1 ) = t + 3t 6 t t + 1 = t t 30. Simplify. (3t w) + (t + w) (3t w) + (t + w) = 1t 10w + t + w = 17t w 31. Simplify. 6x y ( xy 3 z ) 6x y ( xy 3 z ) = 6 ( ) x xyy 3 z = 1x 3 y z 3. Simplify. ( 16x ) ( ) 3 ( 16x ) ( ) 3 = ( 16x ) ( ) 3 = 16x 3 = x 3 = 6x 33. Simplify. 3a ( a + ) 3a ( a + ) = ( 3a) ( a ) + ( 3a) () = 6a 3 1a 9

10 3. Simplify. ( x y 3) ( x y 3) = ( x y 3) ( x y 3) = x y 6 3. Write, 30, 007 in words. 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. Let n represent the number. (n + 3) 1 = n = n Translate the quotient of a number and negative four into a variable expression. Let n represent the number. n = n 3. Translate the difference between twice a number and five is thirty into an equation and solve. Let n represent the number. n = 30 n + = 30 + n = 3 = 3 n = 3 = 171 =

11 39. Solve for x. x 3x = 10 x 3x = 10 x = 10 x + = 10 + x = 1 x = 1 x = 6 0. Solve for x. 3x = x + 9 3x = x + 9 3x 3x = x + 9 3x = x = x = x 1. Solve for x. (x 1) = 10 (x 1) = 10 x = 10 x + = 10 + x = x = x =. Solve for x. 3 0 x = x = 9 3 x 0 0 = 9 0 3x = x = 10 3 x = 60 11

12 3. Solve for x..1x. =.33.1x. =.33.1x. +. = x = x = = 7 = 7 x = Solve for x. 1 = 16 x 1 = 16 x 1 1x = 16 x 1x x = x = = 1 x = 60. If James drives for 3 1 driven? hours at a rate of 60 miles per hour (mph), how far will he have Note, distance equals rate times time. d = d = d = 1 13 d = 19 The distance is 19 miles. 6. A rectangle has an area of square inches. If the length of the rectangle is inches, what is its width? (Note: Area of a rectangle is equal to length times width.) Let w represent the measure of the rectangle s width. The rectangle s width measures 3 inches. = w 3 = w 1

13

14 1. is 60% of what number? Let x represent the number. The answer is 70. = 60% of x = 60 x = 3 x 3 = 3 3 x 1 = x 70 = x. If there are 0 calories in a serving size of cookies, then how many calories are there in one cookie? There are 70 calories in each cookie. 0 = If the landlord increases your current rent of $70 by.6%, how much will your new rent be? The new rent is $79. $70 + $70.6 = $70 + $ = $79. A graphing calculator that costs $ is marked up $60. What is the markup rate and what is the selling price of the graphing calculator? Let x be the markup rate. $ x = $60 $ $ x = $60 $ x = The markup rate is = 1. = 1% and the selling price is $10. 1

15 . A television that regularly sells for $60 is on sale at 0% off the regular price. What is the sale price of the television? The sale price of the television is $336. $60 $ = $60 $ $60 $ = $336 1

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