Pre-Algebra

Study Guide

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Essential Mathematics for Life – Algebra

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This is the first of a two-part study guide for the study of basic algebra. Whether you have already taken some algebra or not, this study guide is designed to help introduce you to the basic principles of the subject. Because this is a self-study program, it is essential that you read the material in the textbook and work some of the sample problems BEFORE you start taking the exams in this study guide. If you try to skip over material or just skim it, chances are you will miss something important and that could affect your grade on one or more exams. Your textbook, Essential Mathematics for Life – Algebra, clearly explains everything you need to know to get a basic understanding of higher mathematics. The book begins with a review of basic arithmetic and positive and negative numbers before moving on to the fundamentals of algebra. As with any other subject, you have to read the material—usually more than once—to get a clear idea of the concept. Appropriately, the writers of Essential Mathematics for Life – Algebra begin the algebra portion of the book with explaining how to read and write algebraic expressions. Students are also shown how to solve equations and word problems. Multiplying and dividing expressions with exponents is fully explained using a variety of examples, and so is factoring, which often causes problems for many math students. The book finishes with two other areas that are often difficult for algebra students to comprehend--graphing equations and inequalities. The writers use a clear style and several examples to explain these concepts. To help students gain an even better understanding of algebra, Life Skill sections are included in each unit. They are designed to demonstrate how algebra can be applied to everyday living. While you are encouraged to work the sample questions in the textbook, the ONLY questions you are REQUIRED to answer are the ones in each EXAM. You will write those answers in the spaces on the answer sheets we provide for you. Do not send in your exam answer sheets until you have completed ALL the exams in this study guide. IMPORTANT: On your FINAL EXAM, you will see a few symbols that are different from those found in your book and study guide. The ^ will be used to indicate that the number following it is an EXPONENT. Division problems will use a slash ( / ) to show that one number is divided by another.

Unit 1 Basic Arithmetic Review (pgs. 1-44)

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Whole Number Operations Numbers are made up of digits. The position of the digit in the number shows its place value. Addition The term sum means that two or more numbers are added together. Example: 4,532 + 73 4,605 Subtraction In subtraction, you find the difference between two numbers by subtracting one from the other. Example: 954 - 67 887 Multiplication You multiply two numbers together to find their product. Example: 65 x 8 520 Division In division, you find a quotient when one number is divided by another number. 121 ÷ 11 = 11 Problem Solving – Whole Number Word Problems

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Review the material on pages 7-8 and pay special attention to the four steps for solving word problems. Also, do some of the practice questions on pages 9-10. Here are some words to remember when trying to solve word problems: Addition Subtraction Multiplication Division total difference product quotient sum remainder times how many times increase how much more of average together how much less apiece shared equally both decreased by altogether diminished by Fractions: Addition and Subtraction Review the material on pages 11-13. Also, do some of the practice questions on pages 14-15. REMEMBER: A fraction is part of a whole. The numerator is the top number in a fraction; the denominator is the bottom number in a fraction. Fractions: Multiplication and Division Review the material on pages 16-17 and pay special attention to the steps for multiplying and dividing fractions and mixed numbers. Also, do some of the practice questions on pgs. 18-19. Decimals: Addition and Subtraction Review the material on pages 21-22. Also, do some of the practice questions on page 22. REMEMBER: Any fraction with a denominator of 10; 100; 1,000; 10,000; etc., can be written as a decimal. Decimals: Multiplication and Division Review the material on pages 23-25 and pay special attention to the steps for changing a fraction to a decimal and for rounding off decimals. Also, do some of the practice questions on pgs. 25-26. Problem Solving – Using Decimals

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Review the material on page 27 and do the practice questions on page 28. REMEMBER: Look for certain key words when trying to solve a word problem. Ratio and Proportion Review the material on pages 29-30 and do some of the practice questions on pages 30-1. REMEMBER: Proportions are useful for solving some word problems. Percents, Decimals, and Fractions Review the material on pages 32-33 and pay special attention to the steps for changing a decimal to a percent; a percent to a decimal; a fraction to a percent; and a percent to a fraction. Percent Problems Review the material on page 34 and pay special attention to the formula for solving percent problems. Also, do some of the practice questions on pages 35-36. Graphs Review the material on pages 38-40 and do the some of the practice questions on pages 40-42. REMEMBER: A graph is a picture that presents certain types of information.

Unit 1 Exam

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Solve. 1. 6,782 408 27,985 + 2,456 A. 36,631 B. 37,613 C. 37,631 D. 35,613 2. 500, 403 - 3,546 A. 496,857 B. 503,949 C. 497,857 D. 46,857 3. 407 x 307 A. 714 B. 125,949 C. 124,949 D. None of these 4. 42,800 ÷ 214 A. 200 B. 0.005 C. 43,014 D. 42,586 5. 9 10 13 2 + 13 A. 9 12 B. 8 8 C. 9 12 D. 8 12 26 13 13 26 6. 3 8

4 x 12 A. 2 B. 1 C. 24 D. 6 4 2 48 12

7. 5 ÷ 5 8 A. 25 B. 1 C. 8 D. 8 8 8 25 8. Add 0.9 and 0.2

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A. 0.11 B. 01.1 C. 1.1 D. None of these 9. Add 9, 7.3, and 0.8 A. 17 B. 17.1 C. 24.3 D. 9 10. Subtract 5.3847 from 627 A. -621.6153 B. 622 C. 621.6153 D. -53220 11. 0.076 x 0.52 A. 0.03952 B. 0039.52 C. 0.596 D. 007.12 12. 0.42 ÷ 0.6 A. 0.252 B. 1.02 C. 7 D. 0.7 13. A woman bought some groceries for her family. How much did she pay altogether? Milk $2.59 Cereal $3.99 4 TV dinners $2.99 each Coffee $5.99 Bottled water $4.99/case A. $20.55 B. $29.56 C. $29.52 D. None of these 14. A kitchen has a countertop that is approximately 2 5/11 inches thick and cabinets that are 27 3/22 inches tall. How tall is the entire set of cabinets including the countertop? A. 29 13/22 B. 29 8/33 C. 25 2/11 D. 25 3/22 15. If the ratio of college graduates to high school graduates is 2:5 in a room and there are 100 high school graduates present, how many college graduates are there? A. 20 B. 40 C. 50 D. 25

This is the End of this exam. Move on to the next lesson. You will need a NEW answer sheet for your next exam.

Unit 2 Positive and Negative Numbers (pgs. 45-74)

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Reading and Writing Positive and Negative Numbers Review the material on page 46 and pay special attention to the number lines. Also, do some of the practice questions on page 47. REMEMBER: Negative numbers are to the LEFT of zero and positive numbers are to the RIGHT of zero. Ordering Positive and Negative Numbers Review the material on page 48 and do some of practice questions on page 49. Adding Positive and Negative Numbers Review the material on page 50 and pay special attention to the rules for adding positive and negative numbers. Also, do some of the practice questions on pages 51-53. Subtracting Positive and Negative Numbers Review the material on page 55 and do some of the practice questions on pages 55-57. Multiplying Positive and Negative Numbers Review the material on page 60 and pay special attention to the rules for multiplying positive and negative numbers. Also, do some of the practice questions on pages 60-62. Dividing Positive and Negative Numbers Review the material on page 64 and pay special attention to the rules for dividing positive and negative numbers. Also, do some of the practice questions on pages 64-65. Order of Operations Review the material on page 68 and pay special attention to the steps for solving problems with several operations. Also, do some of the practice questions on page 69.

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Problem Solving – Using Positive and Negative Numbers Review the material on page 70 and pay special attention to the four steps for solving word problems. Also, do some of the practice questions on pages 71-72. Here are some words to remember when trying to solve word problems: Addition Subtraction Multiplication Division total difference product quotient sum remainder times how many times increase how much more of average than together how much less apiece shared equally than both decreased by altogether diminished by

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Unit 2 Exam

Choose the letter with the correct order of numbers from smallest to largest. 1. A. 77, -45, -3, 22, 15 B. –100, -36, -17, 0, 10 C. 63, 57, 34, -9, 0 D. 19, -43, -62, 15, 1

2. A. 2, 4, 6, -11, -33 B. 29, -30, 31, -32, 33 C. 0, -53, -47, 20, 18 D. -5, 0, 12, 87, 111

3. A. 44, -58, -66, 83, -28 B. -21, -19, -17, 3, -6 C. -55, -40, -33, -22, -4 D. 119, 94, 85, 77, 50 Find the sum of each set of numbers 4. 20, -20, -6, 4 A. -10 B. -2 C. 4 D. 30 5. 13, 35, -17, -3 A. 36 B. 34 C. -68 D. 28 6. 110, -249, 375, -57 A. 179 B. 791 C. -41 D. -781 Simplify 7. 39 – 46 A. 13 B. –7 C. 85 D. 7 8. (-55)(-6) A. –49 B. –330 C. 49 D. 330

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9 .(25)(3)(-2) A. –150 B. 30 C. 26 D. None of these 10. -72 6(2) A. 6 B. –12 C. –6 D. None of these 11. 121 -11 A. 11 B. –110 C. 132 D. -11 12. -289 -17 A. 0.058 B. 17 C. -0.06 D. -17 Place the correct symbol ( < or > ) between the two numbers 13. -23 __ -15 A. < B. > 14. 2 3 __ 42 A. < B. > 15. 1 __ -2 A. < B. >

This is the End of this exam.

Move on to the next lesson. You will need a NEW answer sheet for your next exam.

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Unit 3 Algebraic Expressions (pgs. 75-95)

Reading and Writing Algebraic Expressions Review the material on pages 77-78 and do some of the practice questions on pages 78-79. REMEMBER: Algebra uses a combination of numbers AND letters. Here are some words to remember when trying to solve word problems: Addition Subtraction Multiplication Division sum difference product quotient added to minus times divided by plus less multiplied by divided into increased by decreased by of ratio of more than subtracted from squared less than Recognizing Terms Review the material on page 80 and do some of the practice questions on the same page. Combining Like Terms Review the material on page 81 and do some of the practice questions on pages 81-83. Evaluating Algebraic Expressions Review the material on page 84 and do some of the practice questions on pages 85-87. Problem Solving – Finding Interest Review the material on page 89 and pay special attention to the steps that explain how to solve word problems. Also, do some of the practice questions on page 90. REMEMBER: The interest formula is: I = prt (I is interest; p is principal; r is rate; t is time)

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Evaluating Formulas Review the material on page 92 and do some of the practice questions on pages 92-93.

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Unit 3 Exam

Write the algebraic expression. 1. Twice the sum of a number and three-fifths of the number A. n2 + 3 n B. n + 2 + 3 C. 2n + 3 D. None of these 5 5 5 2. 11 decreased by 5 times a number A. 5n – 11 B. 11 – 5n C. –11 + 5n D. 11 – n5 3. the sum of a number divided by 7 A. n x 7 B. n=7 C. 7 ÷ n D. n or n ÷ 7 7 Combine like terms. 4. 7ab + 4a – 5ab A. 2ab + 4a B. 3b – 5ab C. 6ab D. 7ab - b 5. 12 – 5c + 3 25 A. 7c + 3 B. 12 – 8c C. 12 – c + 3 D. No changes needed 25 25 5 6. 3 ft. + 2 2 ft. – 4 ft. 3 A. 1 2 ft. B. 5 2 ft. – 4 ft. C. -1 1 D. No changes needed 3 3 3 7. 11 + 6g – 3g3 4 A. 11 + 3g2 B. –3g3 + 6g + 11 C. 2 3 + 6g – 3g3 D. No changes needed 4 4 4 8. 45x3 – 55x3 + 37xy +20x3 – x2y A. 10x3 - x2y + 37xy B. –10x3 - x2y + 37xy C. –30x3 + 37xy –x2y D. No changes needed

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9. 19 + 3 + 8b 4 b A. 19 + 35 b B. 19 + 5b C. 19 + 7 1 b D. 19 + 8 3 4 4 4 b 10. -bc3 + 2b – 4bc2 + 5bc3 – 7b + 9bc2 A. 4bc3 + 5bc2 – 5b B. 9bc2 – 7b + 5bc3 – 4bc2 + 2b – bc3 C. –4bc3 + 5bc2 + 5b D. None of these Solve these word problems. 11. A car costs a dealer $4550. He wants to make a profit of 25% of the cost. How much profit does he expect? A. $5,687.50 B. $3,412.50 C. $182 D. $1,137.50 12. If 4 oranges cost x cents, which expression shows the cost of one orange? A. 4 – x = 1 B. x C. 4x –1 D. 4x + 1 4 13. Change 77oF to a Celsius reading. (Refer to the example on page 92 in your textbook) A. 45o B. 60.5o C. 25o D. None of these 14. Distance d equals rate r times time t, or d = rt. Find the distance traveled in 5 3 4 hours at 75 mph. A. 431 1 miles B. 75 miles C. 1,725 miles D. 93 3 miles 4 4 15. Find the interest charged on $775 at 13% for three years. A. $3,627 B. $302.25 C. $103.75 D. $2,286

This is the End of this exam. Move on to the next lesson. You will need a NEW answer sheet for your

next exam.

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Unit 4 Solving Equations (pgs. 96-122)

Equations and Solutions Review the material on page 98 and do some of the practice questions on pages 98-99. Solving Equations Using Addition and Subtraction Review the material on page 100 and pay special attention to the chart that explains which operations to use to solve equations. Also, do some of the practice questions on pages 100-101. Problem Solving – Using Equations Review the material on page 102 and pay special attention to the steps for solving word problems. Also, do some of the practice questions on pages 102-103. Solving Equations Using Multiplication and Division Review the material on pages 104-105 and do some of the practice questions on page 105. REMEMBER: multiplication is the OPPOSITE of division and division is the OPPOSITE of multiplication. Solving Two-Step Equations Review the material on pages 106-107 and do some of the practice questions on pages 108-109. Solving Equations With Like Terms Review the material on page 110 and do some of the practice questions on pages 111-112. Solving Equations That Involve Grouping Review the material on pages 113-114 and do some of the practice questions on page 114.

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Solving Literal Equations Review the material on pages 115-116 and do some of the practice questions on pages 116-117. REMEMBER: When solving literal equations, combine like terms and use opposite operations.

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Unit 4 Exam

Solve these equations for x. 1. 7x + 17 = 66 A. –17 B. 7 C. -7 D. None of these 2. 15x – 35 = 190 A. 15 B. 225 C. 35 D. –15 3. 16 = x 4 A. 1 B. 4 C. –4 D. 64 4 4. 6 8 x = 36 A. –36 B. 8 C. 6 D. 48 5. 27x = 243 A. 9 B. –9 C. –27 D. None of these 6. 3 - 6 = 15 7 x A. –49 B. 21 C. 49 D. 7 7. 5x – 7 = 1 9 A. 16 B. 3 1 C. Both A and B D. None of these 5 5 8. x – 5x + 16 = 72 A. 14 B. –14 C. 5 D. 16 9. 5(2 – x) = -20 + x A. –5 B. 5 C. 20 D -20

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10. 7x = 4.9 A. 7 B. –7 C. 0.07 D. 0.7 11. Mark realized that he had $743.15 in his savings account after he had deposited $57.69. What was the original balance? A. $685.46 B. $800.84 C. $12.88 D. $–685.46 12. An electronics store sells a wide screen television for $1,250. The television has a markup of $575. What is the store’s cost of the television? A. $1,825 B. $2.17 C. $675 D. None of these 13. If you subtract one fourth of a number from the number itself, you get 72. What is the number? A. 24 B. 96 C. 72 D. 4 3 14. A 21-foot piece of paper is cut into three pieces to create small banners for a child’s birthday party. The second piece is half as long as the first piece. The third piece is 4 feet less than the first. What are the lengths of the three pieces? A. 1 , 1, -4 B. 21, 10 1 , -4 C. 2 1 , 5 , 21 D. 5, 10, 6 2 2 2 2 15. There are 10 more science books than social studies books. Together there are 46 books. How many of each kind of book are there?

A. 10 social studies, 28 science B. 36 social studies, 46 science C. 10 social studies, 35 science D. None of these

This is the End of this exam.

Move on to the next lesson. You will need a NEW answer sheet for your next exam.

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Unit 5 Algebra Word Problems

From Words to Equations Review the material on pages 124-125 and pay special attention to the key words used in algebra. Also, do some of the practice questions on pages 125-127. Problem Solving – Checking Solutions Review the material on page 128 and pay special attention to the steps to solving word problems. Also, do some of the practice questions on page 129. Using Algebra to Solve Word Problems Review the material on pages 130-132 and pay special attention to the steps to solving word problems. Also, do some of the practice questions on pages 132-133. Consecutive Integer Word Problems Review the material on pages 136-137 and do some of the practice questions on pages 138-139. Uniform Motion Word Problems Review the material on pages 140-141 and pay special attention to the equation for solving uniform motion problems. Also, do some of the practice questions on page 141. Ratio and Proportion Word Problems Review the material on page 142 and do some of the practice questions on pages 142-143.

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Unit 5 Exam

1. Marie has x apples. Jennifer has 5 times as many as Marie. Express the amount Jennifer has. A. x + 5 B. 5x C. 5 – x D. None of these 2. The sum of note pads (n) and pushpins (p) is 45. Express the number of note pads if p is the number of pushpins. A. 45 – p B. 45 + p C. n + p = 45 D. None of these 3. 8 more than 3 times a number A. 8 + 3n B. 3n8 C. 3n + 8 D. 8(3n) 4. The product of a number and 7 is equal to 56. What is the number? A. 8 B. –8 C. n D. None of these 5. Six-tenths of a number is equal to 42. Find the number. A. 6 B. 7 C. n D. 70 10 6. If 13 is added to the difference of a number and 4, the result is 33. What is the number? A. 24 B. 9 C. –4 D. None of these 7. Find the perimeter of a triangle that has sides of 10 feet, 35 feet, and 17 feet. A. 5950 B. –42 C. 62 D. None of these 8. A cleaning solution is made by mixing detergent and ammonia in a ratio of 3 parts detergent to 4 parts ammonia. How much of each ingredient is need to make 49 gallons of cleaning solution?

A. 7 gallons of detergent; 7 gallons of ammonia B. 3 gallons of detergent; 4 gallons of ammonia C. 49 gallons of detergent; 49 gallons of ammonia D. 21 gallons of detergent; 28 gallons of ammonia

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9. Stephanie has a piece of cloth material that is 8 feet long. She must cut it so that one piece is 2 feet longer than twice the length of the other. What will be the length of each piece of material? A. 2 ft. and 6 ft. B. 6 ft. and 8 ft. C. 2 ft. and 8 ft. D. 2 ft. and 3ft. 10. Bob is helping his son Ken buy a used car. The monthly car payment is $250. They agreed that Bob would pay twice as much as Ken pays each month. How much does each pay?

A. Bob pays $166.67; Ken pays $83.33 B. Bob pays $168; Ken pays $84 C. Bob pays $125; Ken pays $125 D. None of these

11. Vanessa spent 13 hours on a plane. The plane was averaging 600 mph. How far did Vanessa go? A. 613 miles B. 46.15 miles C. 7800 miles D. None of these 12. Miles traveled 490 miles at 70 mph and another 200 miles at 40 mph. How long did his trip take? A. 7 hours B. 5 hours C. 2 hours D. 12 hours 13. If Tiffany left her job at 5:00 p.m. and traveled 25 miles to her home at 75 mph, what time would she reach her destination? A. 5:25 p.m. B. 5:20 p.m. C. 6:15 p.m. 5:30 p.m. 14. A $5.25 sales tax is charged for a $75 purchase. At this rate, what is the sales tax for a $347 purchase? A. $24.29 B. $347.07 C. $322.71 D. None of these 15. If a patient is supposed to take 2 teaspoons of cough medicine every four hours, how many teaspoons would the patient take in 24 hours? A. 2 B. 8 6 C. 24 D. 12

This is the End of this exam. Move on to the next lesson. You will need a NEW answer sheet for your

next exam.

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Unit 6 Multiplying and Dividing

Expressions With Exponents

Multiplying and Dividing Numbers With Exponents Review the material on page 146 and do some of the practice questions on pages 147-148. Exponent Raised to an Exponent Review the material on page 149 and do some of the practice questions on page 149. Using the Distributive Property Review the material on page 150 and pay special attention to the formula for the distributive property. Also, do some of the practice questions on page 151. Multiplying Using F.O.I.L. Review the material on pages 152-153 and do some of the practice questions on pages 153-154. Pay special attention to the steps in the F.O.I.L. method of multiplication. Problem Solving – Working with Exponents and Roots Review the material on page 155 and pay special attention to the steps for solving word problems with exponents and roots. Also, do some of the practice questions on page 156.

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Unit 6 Exam

Simplify 1. c4 ⋅ c6

A. c24 B. c10 C. 2c24 D. c-2

2. x3 ⋅ x15

A. x18 B. x45 C. 2x18 D. x-12

3. 916 ⋅ 913

A. 9208 B. 8113 C. 9208 D. 8129

4. (72)8

A. 710 B. 716 C. 498 D. None of these

5. (a4)10

A. a40 B. a14 C. a-6 D. 4a10

6. (y11)6

A. y5 B. 11y6 C. y17 D. y66

7. (-8x5)(-4x9) A. 32x45 B. 32x14 C. –12x45 D. 4x14 8. 3a(6a + 2) A. 18a2 + 6a B. 18a +6a C. 9a2 + 5 D. None of these 9. 5(4x4 + 9x – 2) A. 20x4 + 14x – 3 B. 20x4 + 45x – 10 C. 9x4 +14x –3 D. 9x4 +45x -10 10. (x + 2)(x + 10) A. 2x2 +10x + 12 B. x2 + 12x + 12 C. x2 +12x + 20 D. None of these

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11. (7x – 5)(9x –3) A. 63x2 – 66x + 15 B. 16x2 – 8x + 2 C. 63x2 + 24 – 15 D. 16x2 + 8 -2 12. (x + 15)(6x – 4) A. 7x + 17x – 11 B. 6x2 + 86x – 60 C. 7x + 17x + 11 D. None of these Find the sides of a square with the following area. 13. A = 81 ft2

A. 9 ft. B. –9 ft. C. 3 ft. D. 27 ft. The volume of a cube is length times width times height. Since the sides of a cube are equal, V = s3. Find the sides of the cube with the following volume. 14. V = 343 cm3

A. 4 cm B. 85.75 cm C. 7 cm D. None of these

Solve the following. 15. How many cubic meters of jellybeans can be placed in a cube-shaped storage bin if a side measures 1.7? A. 5.1 m3 B. 3.4 m3 C. 1.30 m3 D. 4.913 m3

This is the End of this exam. Move on to the next lesson. You will need a NEW answer sheet for your

next exam.

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Unit 7 Factoring

Finding the Greatest Common Factor Review the material on pages 160-161 and do some of the practice questions on page 161. Factoring Three-Term Expressions Review the information on pages 162-163 and pay special attention to the steps for factoring three-term expressions. Also, do some of the practice questions on pages 163-164. Perfect Squares and the Difference of Two Squares Review the information on pages 165-166 and do some of the practice questions on page 166. Solving Equations and Factoring Review the information on page 167 and do some of the practice questions on page 168. Problem Solving – Setting Up the Unknowns Review the information on page 169 and pay special attention to the steps for solving word problems. Also, do some of the practice questions on page 170.

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Unit 7 Exam

Factor these equations and write the letter for the correct answer on your answer sheet. 1. 4x2 - 8x A. 4(x2 – 2x) B. 2(2x2 – 4x) C. 4x(x2 – 2) D. 4x(x – 2) 2. x2 – 8x + 16 A. (x – 4)(x – 4) B. (x + 4)(x – 4) C. (x + 4)(x + 4) D. (x + 8)(x – 2) 3. x2 + 7x – 8 A. (x – 8)(x – 1) B. (x - 8)(x + 1) C. x(x + 7) – 8 D. None of these 4. x2 – 2x – 24 A. (x – 2)(x – 12) B. (x – 4)(x – 6) C. (x + 4)(x – 6) D. (x – 8)(x + 3) 5. x2 + 16x + 63 A. (x – 9)(x – 7) B. (x + 9)(x + 7) C. (x + 21)(x + 3) D. None of these 6. x2 – 49 A. (x – 7)(x – 7) B. (x + 7)(x + 7) C. (x + 7)(x – 7) D. (x – 49)(x + 1) 7. -18x7 – 9x8 + 6x9

A. 3(-6x7 – 3x8 + 2x9) B. 3x7(-6 –3x + 2x2) C. x(-18x6 – 9x7 + 6x8) D. None of these 8. 72 + 36x5

A. 2(36 + 18x5) B. 9(8 + 4x5) C. 36(2 + x5) D. 12(6 + 3x5)

9. 7x2 – 49x A. 7(x2 – 7x) B. 7(x + 7)(x – 7) C. (7x + 7x)(7x – 7x) D. 7x(x – 7) 10. 38x4 – 19x3 + 57x A. 19x(2x3 – x2 + 3) B. 19(2x4 – x3 + 3x) C. x(38x4 – 19x2 + 57) D. None of these

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11. x2 –12x + 35 = 0 A. (x + 7)(x – 5) B. (x – 7)(x – 5) C. (x + 7)(x + 5) D. x(x –12) = -35 12. x2 – x = 30 A. x(x –1) = 30 B. (x – 6)(x – 5) C. (x - 6)(x + 5) D. (x + 10)(x – 3) 13. x2 – 64 = 0 A. (x + 8)(x – 8) B. (x + 8)(x + 8) C. x2 = 64 D. (x + 16)(x – 4) 14. 3x2 – 9x = 0 A. 3(x2 – 3x) B. 3(x + 3)(x – 3) C. 3x(x – 3) D. None of these 15. x2 + x = 42 A. x3 = 42 B. (x + 7)(x – 6) C. (x + 7)(x + 6) D. (x – 7)(x – 6)

This is the End of this exam. Move on to the next lesson. You will need a NEW answer sheet for your

next exam.

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Unit 8 Graphing Equations

Locating Points on a Grid Review the material on pages 175-176 and do some of the practice questions on pages 176-177. Finding the Distance Between Two Points Review the material on pages 178-179 and pay special attention to the formula for the Pythagorean theorem. Also, do some of the practice questions on pages 179-180. Slope Review the material on pages 181-182 and do some of the practice questions on page 183. Solutions to Equations With Two Unknowns Review the material on page 184 and do some of the practice questions on page 185. Graphing the Equation of a Line Review the material on pages 186-187 and do some of the practice questions on pages 187-188. Graphing Two Equations on the Same Graph Review the material on page 189 and do some of the practice questions on pages 189-190. Solving Two Equations by Graphing Review the material on pages 191-192 and do some of the practice questions on pages 192-193. Problem Solving – Graphing Equations Review the material on page pages 194-195 and pay special attention to the steps for solving word problems that deal with graphing equations. Also, do the practice questions on page 195.

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Unit 8 Exam

Use the grid for problems 1-8. Choose the coordinates that are CLOSEST to each point WITHOUT GOING OVER. •B y •E •A •C x •F •D 1. Point A A. (5, 4) B. (4, 5) C. (7, 5) D. (-5, -4) 2. Point B A. (6, 8) B. (-7, -8) C. (-7, 9) D. (-6, 8) 3. Point C A. (3, 1) B. (2, -1) C. (-3, -1) D. (-4, -1) 4. Point D A. (9, 9) B. (10, -9) C. (10, 10) D. (9, -8) 5. Point E A. (-1, -8) B. (2, 7) C. (1, 8) D. (8, 1)

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6. Point F A. (-9, -6) B. (-9, -5,) C. (-10, -5) D. (10, 6) 7. Use the formula at the top of page 180 in your textbook to find the distance between point A and point B. A. 5 or 2.236 units B. 137 or 11.704 units C. 5 D. None of these 8. Use the formula at the top of page 180 in your textbook to find the distance between point C and point D. A. 98 or 9.899 units B. 170 or 13.038 units C. 13.038 units D. None of these

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9. Choose the number that completes the table for each of the equations. y = -x + 6 x y 0 6 1 5 3 A. 3 B. –3 C. 0 D. -6 10. y = x – 8 x y 2 -6 1 5 3 A. 9 B. 7 C. –7 D. 8 Find the slope of the lines through the given points. 11. (3, 4), (7, 6) A. 1 B. 2 C. 1 D. -1 2 4 4 2 12. (0, 0) , (3, 4) A. 1 1 B. 2 C. 4 D. –1 1 3 3 3 3 13. (4, 5), (2, 6) A. –2 B. 2 C. 1 D. -1 4 2 14. (3, -2), (3, 6) A. 8 B. –8 C. undefined D. 4 0

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15. (5, 1 ), (4, 3 1) 4 4 A. –1 B. –3 C. 3 D. 1 3 3

This is the End of this exam. Move on to the next lesson. You will need a NEW answer sheet for your

next exam.

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Unit 9 Inequalities

Inequalities Review the material on page 201 and do some of the practice questions on page 202. Solutions to Inequalities Review the material on page 203 and do some of the practice questions on page 203. Changing the Direction of the Inequality Review the material on page 204 and do some of the practice questions on page 205. Problem Solving – Solving Inequalities Review the material on page 208 and pay special attention to the steps for solving word problems that deal with inequalities. Also, do some of the practice questions on page 208.

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Unit 9 Exam Choose the letter for the symbol that correctly answers each question. 1. -9 ___ -1 A. > B. < C. = D. None of these 2. 0.008 ___ 0.156 A. > B. < C. = D. None of these 3. 0.39 ___ 0.51 A. > B. < C. = D. None of these 4. 15 3 25 __ 5 A. > B. < C. = D. None of these 5. 16 62 19 __ 73 A. > B. < C. = D. None of these Determine whether each equation is true or false. 6. -23 < -15 T (True) or F (False) 7. 0.09 < -0.1 T (True) or F (False) 8. 31 > -78 T (True) or F (False) 9. 1 > 1 4 8 T (True) or F (False)

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10. 1 < 18 3 54 T (True) or F (False) Solve. 11. x – 2 > 30 A. x > 32 B. x > 28 C. x < 32 D. x = 32 12. 17 < x – 25 A. 42 > x B. 25 < x C. x > 42 D. None of these 13. -15 > 5 + x A. –20 < x B. –20 > x C. x < -20 D. Both B and C 14. 2x – 11 < 8x + 13

A. 4 < x B. –4 < x C. x > 1 D. None of these 4 15. 36 – 5x > x + 18 A. 3 < x B. x < 1 C. x = 3 D. 3 > x 3

Congratulations!

You have completed the all the exams

Please send in your answer sheets

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