Algebra Practice Pack WALCH PUBLISHING
Table of Contents Unit 1: Algebra Basics Practice 1 What Are Negative and Positive Numbers?... 1 Practice Larger and Smaller Numbers................ Practice Actual Values and Absolute Values........... Practice 4 Adding Positive and Negative Numbers...... 4 Practice 5 The First Rule for Addition................. 5 Practice 6 The Second Rule for Addition............... 6 Practice 7.1 Subtracting Positive and Negative Numbers... 7 Practice 7. Subtracting Positive and Negative Numbers... 8 Practice 8.1 Multiplying and Dividing Signed Numbers... 9 Practice 8. Multiplying and Dividing Signed Numbers.. 1 Practice 9 Basic Terms and Symbols.................. 11 Practice 1.1 Solving Terms............................ 1 Practice 1. Solving Terms............................ 1 Practice 11 Solving Expressions....................... 14 Practice 1.1 Combining Like Terms.................... 15 Practice 1. Combining Like Terms.................... 16 Practice 1.1 Algebraic Equations...................... 17 Practice 1. Algebraic Equations...................... 18 Practice 14.1 Checking Your Work...................... 19 Practice 14. Checking Your Work...................... Practice 15 Inverse Operations....................... 1 Practice 16 Solving for Variables...................... Unit 1 Review............................... Unit : Solving Equations and Inequalities Practice 17.1 Solving Equations by Subtracting and Adding.............................. 4 Practice 17. Solving Equations by Subtracting and Adding.............................. 5 Practice 18.1 Solving Equations by Dividing and Multiplying.......................... 6 Practice 18. Solving Equations by Dividing and Multiplying.......................... 7 Practice 19.1 Solving Two-Step Equations............... 8 Practice 19. Solving Two-Step Equations............... 9 Practice.1 Combining Like Terms.................... Practice. Combining Like Terms.................... 1 Practice 1 Solving Equations with Fractional Coefficients.................... Practice Solving Equations with Squared Variables........................ Practice.1 Solving Equations with Parentheses......... 4 6 Walch Publishing Algebra Practice Pack iii
Table of Contents, continued iv Practice. Solving Equations with Parentheses......... 5 Practice 4 The Distance Formula..................... 6 Practice 5 Setting Up Algebraic Equations............ 7 Practice 6.1 Inequality Symbols....................... 8 Practice 6. Inequality Symbols....................... 9 Practice 7 Inequalities with Variables................. 4 Practice 8 Rules for Inequalities..................... 41 Practice 9.1 Solving Inequalities....................... 4 Practice 9. Solving Inequalities....................... 4 Practice Solving Inequalities in Two Steps........... 44 Practice 1 Simplifying Inequalities................... 45 Unit Review............................... 46 Algebra Practice Pack Unit : Graphing Linear Equations Practice Vertical Number Lines.................... 47 Practice Graphing Points on the Coordinate Plane.... 48 Practice 4 Graphing Lines on the Coordinate Plane..... 49 Practice 5.1 The Table Method of Graphing Linear Equations......................... 5 Practice 5. The Table Method of Graphing Linear Equations......................... 51 Practice 6 The Intercept Method of Graphing Linear Equations......................... 5 Practice 7 Finding Linear Slope...................... 5 Practice 8.1 The Formula for Finding Slope............. 54 Practice 8. The Formula for Finding Slope............. 55 Practice 9 Positive and Negative Slope................ 56 Practice 4 Graphing a Line When You Know the Slope and One Point........................... 57 Unit Review............................... 58 Unit 4: Polynomial Operations Practice 41 Adding and Subtracting Like Terms......... 59 Practice 4 Ordering Polynomials..................... 6 Practice 4.1 Adding and Subtracting Polynomials........ 61 Practice 4. Adding and Subtracting Polynomials....... 6 Practice 44 Multiplying Variables with Exponents....... 6 Practice 45.1 Multiplying Monomials................... 64 Practice 45. Multiplying Monomials................... 65 Practice 46 Dividing Variables with Exponents.......... 66 Practice 47.1 Dividing Monomials...................... 67 Practice 47. Dividing Monomials...................... 68 Practice 48.1 Multiplying a Polynomial by a Monomial.... 69 6 Walch Publishing
Table of Contents, continued Practice 48. Multiplying a Polynomial by a Monomial.... 7 Practice 49.1 Multiplying Binomials.................... 71 Practice 49. Multiplying Binomials.................... 7 Practice 5 Multiplying Special Binomials............. 7 Practice 51 Finding Factors.......................... 74 Practice 5 Finding the Greatest Common Factor....... 75 Practice 5 The Difference Between Two Squares....... 76 Practice 54.1 Factoring Trinomials...................... 77 Practice 54. Factoring Trinomials...................... 78 Practice 55.1 Factoring Trinomials with Negative Terms... 79 Practice 55. Factoring Trinomials with Negative Terms... 8 Practice 56.1 Factoring Other Negative Trinomials........ 81 Practice 56. Factoring Other Negative Trinomials........ 8 Practice 57 Factoring More Difficult Trinomials......... 8 Practice 58 Combining Factoring Skills................ 84 Unit 4 Review............................... 85 Unit 5: Quadratic Equations Practice 59 What Is a Quadratic Equation?............. 86 Practice 6 Zero Products............................ 87 Practice 61 Making Quadratic Equations Equal Zero.... 88 Practice 6.1 Solving Special Binomial Quadratic Equations...................... 89 Practice 6. Solving Special Binomial Quadratic Equations...................... 9 Practice 6 Solving Perfect Square Quadratic Equations...................... 91 Practice 64.1 Types of Quadratic Equations Solved by Factoring....................... 9 Practice 64. Types of Quadratic Equations Solved by Factoring....................... 9 Practice 65.1 Solving the Four Types of Quadratic Equations...................... 94 Practice 65. Solving the Four Types of Quadratic Equations...................... 95 Practice 66.1 The Quadratic Formula................... 96 Practice 66. The Quadratic Formula................... 97 Practice 67 The Quadratic Formula with Negative Coefficients..................... 98 Practice 68 Using the Quadratic Formula to Solve Word Problems..................... 99 Unit 5 Review.............................. 1 6 Walch Publishing Algebra Practice Pack v
PRACTICE 1 What Are Negative and Positive Numbers? Circle the correct answer for each question. 1. Look at the number line below. Is the circled number positive, negative, or neutral? 5 4 1 1 4 5 a. positive b. negative c. neutral. Look at the number line below. Is the circled number positive, negative, or neutral? 5 4 1 1 4 5 a. positive b. negative c. neutral. Is the number below positive, negative, or neutral? 9 a. positive b. negative c. neutral 4. Is the number below positive, negative, or neutral? a. positive b. negative c. neutral 5. Is the number below positive, negative, or neutral? 8 a. positive b. negative c. neutral 6 Walch Publishing Unit 1: Algebra Basics Algebra Practice Pack 1
PRACTICE Larger and Smaller Numbers Circle the correct answer for each question. 1. Look at the number line below. Which of the circled numbers is smaller? 5 4 1 1 4 5 a. 1 b. 4. Look at the number line below. Which of the circled numbers is larger? 5 4 1 1 4 5 a. b.. Look at the number line below. Which of the circled numbers is smaller? 5 4 1 1 4 5 a. b. 5 4. Look at the numbers below. Which of the numbers is larger? a. 6 b. 1 5. Look at the numbers below. Which of the numbers is smaller? a. b. 7 6. Look at the numbers below. Which of the numbers is larger? a. b. 14 Unit 1: Algebra Basics Algebra Practice Pack 6 Walch Publishing
PRACTICE 4 The Distance Formula Use the distance formula to solve each problem below. Write your answer on the line after each problem. Distance formula: D = r (t) 1. A train travels at an average rate of 6 miles. How long does it take the train to travel 41 miles? t = hours. Melanie jogs 1 miles in.5 hours. What is her average rate? r = mph. A car is traveling at an average rate of 57 miles per hour. If it travels for hours, how many miles will it travel? D = miles 4. A plane travels from California to Chicago in 4 hours. The trip is, miles and the wind is 5 miles per hour. How fast is the plane flying, according to its speedometer? r = miles per hour 5. A cyclist plans to travel 81 miles. If she cycles at an average speed of 1.5 miles per hour, how long will it take her? t = hours 6 Unit : Solving Equations and Inequalities Algebra Practice Pack 6 Walch Publishing
PRACTICE 5 Setting Up Algebraic Equations Write formulas for the problems below. 1. Mari is 5 years younger than Joe. Joe is twice as old as Paul. Write an equation to solve for Paul s age, using Mari s age as the unknown variable. Then use the formula to solve for Paul s age if Mari is 7. Formula: Paul s age:. The weight of substance A is half that of substance B. The weight of substance C is six times that of substance A. Write a formula for the relationship between the weights of substances B and C. Then use the formula to find the weight of substance C if the weight of substance B is 17 grams. Formula: Weight of substance A:. Kanisha has $5 more than Rachael. Kanisha has $5 less than 4 times as much money as Iris. Write a formula for the relationship between the amounts of money possessed by Rachael and Iris. Then use the formula to find the amount of money Iris has if Rachael has $75. Formula: Amount of money Iris has: 6 Walch Publishing Unit : Solving Equations and Inequalities Algebra Practice Pack 7
PRACTICE Graphing Points on the Coordinate Plane Graph each ordered pair below on the coordinate plane. 1. (, 6). ( 1, 5). ( 8, ) 4. (1, ) -1-9 -8-7 -6-5 -4 - - -1 1 9 8 7 6 5 4 1-1 - - -4-5 -6-7 -8-9 -1 1 4 5 6 7 8 9 1 y x Identify the ordered pairs represented by each letter on the graph below. 5. A 6. B 7. C 8. D 1 9 8 D 7 6 A 5 4 1-1 -9-8 -7-6 -5-4 - - -1-1 1 4 5 6 7 8 9 1 C - - -4-5 -6-7 -8-9 -1 B y x 48 Unit : Graphing Linear Equations Algebra Practice Pack 6 Walch Publishing
UNIT 4 REVIEW Circle the correct answer for each question or problem below. 1. Add these monomials: 5ab and 11ab. a. 6ab b. 16ab c. 6ab d.. Which polynomial below is in the correct order? a. x 4x + 19 b. x+ 5x + 7x c. x + 4x+ x d. 16ab x + x+7. Add these polynomials together: 5n 4 4n and n + n 8+ n. Make sure your answer is in the correct order. a. 5n + n n + n 8 b. c. 6n n n 8 d. 6n 4 n + n 8 5n 4 n + n 8 4. Multiply the following monomials: ( 4a ) and ( 1a). a. 4a 4 b. 4a c. 4a d. 5. 4m 5 is a simplification of which of the following? 4 1 16m m 8m a. b. c. d. 5 4m 4m 7m 6. Multiply these binomials using the FOIL method: (a + )(a 4). a. 5a a 1 b. 6a a 1 c. 6a + 6a 1 d. 4a 4 6 6m 5 4m 6a 6a 1 7. Look at the trinomial 6x 4x + 1. What is the greatest common factor of this trinomial? a. 6 b. 6x c. 1 d. 1x 8. Look at the trinomial x 8x. What are the factors of this trinomial? a. (x + )(x 1) b. (x 5)(x + 4) c. (x )(x + 1) d. (x + 5)(x 4) 9. Look at the trinomial a a+. What are the factors of this trinomial? a. (a )(a 16) b. (a 8)(a 4) c. (a 4)(a 8) d. (a + )(a + 16) 1. Look at the binomial 15a 96a. Which set of terms below are the factors of this binomial? a. (a)(1a 8)(a 4) b. (6a)(4a + 4)(4a 4) c. (6a)(5a + 4)(5a 4) d. (1a)(a + )(a + 4) 6 Walch Publishing Unit 4: Polynomial Operations Algebra Practice Pack 85