Algebra Practice Pack WALCH PUBLISHING
Table of Contents Unit 1: Algebra Basics Practice 1 What Are Negative and Positive Numbers?... 1 Practice 2 Larger and Smaller Numbers................ 2 Practice 3 Actual Values and Absolute Values........... 3 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 7.2 Subtracting Positive and Negative Numbers... 8 Practice 8.1 Multiplying and Dividing Signed Numbers... 9 Practice 8.2 Multiplying and Dividing Signed Numbers.. 1 Practice 9 Basic Terms and Symbols.................. 11 Practice 1.1 Solving Terms............................ 12 Practice 1.2 Solving Terms............................ 13 Practice 11 Solving Expressions....................... 14 Practice 12.1 Combining Like Terms.................... 15 Practice 12.2 Combining Like Terms.................... 16 Practice 13.1 Algebraic Equations...................... 17 Practice 13.2 Algebraic Equations...................... 18 Practice 14.1 Checking Your Work...................... 19 Practice 14.2 Checking Your Work...................... 2 Practice 15 Inverse Operations....................... 21 Practice 16 Solving for Variables...................... 22 Unit 1 Review............................... 23 Unit 2: Solving Equations and Inequalities Practice 17.1 Solving Equations by Subtracting and Adding.............................. 24 Practice 17.2 Solving Equations by Subtracting and Adding.............................. 25 Practice 18.1 Solving Equations by Dividing and Multiplying.......................... 26 Practice 18.2 Solving Equations by Dividing and Multiplying.......................... 27 Practice 19.1 Solving Two-Step Equations............... 28 Practice 19.2 Solving Two-Step Equations............... 29 Practice 2.1 Combining Like Terms.................... 3 Practice 2.2 Combining Like Terms.................... 31 Practice 21 Solving Equations with Fractional Coefficients.................... 32 Practice 22 Solving Equations with Squared Variables........................ 33 Practice 23.1 Solving Equations with Parentheses......... 34 26 Walch Publishing Algebra Practice Pack iii
Table of Contents, continued iv Practice 23.2 Solving Equations with Parentheses......... 35 Practice 24 The Distance Formula..................... 36 Practice 25 Setting Up Algebraic Equations............ 37 Practice 26.1 Inequality Symbols....................... 38 Practice 26.2 Inequality Symbols....................... 39 Practice 27 Inequalities with Variables................. 4 Practice 28 Rules for Inequalities..................... 41 Practice 29.1 Solving Inequalities....................... 42 Practice 29.2 Solving Inequalities....................... 43 Practice 3 Solving Inequalities in Two Steps........... 44 Practice 31 Simplifying Inequalities................... 45 Unit 2 Review............................... 46 Algebra Practice Pack Unit 3: Graphing Linear Equations Practice 32 Vertical Number Lines.................... 47 Practice 33 Graphing Points on the Coordinate Plane.... 48 Practice 34 Graphing Lines on the Coordinate Plane..... 49 Practice 35.1 The Table Method of Graphing Linear Equations......................... 5 Practice 35.2 The Table Method of Graphing Linear Equations......................... 51 Practice 36 The Intercept Method of Graphing Linear Equations......................... 52 Practice 37 Finding Linear Slope...................... 53 Practice 38.1 The Formula for Finding Slope............. 54 Practice 38.2 The Formula for Finding Slope............. 55 Practice 39 Positive and Negative Slope................ 56 Practice 4 Graphing a Line When You Know the Slope and One Point........................... 57 Unit 3 Review............................... 58 Unit 4: Polynomial Operations Practice 41 Adding and Subtracting Like Terms......... 59 Practice 42 Ordering Polynomials..................... 6 Practice 43.1 Adding and Subtracting Polynomials........ 61 Practice 43.2 Adding and Subtracting Polynomials....... 62 Practice 44 Multiplying Variables with Exponents....... 63 Practice 45.1 Multiplying Monomials................... 64 Practice 45.2 Multiplying Monomials................... 65 Practice 46 Dividing Variables with Exponents.......... 66 Practice 47.1 Dividing Monomials...................... 67 Practice 47.2 Dividing Monomials...................... 68 Practice 48.1 Multiplying a Polynomial by a Monomial.... 69 26 Walch Publishing
Table of Contents, continued Practice 48.2 Multiplying a Polynomial by a Monomial.... 7 Practice 49.1 Multiplying Binomials.................... 71 Practice 49.2 Multiplying Binomials.................... 72 Practice 5 Multiplying Special Binomials............. 73 Practice 51 Finding Factors.......................... 74 Practice 52 Finding the Greatest Common Factor....... 75 Practice 53 The Difference Between Two Squares....... 76 Practice 54.1 Factoring Trinomials...................... 77 Practice 54.2 Factoring Trinomials...................... 78 Practice 55.1 Factoring Trinomials with Negative Terms... 79 Practice 55.2 Factoring Trinomials with Negative Terms... 8 Practice 56.1 Factoring Other Negative Trinomials........ 81 Practice 56.2 Factoring Other Negative Trinomials........ 82 Practice 57 Factoring More Difficult Trinomials......... 83 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 62.1 Solving Special Binomial Quadratic Equations...................... 89 Practice 62.2 Solving Special Binomial Quadratic Equations...................... 9 Practice 63 Solving Perfect Square Quadratic Equations...................... 91 Practice 64.1 Types of Quadratic Equations Solved by Factoring....................... 92 Practice 64.2 Types of Quadratic Equations Solved by Factoring....................... 93 Practice 65.1 Solving the Four Types of Quadratic Equations...................... 94 Practice 65.2 Solving the Four Types of Quadratic Equations...................... 95 Practice 66.1 The Quadratic Formula................... 96 Practice 66.2 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 26 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 3 2 1 1 2 3 4 5 a. positive b. negative c. neutral 2. Look at the number line below. Is the circled number positive, negative, or neutral? 5 4 3 2 1 1 2 3 4 5 a. positive b. negative c. neutral 3. 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 26 Walch Publishing Unit 1: Algebra Basics Algebra Practice Pack 1
PRACTICE 2 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 3 2 1 1 2 3 4 5 a. 1 b. 4 2. Look at the number line below. Which of the circled numbers is larger? 5 4 3 2 1 1 2 3 4 5 a. b. 2 3. Look at the number line below. Which of the circled numbers is smaller? 5 4 3 2 1 1 2 3 4 5 a. 3 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. 2 b. 14 2 Unit 1: Algebra Basics Algebra Practice Pack 26 Walch Publishing
PRACTICE 26.2 Inequality Symbols Write the correct inequality symbol for each statement below. Example: 34 < 44 1. 1 2. 5 7 3. 6 3 4. 11 11 5. 27 15 1 6. 2 3 7 7..5.1 3 8. 4 1 1 9. 1 1 3 1. 2 9 1 11..9 12. 15 9 13. 5 5.5 1 14. 3 1 3 15. 1 1.1 26 Walch Publishing Unit 2: Solving Equations and Inequalities Algebra Practice Pack 39
PRACTICE 27 Inequalities with Variables Do each exercise that follows. Example: Show the inequality x on the number line below. 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 1. Show the inequality n > 1 on the number line below. 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 2. Show the inequality a 5 on the number line below. 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 3. Look at the number lines below. Circle the letter of the one that shows the inequality x 7. a. 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 b. 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 c. 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 d. 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 4 Unit 2: Solving Equations and Inequalities Algebra Practice Pack 26 Walch Publishing
PRACTICE 51 Finding Factors Factor each number or term at least three ways. Write your answer on the three lines after each problem. Example: 2 2 8x = 2 4 x = 8 x x = 2 2 2 x x 1. 12a 3 2. 25y 2 3. 16c 2 d 4. 5pq 5. 2a 6. 49m 5 74 Unit 4: Polynomial Operations Algebra Practice Pack 26 Walch Publishing
PRACTICE 52 Finding the Greatest Common Factor Factor each polynomial below. Use the greatest common factor. Write your answer on the line after each polynomial. Example: 15a+ 1 = 5( 3a+ 2) 15a+ 1 15a 1 = + = 3a + 2 5 5 5 1. 3 18a = 2. 4xy + 2x = 3. 7b + 14 = 4. 8m 2 24m= 5. 3ab 2 + 21a 2 b = 6. 6wv 2 + 15wv 2 + 12v 2 = 7. ant + ark = 8. 45f 3 g+ 18fg = 9. 7mnp 21np + 3n = 1. 6xy 15x = 26 Walch Publishing Unit 4: Polynomial Operations Algebra Practice Pack 75