Developed in Consultation with Virginia Educators

Developed in Consultation with Virginia Educators

Table of Contents Virginia Standards of Learning Correlation Chart.............. 6 Chapter 1 Expressions and Operations.................... Lesson 1 Square and Cube Roots........................ 10 A.3 Lesson Laws of Exponents............................ 16 A..a Lesson 3 Add and Subtract Polynomials................... 1 A..b Lesson 4 Multiply Polynomials........................... 8 A..b Lesson 5 Factor Polynomials............................ 33 A..c Lesson 6 Divide Polynomials............................ 3 A..b Lesson 7 Write Algebraic Expressions..................... 45 A.1 Lesson 8 Evaluate Algebraic Expressions.................. 4 A.1 Chapter 1 Review........................................ 54 Virginia Standards of Learning Algebra I Chapter Equations and Inequalities..................... 57 Lesson Solve One-Variable Linear Equations Algebraically... 58 A.4.b, A.4.d Lesson 10 Solve Literal Equations......................... 64 A.4.a Lesson 11 Solve One-Variable Linear Equations Graphically.... 67 A.4.d Lesson 1 Slope and Intercepts........................... 7 A.6.a Lesson 13 Graph and Write Equations of Lines............... 78 A.6.a, A.6.b, A.7.f Lesson 14 Changes to the Slope and y-intercept............. 87 A.6.a, A.6.b Lesson 15 Solve Systems of Linear Equations Graphically...... 4 A.4.e Lesson 16 Solve Systems of Linear Equations Algebraically.... 100 A.4.e Lesson 17 Use Linear Equations to Solve Real-World Problems.................... 106 A.4.f, A.7.f Lesson 18 Write and Solve One-Variable Linear Inequalities... 11 A.5.a, A.5.b, A.5.c Lesson 1 Solve and Graph Two-Variable Linear Inequalities... 10 A.5.a, A.5.b, A.5.c, A.6.a, A.6.b Lesson 0 Solve Systems of Inequalities................... 18 A.5.d Lesson 1 Solve Quadratic Equations Graphically........... 134 A..c, A.4.c, A.7.f Lesson Solve Quadratic Equations Algebraically.......... 141 A..c, A.4.c Chapter Review....................................... 147 4

Chapter 3 Functions.................................. 153 Lesson 3 Determine If a Relation Is a Function............. 154 A.7.a, A.7.f Lesson 4 Represent Functions in Multiple Forms........... 16 A.7.f Lesson 5 Domain and Range........................... 168 A.7.b, A.7.e Lesson 6 Zeros and Intercepts of Functions............... 175 A.7.c, A.7.d Lesson 7 Direct Variation.............................. 18 A.8 Lesson 8 Inverse Variation............................. 188 A.8 Chapter 3 Review....................................... 1 Virginia Standards of Learning Algebra I Chapter 4 Statistics.................................. 17 Lesson Mean Absolute Deviation...................... 18 A. Lesson 30 Variance and Standard Deviation................ 05 A. Lesson 31 Compare Mean Absolute Deviation and Standard Deviation....................... 13 A. Lesson 3 Z-scores................................... 1 A. Lesson 33 Box-and-Whisker Plots........................ 4 A.10 Lesson 34 Line of Best Fit.............................. 30 A.11 Lesson 35 Curve of Best Fit............................. 38 A.11 Chapter 4 Review....................................... 45 Glossary.............................................. 50 Practice Test 1......................................... 55 Practice Test......................................... 71 Algebra I Formula Sheet................................. 87 5

Chapter 1 Lesson 1 Square and Cube Roots SOL: A.3 To square a number means to raise it to the power of or to multiply it by itself. For example, 8 is read as eight squared. 8 8 8 64 The opposite, or inverse, of squaring a number is taking its square root. The radical symbol,, is used to indicate a square root. The number under that symbol is called the radicand. 64 8, because 8 64. Since ( 8) is also equal to 64, the number 8 is another square root of 64. The positive number 8 is called the principal square root of 64. It is a mathematical convention to consider only the principal, or positive, square root. To indicate the negative square root, write 64. Any number that has a whole-number square root is a perfect square. For example, 64 is a perfect square because 64 is equal to a whole number, 8. Below are the first 5 consecutive perfect squares. 1, 4,, 16, 5, 36, 4, 64, 81, 100, 11, 144, 16, 16, 5, 56, 8, 34, 361, 400, 441, 484, 5, 576, 65 To take the square root of a perfect square, ask yourself: what whole number multiplied by itself equals that number? Example 1 What is the value of _ 5? Decide if the radicand is a perfect square. If so, decide which whole number can be multiplied by itself to get that number. Step 1 Decide if the radicand is a perfect square. Look back at the list of perfect squares. 5 is a perfect square. Step Ask yourself what whole number multiplied by itself is equal to 5. If you do not know the answer from memory, use guess and check. Since the last digit in 5 is 5, 5 is a multiple of 5 but not a multiple of 10. Guess 5: 5 5 65 5 is too high. Guess 15: 15 15 5 15 works. Solution The value of _ 5 is 15 because 15 5. 10

A square root in simplest form is one in which the radicand has no perfect square factors other than 1. The properties below will help you simplify square roots. Product Property of Square Roots The square root of a product is equal to the product of the square roots of the factors. ab a b 50 5 5 5 Quotient Property of Square Roots The square root of a quotient is equal to the quotient of the square root of the dividend and the square root of the divisor. a b a b _ 16 16 3 4 Example Simplify: 7 Use the product property of square roots. Step 1 Step Step 3 Solution Find factors of 7 that are perfect squares. 7 8 ( 4) Note: 4 and are perfect squares. Rewrite 7 as a product of square roots. 7 4 4 Simplify by taking the square roots of the perfect squares. 7 4 7 3 7 6 7 6 7 6 11

You can also use what you know about square roots to simplify algebraic expressions. An algebraic expression is a combination of numbers and variables that are connected by one or more operations. A variable is a symbol or letter, such as x, that is used to represent a number. Example 3 Simplify: 4a b First simplify the numerator. Then simplify the denominator. Step 1 Step Step 3 Step 4 Step 5 Solution Rewrite the algebraic expression under the square root symbol as the quotient of two square roots. 4a b 4a b Rewrite the numerator, 4a, as the product of two factors. 4a 4 a Evaluate each factor in the numerator. 1st factor: 4 nd factor: a a a a 4a 4 a a a Evaluate the denominator. b b b b Simplify the original expression. 4a b a b The expression can be simplified as a b. 1 Chapter 1: Expressions and Operations

Lesson 1: Square and Cube Roots To cube a number means to raise it to the power of 3. 3 8 The inverse of cubing a number is taking its cube root. The cube root is denoted by 3. A perfect cube, such as 8, has a cube root that is an integer. 3 8 3 The product and quotient properties of radicals that apply to square roots also extend to the cube root and the nth root of a number. Although you can take the square root of only positive numbers and zero in the real number system, you can take the cube root of any real number: positive, negative, or zero. 3_ 8 3 ( ) ( ) ( ) Example 4 Simplify: 3 64 Step 1 Step Step 3 Solution Use the product property of square roots. Write 64 as a product of its perfect cube factors. 3 64 3 8 8 Apply the property. 3 8 8 3 8 3 8 Simplify. 3 8 3 8 4 3 64 4 13

A cube root in simplest form is one in which the radicand has no perfect cube factors other than 1. Example 5 Simplify: 3 50 Use the product property of radicals. Step 1 Find perfect cube factors of 50. Fully factoring a number will help in identifying perfect cube factors. 50 15 5 5 5 5 5 Step Step 3 Solution Write 50 as a product of cube roots, with the perfect cube as the negative factor. 3 50 3 ( 15) 3 3 15 Simplify. 3 3 ( 5) 3 3 ( 5) 5 3 When simplified, 3 50 5 3. Coached Example Simplify: x 3 y 4 Rewrite as a product of two square roots. _ x 3 y 4 x 3 The term x 3 is the product of the perfect square and. Simplify x 3 using the square root of the perfect square factor. x 3 Simplify y 4. y 4 Simplify the original expression. _ x 3 y 4 The simplest form of _ x 3 y 4 is. 14 Chapter 1: Expressions and Operations

Lesson 1: Square and Cube Roots Lesson Practice Choose the correct answer. 1. What is the value of _ 16? A. 13 B. 14 C. 16 D. 8. What is the value of 3 8 15? A. 5 B. 4 5 C. _ 5 D. 4_ 5 3. Simplify: 8 A. 7 B. C. 7 D. 7 7 5. Simplify: 3 _ 54 A. 3 3 6 B. 3 3 C. 3 3 D. 3 3 6 6. Simplify: 3 81 A. 16 B. 3 C. D. 4 7. Simplify: 3 7 A. 3 3 B. 3 C. 6 D. 6 4. Simplify: y 5 A. 3y _ y B. 3y 3 C. 3y 4 _ y D. 3y y 8. Simplify: 16a 4 b 6 A. 8a b 4 B. 4a b C. 8a b 3 D. 4a b 3 15