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Holt McDougal Florida Larson Algebra 1 Chapter Resources Volume 1: Chapters 1-6 LAHA111FLCRB_FMv1_00i-0vi.indd 1 2/10/09 7:44:24 PM Copyright © Holt McDougal, a division of Houghton Miffl in Harcourt Publishing Company. All rights reserved. Warning: No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system without the prior written permission of Holt McDougal unless such copying is expressly permitted by federal copyright law. Teachers using HOLT McDOUGAL FLORIDA LARSON ALGEBRA 1 may photocopy complete pages in suffi cient quantities for classroom use only and not for resale. HOLT McDOUGAL is a trademark of Houghton Miffl in Harcourt Publishing Company. Printed in the United States of America If you have received these materials as examination copies free of charge, Holt McDougal retains title to the materials and they may not be resold. Resale of examination copies is strictly prohibited. Possession of this publication in print format does not entitle users to convert this publication, or any portion of it, into electronic format. ISBN 13: 978-0-547-25017-5 ISBN 10: 0-547-25017-7 1 2 3 4 5 6 7 8 9 XXX 15 14 13 12 11 10 09 LAHA111FLCRB_FMv1_00i-0vi.indd ii LAHA111FLCRB_FMv1_00i-0vi.indd ii 9/24/09 7:26:48 PM 9/24/09 7:26:48 PM Algebra 1 Chapter Resource Book iii Contents Chapter 1 Expressions, Equations, and Functions Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–4 1.1 Evaluate Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–10 1.2 Apply Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–19 1.3 Write Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20–25 1.4 Write Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26–32 1.5 Use a Problem Solving Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33–39 1.6 Represent Functions as Rules and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40–46 1.7 Represent Functions as Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47–57 Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Chapter 2 Properties of Real Numbers Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61–64 2.1 Use Integers and Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65–73 2.2 Add Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74–79 2.3 Subtract Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80–87 2.4 Multiply Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88–94 2.5 Apply the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95–101 2.6 Divide Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102–107 2.7 Find Square Roots and Compare Real Numbers . . . . . . . . . . . . . . . . . . . . 108–117 Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 LAHA111FLCRB_FMv1_00i-0vi.indd 3 1/30/09 11:42:25 AM Copyright © Holt McDougal. All rights reserved. Algebra 1 Chapter Resource Book iv Chapter 3 Solving Linear Equations Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119–122 3.1 Solve One-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123–129 3.2 Solve Two-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130–138 3.3 Solve Multi-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139–144 3.4 Solve Equations with Variables on Both Sides . . . . . . . . . . . . . . . . . . . . . . 145–152 3.5 Write Ratios and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153–159 3.6 Solve Proportions Using Cross Products . . . . . . . . . . . . . . . . . . . . . . . . . . 160–165 3.7 Solve Percent Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166–174 3.8 Rewrite Equations and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175–181 Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Chapter 4 Graphing Linear Equations and Functions Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183–186 4.1 Plot Points in a Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187–198 4.2 Graph Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199–212 4.3 Graph Using Intercepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213–222 4.4 Find Slope and Rate of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223–231 4.5 Graph Using Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232–246 4.6 Model Direct Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247–255 4.7 Graph Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256–265 Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 LAHA111FLCRB_FMv1_00i-0vi.indd 4 1/30/09 11:42:26 AM Copyright © Holt McDougal. All rights reserved. Algebra 1 Chapter Resource Book v Chapter 5 Writing Linear Equations Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267–270 5.1 Write Linear Equations in Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . 271–277 5.2 Use Linear Equations in Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . . 278–283 5.3 Write Linear Equations in Point-Slope Form . . . . . . . . . . . . . . . . . . . . . . . 284–296 5.4 Write Linear Equations in Standard Form . . . . . . . . . . . . . . . . . . . . . . . . . 297–303 5.5 Write Equations of Parallel and Perpendicular Lines . . . . . . . . . . . . . . . . 304–310 5.6 Fit a Line to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311–320 5.7 Predict with Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321–330 Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Chapter 6 Solving and Graphing Linear Inequalities Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333–336 6.1 Solve Inequalities Using Addition and Subtraction . . . . . . . . . . . . . . . . . . 337–345 6.2 Solve Inequalities Using Multiplication and Division . . . . . . . . . . . . . . . . 346–355 6.3 Solve Multi-Step Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356–367 6.4 Solve Compound Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368–378 6.5 Solve Absolute Value Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379–388 6.6 Solve Absolute Value Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389–397 6.7 Linear Inequalities in Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398–409 Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 Gridded Response Answer Sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Resource Book Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1–A72 LAHA111FLCRB_FMv1_00i-0vi.indd v LAHA111FLCRB_FMv1_00i-0vi.indd v 9/24/09 7:27:06 PM 9/24/09 7:27:06 PM Copyright © Holt McDougal. All rights reserved. Algebra 1 Chapter Resource Book vi Contents Descriptions of Resources This Chapter Resource Book is organized by lessons within the chapter in order to make your planning easier. The following materials are provided: Family Letter This guide helps families contribute to student success by providing an overview of the chapter along with questions and activities for families to work on together. Graphing Calculator Activities with Keystrokes Keystrokes for two models of calculators are provided for each Graphing Calculator Activity in the Student Edition. Activity Support Masters These blackline masters make it easier for students to record their work on selected activities in the Student Edition. Practice A, B, and C These exercises offer additional practice for the material in each lesson, including application problems. There are three levels of practice for each lesson: A (basic), B (average), and C (advanced). Review for Mastery These two pages provide additional instruction, worked-out examples, and practice exercises covering the key concepts and vocabulary in each lesson. Problem Solving Workshops These blackline masters provide extra problem solving opportunities in addition to the workshops given in the textbook. There are three types of workshops: Alternative Methods, Worked-Out Examples, and Mixed Problem Solving. Challenge Practice These exercises offer challenging practice on the mathematics of each lesson. Chapter Review Game This worksheet offers fun practice at the end of the chapter and provides an alternative way to review the chapter content in preparation for the Chapter Test. Gridded Response Answer Sheet This page provides 12 answer grids for the teacher to copy and distribute as needed for use with the gridded response questions in the Problem Solving Workshops. LAHA111FLCRB_FMv1_00i-0vi.indd 6 2/10/09 7:44:27 PM Name ——————————————————————— Date ———————————— Copyright © Holt McDougal. All rights reserved. 1 Algebra 1 Chapter 1 Resource Book CHAPTER 1 Chapter Overview One way you can help your student succeed in Chapter 1 is by discussing the lesson goals in the chart below. When a lesson is completed, ask your student the following ques- tions. “What were the goals of the lesson? What new words and formulas did you learn? How can you apply the ideas of the lesson to your life?” Lesson Title Lesson Goals Key Applications 1.1: Evaluate Expressions Evaluate algebraic expressions and use exponents. • Movies • Storage Cubes • Football 1.2: Apply Order of Operations Focus on Reasoning Use the order of operations to evaluate expressions. Determine whether statements are always, sometimes, or never true. • Litter Collection • Sales • Online Shopping 1.3: Write Expressions Translate verbal phrases into expressions. • Tips • Training • Cycling 1.4: Write Equations and Inequalities Translate verbal sentences into equations or inequalities. • Mountain Biking • Compact Discs • Baking Measurements 1.5: Use a Problem Solving Plan Use a problem solving plan to solve problems. • Running • Framing • Hiking 1.6: Represent Functions as Rules and Tables Represent functions as rules and as tables. • Concert Tickets • Yard Sale • Savings 1.7: Represent Functions as Graphs Focus on Functions Represent functions as graphs. Determine whether a relation is a function when the relation is represented by a table or a graph. • SAT Scores • Guitar Sales • Elections Key Ideas for Chapter 1 In Chapter 1, you will apply the key ideas listed in the Chapter Opener (see page 1) and reviewed in the Chapter Summary (see page 53). 1. Writing and evaluating algebraic expressions 2. Using expressions to write equations and inequalities 3. Representing functions as verbal rules, equations, tables, and graphs Family Letter For use with Chapter 1 CHAPTER 1 CHAPTER SUPPORT LAHA111FLCRB_C01_001-002.indd 1 LAHA111FLCRB_C01_001-002.indd 1 1/16/09 5:21:44 PM 1/16/09 5:21:44 PM Name ——————————————————————— Date ———————————— Copyright © Holt McDougal. All rights reserved. 2 Algebra 1 Chapter 1 Resource Book CHAPTER 1 Family Letter continued For use with Chapter 1 Key Ideas Your student can demonstrate understanding of key concepts by working through the following exercises with you. Lesson Exercise 1.1 Find the volume of a cube-shaped CD player, where each side s is 23 centimeters. Use the formula V 5 s3. 1.2 Evaluate 10(x 2 3) 1 6 and 10x 2 3 1 6 when x 5 5. Focus on Reasoning Tell whether the statement is always, sometimes, or never true: For a given whole number x, the product 6x is an odd whole number. 1.3 The student council is holding a craft show as a fundraiser. Each exhibitor is charged $40 for a table and the admission price is $3.50 per person. Write an expression for the amount (in dollars) raised. There are 38 exhibitors and 420 people attend the craft show. Find the amount raised. 1.4 It costs $380 to attend a leadership conference. The school will contribute $75. You can save $35 per week. Use the inequality 35w 1 75 ≥ 380 to model the situation. What does w represent? How many weeks will it take to save enough money? 1.5 You are framing a picture that is 9.5 inches long and 7 inches wide. The picture is bordered by 2-inch matting. The wood to make the frame is 1.5 inches wide. Find the length and width of the frame. What is the total area of the framed picture? Use a problem solving plan to find the solution. 1.6 Make a table for the function y 5 2x 2 2 with domain 1, 2, 3, 4, and 5. Identify the range of the function. 1.7 Graph the function y 5 3x 1 1 with domain 0, 1, 2, 3, and 4. Focus on Functions Tell whether the pairing of x-values and y-values is necessarily a function: A teacher makes a table that lists the year x and the population of Miami y each year during a ten-year period. Home Involvement Activity Directions Use exactly five 5’s and grouping symbols to make each whole number from one to ten. For example, 1 5 5 } 5 1 1 5 2 5 } 5 2 . Answers 1.1: 12,167 cm3 1.2: 26; 53 Focus on Reasoning: never 1.3: 40e 1 3.5p; $2990 1.4: w represents the number of weeks needed to save; 9 weeks 1.5: 16.5 in.; 14 in.; 321 in.2 1.6: x 1 2 3 4 5 y 0 2 4 6 8 ; range: 0, 2, 4, 6, 8 1.7 x y O 1 2 3 2 4 5 4 6 8 10 12 14 Focus on Functions: yes CHAPTER SUPPORT LAHA111FLCRB_C01_001-002.indd 2 LAHA111FLCRB_C01_001-002.indd 2 1/16/09 5:21:45 PM 1/16/09 5:21:45 PM Nombre —————————————————————— Fecha ——————————— Copyright © Holt McDougal. All rights reserved. 3 Algebra 1 Chapter 1 Resource Book CHAPTER 1 CAPÍTULO 1 Vistazo al capítulo Una manera en que puede ayudar a su hijo a tener éxito en el Capítulo 1 es hablar sobre los objetivos de la lección en la tabla a continuación. Cuando se termina una lección, pregúntele a su hijo lo siguiente: “¿Cuáles fueron los objetivos de la lección? ¿Qué palabras y fórmulas nuevas aprendiste? ¿Cómo puedes aplicar a tu vida las ideas de la lección?” Título de la lección Objetivos de la lección Aplicaciones clave 1.1: Evaluar expresiones Evaluar las expresiones algebraicas y usar exponentes • Películas • Almacenaje • Fútbol americano 1.2: Aplicar el orden de las operaciones Enfoque en el razonamiento Usar el orden de las operaciones para evaluar expresiones Determinar si enunciados son siempre, a veces o nunca verdaderos • Recolecta de basura • Ventas • De compras en línea 1.3: Escribir expresiones Convertir frases verbales en expresiones • Pautas • Entrenamiento • Ciclismo 1.4: Escribir ecuaciones y desigualdades Convertir oraciones verbales en ecuaciones o desigualdades • Bicicletas de montañas • Discos compactos • Medidas de cocina 1.5: Usar un plan de resolución de problemas Usar un plan para resolver problemas • Correr • Enmarcar • Alpinismo 1.6: Representar funciones como reglas y tablas Representar funciones como reglas y tablas • Entradas de concierto • Mercadillo • Ahorros 1.7: Representar funciones como gráfi cas Enfoque en las funciones Representar funciones como gráfi cas Determinar si una relación es una función cuando la relación se representa por una tabla o una gráfi ca • Puntajes del SAT • Ventas de guitarras • Elecciones Ideas clave para el Capítulo 1 En el Capítulo 1, aplicarás las ideas clave enumeradas en la Presentación del capítulo (ver la página 1) y revisadas en el Resumen del capítulo (ver la página 53). 1. Escribir y evaluar expresiones algebraicas 2. Usar expresiones para escribir ecuaciones y desigualdades 3. Representar funciones como reglas verbales, ecuaciones, tablas y gráficas Carta para la familia Usar con el Capítulo 1 CHAPTER SUPPORT LAHA111FLCRB_C01_003-004.indd 3 LAHA111FLCRB_C01_003-004.indd 3 1/16/09 5:21:51 PM 1/16/09 5:21:51 PM Nombre —————————————————————— Fecha ——————————— Copyright © Holt McDougal. All rights reserved. 4 Algebra 1 Chapter 1 Resource Book CHAPTER 1 CAPÍTULO 1 Carta para la familia continúa Usar con el Capítulo 1 Ideas clave Su hijo puede demostrar la comprensión de las ideas clave al hacer los siguientes ejercicios con usted. Lección Ejercicio 1.1 Halla el volumen de un tocador de CD en forma de cubo, donde cada lado I mide 23 centímetros. Usa la fórmula V 5 P. 1.2 Evalúa 10(x 2 3) 1 6 y 10x 2 3 1 6 cuando x 5 5. Enfoque en el razonamiento Determina si cada enunciado es siempre, a veces o nunca verdadero: Para un número entero x, el producto 6x es siempre un número entero impar. 1.3 El consejo escolar planifica una exhibición de manualidades para recaudar dinero. Se le cobran $40 a cada expositor para una mesa y el costo de entrada es $3.50 por persona. Escribe una expresión para el total (en dólares) que se recaudó. Había 38 expositores y 420 personas fueron a la exhibición. Halla el total de dinero recaudado. 1.4 Cuesta $380 para asistir a una conferencia de liderazgo. Tu escuela pagará $75. Tú puedes ahorrar $35 por semana. Usa la desigualdad 35s 1 75 ≥ 380 para hacer un modelo de la situación. ¿Qué representa s? ¿Por cuántas semanas tendrás que ahorrar hasta tener el dinero suficiente? 1.5 Vas a enmarcar un cuadro que mide 9.5 pulgadas de largo y 7 pulgadas de ancho. El cuadro se borda por una esfera de 2 pulgadas. La madera que se usa para hacer el marco mide 1.5 pulgadas de ancho. Halla la longitud y el ancho del marco. ¿Qué es el área total del cuadro enmarcado? Usa un plan para resolver el problema. 1.6 Grafica la función y 5 2x 2 2 con el dominio 1, 2, 3, 4 y 5. Identifica el rango de la función. 1.7 Grafica la función y 5 3x 1 1 con el dominio 1, 2, 3 y 4. Enfoque en las funciones Determina si la combinación de valores x e y es una función: Un maestro hace una tabla que enumera el año x y la población de Miami y cada año durante un período de diez años. Actividad para la familia Instrucciones Usa precisamente cinco 5 y símbolos de agrupación para formar cada número entero desde el uno hasta el diez. Por ejemplo, 1 5 5 } 5 1 1 5 2 5 } 5 2 . Respuestas 1.1: 12,167 cm3 1.2: 26; 53 Enfoque en el razonamiento: nunca 1.3: 40e 1 3.5p; $2990 1.4: s representa el número de semanas necesarias para ahorrar; 9 semanas 1.5: 16.5 pulg; 14 pulg; 321 pulg2 1.6: x 1 2 3 4 5 y 0 2 4 6 8 ; rango: 0, 2, 4, 6, 8 1.7 x y O 1 2 3 2 4 5 4 6 8 10 12 14 Enfoque en las funciones: sí CHAPTER SUPPORT LAHA111FLCRB_C01_003-004.indd 4 LAHA111FLCRB_C01_003-004.indd 4 1/16/09 5:21:52 PM 1/16/09 5:21:52 PM Name ——————————————————————— Date ———————————— Copyright © Holt McDougal. All rights reserved. 5 Algebra 1 Chapter 1 Resource Book LESSON 1.1 Practice A For use with pages 2–7 Name the operation indicated by the expression. 1. 19x 2. 5 2 b 3. 14 4 m 4. a 1 24 Evaluate the expression. 5. y 1 7 when y 5 5 6. 13 2 x when x 5 2 7. 4a when a 5 2.1 8. 9 1 m when m 5 8.2 9. h 1 6 when h 5 1.7 10. 42 4 g when g 5 2 11. x } 5 when x 5 100 12. 52 } d when d 5 13 13. 2 } 3 p t when t 5 6 14. r(8.3) when r 5 10 15. w 1 1 } 4 when w 5 3 } 4 16. n } 14 when n 5 28 Write the power in words and as a product. 17. 72 18. 45 19. 28 Write the power represented by the words or product. 20. 5 p 5 p 5 21. six squared 22. x p x p x p x Evaluate the power. 23. 32 24. 24 25. 15 Evaluate the expression. 26. x2 when x 5 5 27. y3 when y 5 3 28. m8 when m 5 1 29. Window Treatments You are ordering custom blinds for your bedroom windows. The ordering instructions are to measure the width of the window in inches and add a half-inch to this measurement. So, the blind width you order is given by the expression w 1 0.5 where w is the width of your window. a. One of your windows measures 27 inches wide. What width blind should you order? b. The other window measures 28.5 inches wide. What width blind should you order? 30. Skateboarding A skate park charges $10 per person for an all-day admission to the park. The total cost for n people to go to the park all day is 10n. Eight friends go to the park on Saturday. What is the total cost of admission? 31. Geometry The area of a square with a side length of s is given by the expression s2. What is the area of the square shown? 4 in. 4 in. LESSON 1.1 LAHA111FLCRB_C01_005-010.indd 5 LAHA111FLCRB_C01_005-010.indd 5 1/16/09 5:21:57 PM 1/16/09 5:21:57 PM Name ——————————————————————— Date ———————————— Copyright © Holt McDougal. All rights reserved. 6 Algebra 1 Chapter 1 Resource Book Evaluate the expression. 1. y 1 12 when y 5 29 2. 47 2 x when x 5 38 3. 0.8a when a 5 7.5 4. 12.5 1 m when m 5 7.6 5. r(4.6) when r 5 8.1 6. 6.25 4 g when g 5 2.5 7. x} 0.9 when x 5 54 8. 62 }d when d 5 3.1 9. 4}7 p t when t 5 7}8 10. r(8.3) when r 5 10.2 11. w 1 2}5 when w 5 1}2 12. n } 2.4 when n 5 12 Write the power in words and as a product. 13. 87 14. (0.1)4 15. x5 Evaluate the power. 16. 92 17. 26 18. (0.4)3 Evaluate the expression. 19. x2 when x 5 1}5 20. m4 when m 5 0.6 21. 2y3 when y 5 4 22. Side Table A side table has interior storage space in the shape of a cube. What is the volume of the storage space if the interior length is 12 inches? 12 in. 12 in. 12 in. 23. Playing Cards There are 52 cards in a standard deck of playing cards. You are combining decks of cards so that you can play a game with a large number of people. The expression 52d represents the number of cards in d decks. If you combine 4 decks of cards, how many cards will you have altogether? 24. Sales Tax An item costs c dollars and 6% sales tax is charged. The total cost including sales tax is given by the expression 1.06c. You are buying a skateboard that costs $75. What is the cost of the skateboard including sales tax? 25. Flower Arranging You are creating a fl ower arrangement for a friend. The total cost (in dollars) for one vase and f fl owers is given by the expression 8 1 2.5f. How much will it cost to make an arrangement with 8 fl owers? Practice B For use with pages 2–7 LESSON 1.1 LESSON 1.1 LAHA111FLCRB_C01_005-010.indd 6 LAHA111FLCRB_C01_005-010.indd 6 1/19/09 4:43:03 PM 1/19/09 4:43:03 PM Name ——————————————————————— Date ———————————— Copyright © Holt McDougal. All rights reserved. 7 Algebra 1 Chapter 1 Resource Book Practice C For use with pages 2–7 Evaluate the expression. 1. 5y when y 5 6 2. 18 2 x when x 5 7 3. 0.4a when a 5 32 4. 4 1 m when m 5 9.7 5. h 2 3 when h 5 5.1 6. 48 4 g when g 5 3 7. x } 8 when x 5 72 8. 60 } d when d 5 1.5 9. 4 } 9 p t when t 5 7 } 16 10. 2x 1 y when x 5 3 and y 5 2 11. m } 5 2 n when m 5 4 and n 5 2 } 3 12. 12b } a when a 5 2.4 and b 5 0.6 13. 4.5x } y when x 5 8.4 and y 5 1.5 Evaluate the power. 14. (0.5)4 15. 1 1 } 3 2 5 16. 1 4 } 5 2 3 Evaluate the expression. 17. 6x when x 5 3 18. (4y)2 when y 5 5 19. (a 2 b)5 when a 5 10 and b 5 6 20. 4m 1 n3 when m 5 7 and n 5 10 21. 3x4 1 2y when x 5 5 and y 5 13 22. (3y)2 2 x2 when x 5 9 and y 5 4 23. Baseball Display A baseball display case is in the shape 9.8 cm 9.8 cm 9.8 cm of a cube. What is the volume of the display case if the side length is 9.8 centimeters? 24. Sales Tax An item costs c dollars and 6.25% sales tax is charged. The total cost including sales tax is given by the expression 1.0625c. You are buying a skateboard that costs $82. What is the cost of the skateboard including sales tax? Round your answer to the nearest cent. 25. Planter You are creating concrete planters for a 11 in. 11 in. 15 in. 15 in. 15 in. 11 in. garden border by placing the concrete in a large cube and then placing a smaller cube inside. The amount of concrete you need can be found using the expression V 2 v where V is the volume of the larger cube and v is the volume of the smaller cube. How much concrete do you need to make one planter? 26. Music A music store sells new CDs for $13.95 and used CDs for $6.50. The total cost of buying x new CDs and y used CDs can be found using the expression 13.95x 1 6.5y. You buy 3 new CDs and 4 used CDs. Find the total cost. LESSON 1.1 LESSON 1.1 LAHA111FLCRB_C01_005-010.indd 7 LAHA111FLCRB_C01_005-010.indd 7 1/16/09 5:21:59 PM 1/16/09 5:21:59 PM Name ——————————————————————— Date ———————————— Copyright © Holt McDougal. All rights reserved. 8 Algebra 1 Chapter 1 Resource Book Evaluate algebraic expressions and use exponents. Vocabulary A variable is a letter used to represent one or more numbers. An algebraic expression, or variable expression, consists of numbers, variables, and operations. To evaluate an expression, substitute a number for the variable, perform the operation(s), and simplify the result if necessary. A power is an expression that represents repeated multiplication of the same factor. A power can be written in a form using two numbers, a base and an exponent. The exponent represents the number of times the base is used as a factor. GOAL Review for Mastery For use with pages 227 LESSON 1.1 Evaluate algebraic expressions Evaluate the expression when x 5 5. a. 7x b. 12 1 x Solution a. 7x 5 7(5) Substitute 5 for x. 5 35 Multiply. b. 12 1 x 5 12 1 5 Substitute 5 for x. 5 17 Add. Exercises for Example 1 Evaluate the expression for the given value of the variable. 1. 15 2 a when a 5 3 2. 3b when b 5 7 3. 11 1 c when c 5 10 4. 28 } d when d 5 4 5. 1 } 2 n when n 5 18 6. 0.4f when f 5 8 EXAMPLE 1 LESSON 1.1 LAHA111FLCRB_C01_005-010.indd 8 LAHA111FLCRB_C01_005-010.indd 8 1/16/09 5:22:00 PM 1/16/09 5:22:00 PM Name ——————————————————————— Date ———————————— Copyright © Holt McDougal. All rights reserved. 9 Algebra 1 Chapter 1 Resource Book Evaluate an expression The cost of fi lling a car’s gas tank can be represented by the expression xy where x is the price per gallon of gasoline and y is the number of gallons purchased. You purchase 10 gallons of gasoline when the price per gallon is $2.35. Find the total cost. Solution Total Cost 5 xy Write expression. 5 2.35(10) Substitute 2.35 for x and 10 for y. 5 23.50 Multiply. The total cost is $23.50. Exercises for Example 2 7. You purchase 5 gallons of gasoline when the price of gasoline is $2.26 per gallon. Find the total cost. 8. You purchase 8 gallons of gasoline when the price of gasoline is $2.20 per gallon. Find the total cost. EXAMPLE 2 Read and write powers Write the power in words and as a product. a. 83 b. m6 Solution a. eight to the third power, or eight cubed; 8 p 8 p 8 b. m to the sixth power; m p m p m p m p m p m Exercises for Example 3 Write the power in words and as a product. 9. 48 10. 1 1 } 3 2 4 11. x2 EXAMPLE 3 Review for Mastery continued For use with pages 227 LESSON 1.1 LESSON 1.1 LAHA111FLCRB_C01_005-010.indd 9 LAHA111FLCRB_C01_005-010.indd 9 1/16/09 5:22:01 PM 1/16/09 5:22:01 PM

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