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file ple m Sa Copyright 2007 - 2011 Taina Maria Miller. All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, or by any information storage and retrieval system, without permission in writing from the author. Copying permission: Permission IS granted to reproduce this material for one (1) teacher's students by virtue of the purchase of this book. In other words, one (1) teacher MAY make copies of these worksheets to be used with his/her students. Permission is not given to reproduce the material for resale. If you have other needs, such as school-wide licensing, contact the author at www.MathMammoth.com/contact.php. Please visit www.MathMammoth.com for more information about ebooks and books by Maria Miller. 2 Contents Introduction ........................................................................... 6 Introduction to Algebra Variables and Expressions .................................................. Order of Operations ............................................................ Sets ..................................................................................... Sets and Open Sentences .................................................. Words into Symbols 1 ......................................................... Words into Symbols 2 ......................................................... Writing Equations ................................................................ Writing Simple Formulas and Equations ............................. 7 8 9 10 11 12 13 14 Real Numbers and Their Properties Sa m ple file The Real Number Line ........................................................ Opposites and Absolute Value ........................................... Reviewing Addition and Subtraction ................................... Reviewing Multiplication and Division ................................. . The Distributive Property .................................................... Properties of Operations 1 .................................................. Properties of Operations 2 .................................................. Rules with Addition ............................................................. Rules with Subtraction ........................................................ Rules with Multiplication ..................................................... Rules with Division .............................................................. 15 16 17 18 19 20 21 22 23 24 25 Solving Linear Equations Solving Equations 1: Addition and Subtraction .................... 26 Solving Equations 2: Multiplication and Division .................. 27 Solving Equations 3: Many Steps ....................................... 28 Solving Equations 4: Many Steps ....................................... 29 Word Problems .................................................................. Variable on Both Sides ....................................................... Word Problems ................................................................... Formulas ............................................................................. Using Formulas .................................................................. Ratios and Proportions ....................................................... More on Ratios and Proportions ......................................... 3 30 31 32 33 34 35 36 Solving Linear Equations (cont.) Percent .............................................................................. Percent of Change ............................................................ Mixture Problems .............................................................. Uniform Motion .................................................................. More Word Problems ........................................................ 37 38 39 40 41 Graphing Linear Equations and Functions 42 43 44 45 46 Functions .......................................................................... Horizontal and Vertical Lines ............................................ X and Y-Intercepts ............................................................ Slope ................................................................................ 47 48 49 50 The Slope-Intercept From / Parallel Lines ....................... The Point-Slope and Standard Forms ............................. Writing Linear Equations .................................................. Parallel and Perpendicular Lines ..................................... More on Graphing Linear Equations ................................ 51 52 53 54 55 Direct Variation 1 ............................................................. Direct Variation 2 ............................................................. Modeling with Linear Equations 1 .................................... Modeling with Linear Equations 2 .................................... Modeling with Linear Equations 3 .................................... 56 57 58 59 60 Sa m ple file Coordinate Plane .............................................................. Relations ........................................................................... Relations From Equations ................................................ Graph Linear Equations .................................................... Explore Graphs of Linear Equations ................................. Solving and Graphing Linear Inequalities Solving Inequalities 1 - Add/Subtract ............................... Solving Inequalities 2 - Mult/Div ....................................... Multi-Step Inequalities ...................................................... Word Problems ................................................................. 61 62 63 64 Compound Inequalities Involving 'And' ............................. 65 Compound Inequalities Involving 'Or' ............................... 66 More Inequalities .............................................................. 67 Absolute Value Equations ................................................ Absolute Value Inequalities .............................................. 68 69 More Practice with Inequalities ......................................... 70 Graphing Linear Inequalities in Two Variables ................. 71 4 Systems of Linear Equations and Inequalities Graphing System of Linear Equations ............................... Graphing System of Linear Equations 2 ............................ Solving Linear Systems by Substitution ............................ Solving Linear Systems by Elimination ............................. Linear Combinations ......................................................... 72 73 74 75 76 Word Problems ................................................................. Systems of Equations — More Problems ......................... Graphing Compound Inequalities ...................................... Solving Linear Systems by Substitution ............................ 77 78 79 80 Sa m ple file More from Math Mammoth ................................................ 81 5 Introduction Math Mammoth Algebra 1-A Worksheets Collection has been created with teachers' needs in mind: each worksheet is exactly one page, concentrating on one topic; therefore is easy to assign for students. Please note that this is a worksheet collection and does not contain textbook explanations. These algebra worksheets have been “handcrafted” one by one. Each worksheet is on one topic, but contains varying problems about that topic. The problems include some that lead to a concept, basic practice problems about the topic on hand, and most worksheet also include 1-2 challenging problems. This collection contains a lot of word problems. In essence, the worksheets are like the problem section of a math book, and far from the mechanical worksheets created by a script. ple file This collection at hand covers the first half of a typical algebra 1 course topics. The first section of the book contains introductory problems about variables, expressions, translating words into symbols, and building equations. Sa m The second section covers basic properties of real numbers. Next follows a section on solving linear equations, which also covers ratio, proportion, and percent problems. I have also included lots of word problems here. The next section, Graphing Linear Equations and Functions, starts with problems about relations, then has worksheets for all the graphing-related concepts, such as slope and parallel and perpendicular lines. Lastly in this section I have included three worksheets about modeling with linear equations. The next section concentrates on solving and graphing linear inequalities including absolute value inequalities. Lastly in this collection we have systems of linear equations and inequalities. The Algebra 1-B collection covers the latter half of algebra 1: powers, polynomials, factoring, quadratic equations, rational expressions and equations, radicals and geometry. I wish you success with math teaching! Maria Miller, the author 6 Name: Date: Variables and Expressions 1. For each of the following indicate if it is a variable or an expression. a. s b. 74t d. x2 c. K e. xy f. zz 2. Write an algebraic expression for each verbal expression. a. the sum of p and 9 b. n divided by the sum of m and 10 c. the product of r, s, and t d. a number x to the 7th power e. the sum of 4T and T cubed f. seven times y squared g. a number s decreased by 10 h. y increased by twice x i. a divided by the difference of a and 2. j. five-sixths of the square of a number y 3. Write as expressions using exponents. b. 45 · y · y · y · 45 d. (2m)(2m)(2m) e. ststststst c. b · b · b · b · b · a · a f. 5m · 2m · 3n ple file a. x · x · x · x 4. Write a verbal expression for each algebraic expression. e. a+c 4 d. 2k12 Sa c. 6xy b. p2 + 5 m a. m + 2n f. 1 x−4 h. 40 − y3 g. 40 − y Expressions in parentheses are considered as one quantity. You can read them using the word “quantity”. 5. Write an algebraic expression for each verbal expression. a. the product of the quantity x plus y and the quantity x minus y b. the difference of 100 and b divided by the quantity 2b plus 10 c. the quotient of the quantity 5 minus T squared and T. d. 8a reduced by the quantity b plus c. e. n cubed increased by the quantity 6 minus n squared f. two-thirds the quantity x squared minus y squared 7 3(x + y ) “three times the quantity x plus y”