Transcription of Algebra Cheat Sheets
1 Algebra Cheat SheetsCopyright 2004 Senari Programs Cheat Sheets provide you with a tool for teaching your studentsnote-taking, problem- solving , and organizational skills in the context ofalgebra lessons. These Sheets teach the concepts as they are presented inthe Algebra Class SheetAdding Integers1 Subtracting Integers2 Multiplying Integers3 Dividing Integers4 Absolute Value5 Combining Like Terms6 Distributive Property I7 Adding Expressions8 Subtracting Expressions9 Writing Expressions10 Evaluating Expressions11 solving Equations12 solving Inequalities13 Writing Equations14 Writing Inequalities15 solving Literal Equations16 Points on the Coordinate Plane17 Graphing Using Slope and Intercept18 Graphing Using Function Tables19 Find the Slope of a Line from Two Points20 Equation of a
2 Line21 Graphing Inequalities22 Algebra Cheat SheetsCopyright 2004 Senari Programs SheetForms of Linear Equations23 solving Equations II24 Multiplying Monomials25 Dividing Monomials26 Raising Monomials to a Power27 Negative Powers of Monomials28 Dividing by a Monomial29 Greatest Common Factor (GCF)30 Combining Like Terms II31 Adding Polynomials32 Subtracting Polynomials33 Missing Factors34 Degree of a Polynomial35 Multiplying Polynomials by 136 Multiplying a Polynomial by a Variable37 Multiplying a Polynomial by an Integer38 Multiplying a Polynomial by a Monomial39 Multiplying Two Binomials40 Copyright 2004 Senari Algebra CheatSheet 1 Adding Integers Adding means combining1.
3 If the signs are the same, thenadd and use the same If the signs are different, thensubtract and use the sign of thelarger number. 8 + 4 = 12 8 + 4 = 12 8 + 4 = 4 8 + 4 = 4 Adding Integers ExamplesCopyright 2004 Senari Algebra CheatSheet 2 SubtractingIntegersSubtracting is the opposite of adding. Change the sign of the second term and add. 8 (+4) = 8 4 = 4 8 (+4) = 8 4 = 128 ( 4) = 8 + 4 = 12 8 ( 4) = 8 + 4 = 4 Subtracting Integers ExamplesCopyright 2004 Senari Algebra CheatSheet 3 MultiplyingIntegersMultiply integers as you would whole numbers,then apply the sign rules to the If the signs are the same, theproduct is If the signs are different, theproduct is negative.
4 (8) (4) = 32( 8) ( 4) = 32( 8) (4) = 32 (8) ( 4) = 32 Multiplying Integers ExamplesCopyright 2004 Senari Algebra CheatSheet 4 Dividing IntegersDivide integers as you would whole numbers, thenapply the sign rules to the If the signs are the same, thequotient is If the signs are different, thequotient is 8 = 4 32 8 = 432 8 = 4 32 8 = 4 Dividing Integers ExamplesCopyright 2004 Senari Algebra CheatSheet 5 Absolute ValueThe absolute value of a number is the distance anumber is from 0 on the number absolute values of 7 and -7 are 7 since bothnumbers have a distance of 7 units from 0.
5 Absolute value ExamplesCopyright 2004 Senari Algebra CheatSheet 6 Combining LikeTermsTo combine terms, the variables must be Put the terms in alphabetical Combine each set of like Put the answers Like Terms Examples3a + 4b + 2c + 5a 6c 2b1. Put the terms in alphabetical order:3a + 5a + 4b 2b + 2c 6c2. Combine each set of like terms: 3a + 5a = 8a 4b 2b = 2b 2c 6c = 4c3. Put the answer together:8a + 2b 4cCopyright 2004 Senari Algebra CheatSheet 6 Combining LikeTermsTo combine terms, the variables must be Put the terms in alphabetical Combine each set of like Put the answers Like Terms ExamplesCopyright 2004 Senari Algebra CheatSheet 7 DistributiveProperty IMultiply each term inside the parenthesis by theterm on the outside of the parenthesis.
6 C(a + b) = ca + cb c(a - b) = ca - cbDistributive Property Examples3b (a + 4) =3b (a) + 3b (4) =3ab + 12bCopyright 2004 Senari Algebra CheatSheet 7 DistributiveProperty IMultiply each term inside the parenthesis by theterm on the outside of the parenthesis. c(a + b) = ca + cb c(a - b) = ca - cbDistributive Property ExamplesCopyright 2004 Senari Algebra CheatSheet 8 AddingExpressions1. Set the problem up Combine the Expressions ExamplesWrite the problem vertically: 8c + 2d - 4g-7c + 4d - 8g1. Combine the c s:8c - 7c = c2. Combine the d s:2d + 4d = 6d3. Combine the g s:-4g - 8g = -12g4.
7 The answer is:c + 6d - 12gCopyright 2004 Senari Algebra CheatSheet 8 AddingExpressions1. Set the problem up Combine the Expressions ExamplesCopyright 2004 Senari Algebra CheatSheet 9 SubtractingExpressions3. Set the problem up Change the signs of each term on the bottom Combine the Expressions ExamplesChange the bottom signs:8c + 2d - 4g- 7c - 4d + 8gCombine the terms:8c + 2d - 4g -7c + 4d - 8g1. Combine the c s:8c - 7c = c2. Combine the d s:2d + 4d = 6d3. Combine the g s:-4g - 8g = -12g4. The answer is:c + 6d - 12gCopyright 2004 Senari Algebra CheatSheet 9 SubtractingExpressions1.
8 Set the problem up Change the signs of each term on the bottom Combine the Expressions ExamplesCopyright 2004 Senari Algebra CheatSheet 10 WritingExpressionsLook for clue words:1. For the clue words, the product of place theconstant before the variable. Do not use a The clue words more than and less than indicate inverted If there are no clue words, write the expression inthe order that the words Expressions Examples1. The product of 4 and xThe product of y and 54x5y2. x more than threethirteen less than y3 + xy 133. the sum of ten and xthe difference betweeny and 410 + xy 4 Copyright 2004 Senari Algebra CheatSheet 10 WritingExpressionsLook for clue words:1.
9 For the clue words, the product of place theconstant before the variable. Do not use a The clue words more than and less than indicate inverted If there are no clue words, write the expressionin the order that the words Expressions ExamplesCopyright 2004 Senari Algebra CheatSheet 11 EvaluatingExpressionsStep 1. Replace the variable with 2. Place the value of the variable inside 3. Calculate the Expressions ExamplesEvaluate 10x + 7, when x = 1. 10 ( ) + 7 Step 2. 10 (5) + 7 Step 3. 50 + 7 = 57 Copyright 2004 Senari Algebra CheatSheet 11 EvaluatingExpressionsStep 1.
10 Replace the variable with 2. Place the value of the variable inside 3. Calculate the Expressions ExamplesCopyright 2004 Senari Algebra CheatSheet 12 solving EquationsStep 1. Get all the variables on the left and all thenumbers on the right of the equal sign by 2. Divide by the coefficient of the variable todetermine its Equations Examples2d + 3 = 71. 3 = 32d = 102. d = 5 Copyright 2004 Senari Algebra CheatSheet 12 solving EquationsStep 1. Get all the variables on the left and all thenumbers on the right of the equal sign by 2. Divide by the coefficient of the variable todetermine its Equations ExamplesCopyright 2004 Senari Algebra CheatSheet 13 SolvingInequalitiesStep 3.
