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My Math GPS: Elementary Algebra Guided Problem Solving (2016 Edition) City University of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Community College 2016 My Math GPS: Elementary Algebra Guided Problem Solving (2016 Edition) Jonathan Cornick CUNY Queensborough Community College G Michael Guy CUNY Queensborough Community College Karan Puri CUNY Queensborough Community College How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/qb_oers/15 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] Name:_________________ Instructor:_________________ My Math GPS: Elementary Algebra Guided Problem Solving 2016 Edition Jonathan Cornick G. Michael Guy Karan Puri http://MyMathGPS.com GPS 1-6 is loosely based on work completed with Francis Gardella and Brooke Nixon-Freidheim as part of the Graduate NYC! Curriculum Alignment Project. We are grateful for their collaboration on earlier versions of these introductory lessons. More information on this work is available at http://gradnyc.com/curriculum-alignment- project/ This textbook aligns to the 2016 CUNY Elementary Algebra Learning Outcomes. For more information about these learning outcomes and accompanying final exam, please visit http://cuny.edu/testing Authors may be contacted via email. Jonathan Cornick [email protected] G. Michael Guy [email protected] http://gmichaelguy.com Karan Puri [email protected] http://www.karanpuri.net This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/. Table of Contents LINEAR EQUATIONS AND INEQUALITIES ........................................................................................................................... 5 GPS 1: UNDERSTANDING LINEAR EQUATIONS ................................................................................................................................... 5 GPS 2: SOLVING LINEAR EQUATIONS WITH WHOLE NUMBERS ........................................................................................................... 21 GPS 3: ADDING SIGNED NUMBERS ............................................................................................................................................... 27 GPS 4: SUBTRACTING SIGNED NUMBERS ........................................................................................................................................ 33 GPS 5: MULTIPLYING AND DIVIDING SIGNED NUMBERS .................................................................................................................... 37 GPS 6: SOLVING LINEAR EQUATIONS WITH SIGNED NUMBERS ............................................................................................................ 43 GPS 7: TRANSLATING WORDS INTO EXPRESSIONS AND EQUATIONS ..................................................................................................... 47 GPS 8: SOLVING LINEAR INEQUALITIES, PART 1 ............................................................................................................................... 51 GPS 9: SOLVING LINEAR INEQUALITIES, PART 2 ............................................................................................................................... 57 GPS 10: SOLVING LINEAR EQUATIONS WITH FRACTIONS ................................................................................................................... 61 GPS 11: MORE LINEAR EQUATIONS WITH FRACTIONS ...................................................................................................................... 65 GPS 12: SOLVING LITERAL LINEAR EQUATIONS ................................................................................................................................ 69 THE COORDINATE PLANE AND LINES .............................................................................................................................. 73 GPS 13: INTRODUCTION TO THE COORDINATE PLANE ....................................................................................................................... 73 GPS 14: INTERCEPTS OF A LINE .................................................................................................................................................... 81 GPS 15: SLOPE AND EQUATIONS OF A LINE .................................................................................................................................... 89 GPS 16: THE SLOPE-INTERCEPT EQUATION OF A LINE ....................................................................................................................... 95 GPS 17: SLOPE-INTERCEPT EQUATION AND GRAPHING ................................................................................................................... 101 GPS 18: GRAPHING LINES IN SLOPE-INTERCEPT FORM .................................................................................................................... 105 GPS 19: FINDING AN EQUATION OF A LINE FROM ITS GRAPH ............................................................................................................ 111 GPS 20: HORIZONTAL AND VERTICAL LINES .................................................................................................................................. 115 SYSTEMS OF LINEAR EQUATIONS ................................................................................................................................. 123 GPS 21: INTRODUCTION TO SYSTEMS OF LINEAR EQUATIONS AND SOLVING GRAPHICALLY ..................................................................... 123 GPS 22: MORE ON SOLVING SYSTEMS GRAPHICALLY ...................................................................................................................... 131 GPS 23: SOLVING SYSTEMS OF LINEAR EQUATIONS ALGEBRAICALLY .................................................................................................. 143 GPS 24: MORE ON SOLVING SYSTEMS ALGEBRAICALLY ................................................................................................................... 151 EXPONENTS ................................................................................................................................................................. 161 GPS 25: RULES OF EXPONENTS, PART 1 ....................................................................................................................................... 161 GPS 26: RULES OF EXPONENTS, PART 2 ....................................................................................................................................... 169 POLYNOMIALS AND OPERATIONS ................................................................................................................................ 179 GPS 27: INTRODUCTION TO POLYNOMIALS AND OPERATIONS .......................................................................................................... 179 GPS 28: MULTIPLYING POLYNOMIALS ......................................................................................................................................... 185 GPS 29: REMOVING THE GREATEST COMMON FACTOR .................................................................................................................. 199 GPS 30: FACTORING BY GROUPING ............................................................................................................................................. 205 GPS 31: FACTORING TRINOMIALS BY GROUPING – PART 1 .............................................................................................................. 215 GPS 32: FACTORING TRINOMIALS BY GROUPING – PART 2 .............................................................................................................. 221 GPS 33: FACTORING TRINOMIALS BY GROUPING – PART 3 .............................................................................................................. 225 GPS 34: FACTORING TRINOMIALS BY GROUPING – PART 4 .............................................................................................................. 229 4 GPS 35: FACTORING A DIFFERENCE OF SQUARES ........................................................................................................................... 235 GPS 36: MULTISTEP FACTORING ................................................................................................................................................ 239 GPS 37: SOLVING QUADRATIC EQUATIONS BY FACTORING .............................................................................................................. 243 ALGEBRAIC EXPRESSIONS ............................................................................................................................................. 249 GPS 38: EVALUATING ALGEBRAIC EXPRESSIONS ............................................................................................................................. 249 SQUARE ROOTS AND OPERATIONS ............................................................................................................................... 251 GPS 39: INTRODUCTION TO SQUARE ROOTS ................................................................................................................................. 251 GPS 40: OPERATIONS WITH SQUARE ROOTS ................................................................................................................................
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