Table of Contents Introduction... xiii Facts & Strategies for Passing the New York Algebra 2 and Trigonometry Exam... xiv Diagnostic Tests... xxxvi Chapter 1 The Real Number System 1.1 Properties of Real Numbers.... 2 Foundational standards coverage 1.2 Integers as Exponents... 4 A2.A.9 Rewrite expressions with exponents 1.3 Absolute Value.... 6 A2.A.1 Solve absolute value equations 1.4 Order of Operations... 8 Foundational standards coverage 1.5 Finding Square Roots of Non-Perfect Squares... 10 Foundational standards coverage Chapter 1 Preparing for the New York Algebra 2 and Trigonometry Exam....12 Chapter 2 Exponents and Radicals 2.1 Radical Notation... 16 A2.N.1 Evaluate expressions with exponents N.RN.1 N.RN.2 A2.N.2 A2.A.10 A2.A.13 Perform operations on irrational Rewrite fractional exponents as radicals Simplify radical expressions 2.2 Simplify Radical Expressions.... 18 A.REI.2 A2.N.2 Perform operations on irrational N.RN.2 A2.N.4 Perform operations on irrational expressions A2.A.13 A2.A.14 Simplify radical expressions Add, subtract, multiply, divide radicals 2.3 Operations with Radical Expressions... 20 A2.N.5 Rationalize radical denominators A2.N.15 A2.A.16 Rationalize denominators Use operations with rational expressions iii BR14_SE_NY_A2_FM_TOC.indd Page 3 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...
2.4 Rational Exponents.... 24 A2.A.8 Simplify expressions with exponents N.RN.1 A.SSE.3.c A2.A.9 A2.A.11 Rewrite expressions with exponents Rewrite radicals as fractional exponents 2.5 Radical Equations with Rational Exponents... 28 A2.A.22 Solve radical equations A.REI.2 Chapter 2 Preparing for the New York Algebra 2 and Trigonometry Exam....30 Chapter 3 Rational Expressions 3.1 Simplify, Multiply, and Divide Rational Expressions... 34 A2.N.3 Perform operations with polynomials A.APR.1 3.2 Addition and Subtraction with Rational Expressions.... 38 A2.N.3 Perform operations with polynomials A.APR.7 3.3 Complex Rational Expressions... 42 A2.N.3 Perform operations with polynomials A2.A.17 Simplify complex fractional expressions 3.4 Solve Rational Equalities and Inequalities... 46 A2.N.3 Perform operations with polynomials Chapter 3 Preparing for the New York Algebra 2 and Trigonometry Exam....50 A2.A.23 Solve rational equations/inequalities Chapter 4 Polynomial Operations 4.1 Addition and Subtraction of Polynomials.... 54 A2.N.3 Perform operations with polynomials A.APR.1 4.2 Multiplication and Division of Polynomials... 60 A2.N.3 Perform operations with polynomials 4.3 Factoring Polynomials.... 66 A2.A.7 Perform operations with polynomials A.SSE.2 A.SSE.3.a Chapter 4 Preparing for the New York Algebra 2 and Trigonometry Exam....70 iv BR14_SE_NY_A2_FM_TOC.indd Page 4 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...
Chapter 5 Linear Equations and Inequalities 5.1 Linear Equations... 74 Foundational standards coverage 5.2 Linear Inequalities.... 78 Foundational standards coverage 5.3 Absolute Value Equations and Inequalities... 82 A2.A.1 Solve absolute value 5.4 Graphing Linear Equations... 86 Foundational standards coverage 5.5 Graphing Linear Inequalities.... 92 Foundational standards coverage Chapter 5 Preparing for the New York Algebra 2 and Trigonometry Exam....96 Chapter 6 Quadratic Functions and Equations 6.1 Factoring and the Zero-Product Property... 100 A2.A.26 Solve higher-degree polynomial A.SSE.3.a equations 6.2 Completing the Square... 104 A2.A.24 Complete the square A.REI.4.a F.IF.8.a A2.A.26 Solve higher-degree polynomial equations 6.3 The Quadratic Formula.... 108 A2.A.2 Use the discriminant A.REI.4.b A2.A.25 Use the quadratic formula 6.4 Sum and Product of the Roots... 112 A2.A.20 Find sum and product of quadratic roots A2.A.21 Determine quadratic equations Chapter 6 Preparing for the New York Algebra 2 and Trigonometry Exam....114 Chapter 7 Applications of Quadratic Functions 7.1 Graphing Quadratic Equations... 118 A2.A.2 Use the discriminant 7.2 Circles... 122 A2.A.47 Determine equation of a circle G.GPE.1 A2.A.48 Write equation of circle given a point A2.A.49 Write equation of circle from its graph v BR14_SE_NY_A2_FM_TOC.indd Page 5 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...
7.3 Solving Quadratic-Linear Systems and Quadratic Inequalities... 126 A2.A.3 Solve systems of equations A.REI.7 A2.A.4 Solve quadratic inequalities 7.4 Applications of Quadratic Functions... 132 A2.A.25 Use the quadratic formula A.REI.4.b Chapter 7 Preparing for the New York Algebra 2 and Trigonometry Exam....136 Chapter 8 Relations, Functions, and Graphs 8.1 Relations and Functions... 140 A2.A.37 Define a relation and function F.IF.1 F.IF.2 A2.A.38 A2.A.39 A2.A.40 Determine when a relation is a function Determine domain and range Write functions in functional notation 8.2 Operations with Functions.......................... 146 A2.A.41 Use functional notation F.IF.2 8.3 One-to-One and Onto Functions.... 152 A2.A.43 Determine if function is one-to-one or onto 8.4 Composition of Functions.... 154 A2.A.42 Find the composition of functions F.BF.1.c F.BF.4.b 8.5 Inverse Relations and Functions... 156 A2.A.44 Define the inverse of a function F.BF.4.a F.BF.4.b A2.A.45 Determine the inverse of a function 8.6 Transformations... 160 A2.A.46 Perform transformations of functions F.BF.3 Chapter 8 Preparing for the New York Algebra 2 and Trigonometry Exam....164 vi BR14_SE_NY_A2_FM_TOC.indd Page 6 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...
Chapter 9 Complex Numbers 9.1 The Meaning of i... 168 A2.N.6 Write imaginary N.CN.1 A2.N.7 Simplify powers of i 9.2 Operations with Complex Numbers... 172 A2.N.9 Perform operations on complex N.CN.2 9.3 Complex Numbers and Conjugates.... 176 N.CN.2 A2.N.8 Determine conjugates of complex N.CN.3 A2.N.9 Perform operations on complex Chapter 9 Preparing for the New York Algebra 2 and Trigonometry Exam....180 Chapter 10 Polynomial Functions and Variations 10.1 Polynomial Functions... 184 A2.A.26 Solve higher-degree polynomial N.CN.9 equations A2.A.50 Solve polynomials using graph A2.A.51 Determine domain and range from graph 10.2 Zeros, Solutions, and Intercepts... 190 A2.A.26 Solve higher-degree polynomial N.CN.9 equations 10.3 Direct and Inverse Variation... 196 A2.A.5 Use direct and inverse variation Chapter 10 Preparing for the New York Algebra 2 and Trigonometry Exam....198 Chapter 11 Exponential and Logarithmic Functions 11.1 Exponential and Logarithmic Functions... 202 A.CED.1 A2.A.6 Solve exponential function applications A2.A.54 Graph logarithmic functions vii BR14_SE_NY_A2_FM_TOC.indd Page 7 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...
11.2 Exponential Functions of Base e and Properties of Logarithms....................................... 208 A2.A.12 Evaluate expressions with base e A2.A.53 A2.A.54 Graph exponential functions Graph logarithmic functions 11.3 Solving Exponential and Logarithmic Equations... 212 A2.A.27 Solve exponential equations A2.A.28 Solve logarithmic equations 11.4 Applications of Exponential and Logarithmic Functions. 216 A2.A.12 Evaluate expressions with base e Chapter 11 Preparing for the New York Algebra 2 and Trigonometry Exam....220 A2.A.27 A2.A.53 A2.A.54 Solve exponential equations Graph exponential functions Graph logarithmic functions Chapter 12 Circular Functions 12.1 Radian Measure.... 224 A2.A.61 Determine length of an arc of a circle F.TF.1 A2.M.1 A2.M.2 Define radian measure Convert between radians and degrees 12.2 Right Triangle Trigonometry... 228 A2.A.55 Express trigonometric functions F.TF.3 A2.A.56 A2.A.59 Know values of sine, cosine, and tangent Use co-function relationships 12.3 The Unit Circle... 234 A2.A.57 Use reference angle for standard F.TF.3 angles A2.A.58 Apply co-function relationships A2.A.60 Sketch unit circle 12.4 Graphing Trigonometric Functions................... 238 A2.A.69 Determine amplitude, period, frequency A2.A.70 A2.A.71 A2.A.72 Recognize one cycle of a trig function Graph sec(x), csc(x), tan(x), cot(x) Write trig functions given a graph viii BR14_SE_NY_A2_FM_TOC.indd Page 8 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...
12.5 Graphing Inverse Trigonometric Functions... 244 A2.A.63 Restrict domain of trig functions F.TF.6 Chapter 12 Preparing for the New York Algebra 2 and Trigonometry Exam....250 A2.A.64 A2.A.65 Use inverse functions to measure angles Sketch graph of inverse trig functions Chapter 13 Trigonometric Equations and Identities 13.1 Trigonometric Identities... 254 A2.A.67 Justify the Pythagorean identities F.TF.8 A2.A.76 A2.A.77 Apply angle sum/difference formulas Apply double-/half-angle formulas 13.2 Trigonometric Equations... 260 A2.A.68 Solve trigonometric equations 13.3 Law of Sines and Cosines... 266 A2.A.73 Use Law of Sines or Law of Cosines G.SRT.10 G.SRT.11 A2.A.74 Determine area of triangle/ parallelogram 13.4 The Ambiguous Case (SSA).... 272 A2.A.75 Determine solution from SSA situation Chapter 13 Preparing for the New York Algebra 2 and Trigonometry Exam....274 Chapter 14 Sequences and Series 14.1 Arithmetic and Geometric Sequences... 278 A2.A.29 Find formula for nth term of sequence F.BF.2 A2.A.30 A2.A.31 A2.A.32 A2.A.33 Determine common difference Determine common ratio Determine specified term of a sequence Specify terms of a sequence 14.2 Arithmetic and Geometric Series and Their Sums... 282 A2.N.10 Know and apply sigma notation A2.A.34 A2.A.35 Represent sum of a series Determine sum of first n terms of series ix BR14_SE_NY_A2_FM_TOC.indd Page 9 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...
14.3 The Binomial Theorem... 288 A2.A.36 Apply binomial theorem A.APR.5 Chapter 14 Preparing for the New York Algebra 2 and Trigonometry Exam....292 Chapter 15 Statistics 15.1 Gathering Data... 296 A2.S.1 Understand difference among studies S.IC.4 A2.S.2 Determine factors which affect outcome 15.2 Measures of Central Tendency.... 300 A2.S.3 Calculate measures of central S.ID.2 tendency A2.S.4 Calculate measures of dispersion 15.3 Measures of Dispersion... 304 A2.S.4 Calculate measures of dispersion 15.4 Normal Distribution... 310 A2.S.5 Know and apply normal distribution S.ID.4 15.5 Regression Models... 316 S.ID.6 A2.S.6 Determine appropriate regression model S.ID.6.c A2.S.7 Determine and use regression functions Chapter 15 Preparing for the New York Algebra 2 and Trigonometry Exam....322 A2.S.8 Use correlation coefficient Chapter 16 Probability 16.1 Probabilities... 326 A2.S.13 Calculate theoretical probabilities S.MD.3 A2.S.14 Calculate empirical probabilities S.MD.4 16.2 Applying Probability.... 330 A2.S.13 Calculate theoretical probabilities S.MD.3 A2.S.14 Calculate empirical probabilities S.MD.4 x BR14_SE_NY_A2_FM_TOC.indd Page 10 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...
16.3 Combinations and Permutations... 336 A2.S.9 Differentiate permutations/ S.CP.9 combinations A2.S.10 Calculate the number of permutations A2.S.11 A2.S.12 Calculate the number of combinations Use Fundamental Principle of Counting 16.4 Binomial Probability Formula... 342 A2.S.15 Apply the binomial probability formula 16.5 Normal Approximation of Binomial Probabilities... 344 A2.S.16 Use the normal distribution Chapter 16 Preparing for the New York Algebra 2 and Trigonometry Exam....348 Correlations Chart... C-1 Common Core Performance Tasks... P-1 Glossary...G-1 Practice Tests... T-1 Reference Sheet.... T-20 Selected Answers.... S-1 Index.................................................... I-1 Acknowledgments...A-1 January 2014 Regents Examination June 2013 Regents Examination January 2013 Regents Examination June 2012 Regents Examination January 2012 Regents Examination June 2011 Regents Examination xi BR14_SE_NY_A2_FM_TOC.indd Page 11 05/09/14 9:48 PM s-w-047 /113/PE01374_MATH_R1/NY_BRIEF_REVIEW/NY/ANCILLARY/ALG2_TRIG_SE/G9_12/XXXXXXXXXX_G...