Chapter 1 The Real Number System. Chapter 2 Exponents and Radicals. iii

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1 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 Foundational standards coverage 1.2 Integers as Exponents... 4 A2.A.9 Rewrite expressions with exponents 1.3 Absolute Value 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 Foundational standards coverage Chapter 1 Preparing for the New York Algebra 2 and Trigonometry Exam Chapter 2 Exponents and Radicals 2.1 Radical Notation 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 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 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 2.4 Rational Exponents 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 A2.A.22 Solve radical equations A.REI.2 Chapter 2 Preparing for the New York Algebra 2 and Trigonometry Exam Chapter 3 Rational Expressions 3.1 Simplify, Multiply, and Divide Rational Expressions A2.N.3 Perform operations with polynomials A.APR Addition and Subtraction with Rational Expressions A2.N.3 Perform operations with polynomials A.APR Complex Rational Expressions A2.N.3 Perform operations with polynomials A2.A.17 Simplify complex fractional expressions 3.4 Solve Rational Equalities and Inequalities A2.N.3 Perform operations with polynomials Chapter 3 Preparing for the New York Algebra 2 and Trigonometry Exam A2.A.23 Solve rational equations/inequalities Chapter 4 Polynomial Operations 4.1 Addition and Subtraction of Polynomials A2.N.3 Perform operations with polynomials A.APR Multiplication and Division of Polynomials A2.N.3 Perform operations with polynomials 4.3 Factoring Polynomials 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 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...

3 Chapter 5 Linear Equations and Inequalities 5.1 Linear Equations Foundational standards coverage 5.2 Linear Inequalities Foundational standards coverage 5.3 Absolute Value Equations and Inequalities A2.A.1 Solve absolute value 5.4 Graphing Linear Equations Foundational standards coverage 5.5 Graphing Linear Inequalities Foundational standards coverage Chapter 5 Preparing for the New York Algebra 2 and Trigonometry Exam Chapter 6 Quadratic Functions and Equations 6.1 Factoring and the Zero-Product Property A2.A.26 Solve higher-degree polynomial A.SSE.3.a equations 6.2 Completing the Square 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 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 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 Chapter 7 Applications of Quadratic Functions 7.1 Graphing Quadratic Equations A2.A.2 Use the discriminant 7.2 Circles 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...

4 7.3 Solving Quadratic-Linear Systems and Quadratic Inequalities A2.A.3 Solve systems of equations A.REI.7 A2.A.4 Solve quadratic inequalities 7.4 Applications of Quadratic Functions A2.A.25 Use the quadratic formula A.REI.4.b Chapter 7 Preparing for the New York Algebra 2 and Trigonometry Exam Chapter 8 Relations, Functions, and Graphs 8.1 Relations and Functions 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 A2.A.41 Use functional notation F.IF One-to-One and Onto Functions A2.A.43 Determine if function is one-to-one or onto 8.4 Composition of Functions A2.A.42 Find the composition of functions F.BF.1.c F.BF.4.b 8.5 Inverse Relations and Functions 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 A2.A.46 Perform transformations of functions F.BF.3 Chapter 8 Preparing for the New York Algebra 2 and Trigonometry Exam 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...

5 Chapter 9 Complex Numbers 9.1 The Meaning of i A2.N.6 Write imaginary N.CN.1 A2.N.7 Simplify powers of i 9.2 Operations with Complex Numbers A2.N.9 Perform operations on complex N.CN Complex Numbers and Conjugates 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 Chapter 10 Polynomial Functions and Variations 10.1 Polynomial Functions 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 A2.A.26 Solve higher-degree polynomial N.CN.9 equations 10.3 Direct and Inverse Variation A2.A.5 Use direct and inverse variation Chapter 10 Preparing for the New York Algebra 2 and Trigonometry Exam Chapter 11 Exponential and Logarithmic Functions 11.1 Exponential and Logarithmic Functions 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...

6 11.2 Exponential Functions of Base e and Properties of Logarithms 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 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 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 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 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 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 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...

7 12.5 Graphing Inverse Trigonometric Functions A2.A.63 Restrict domain of trig functions F.TF.6 Chapter 12 Preparing for the New York Algebra 2 and Trigonometry Exam 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 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 A2.A.68 Solve trigonometric equations 13.3 Law of Sines and Cosines 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) A2.A.75 Determine solution from SSA situation Chapter 13 Preparing for the New York Algebra 2 and Trigonometry Exam Chapter 14 Sequences and Series 14.1 Arithmetic and Geometric Sequences 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 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...

8 14.3 The Binomial Theorem A2.A.36 Apply binomial theorem A.APR.5 Chapter 14 Preparing for the New York Algebra 2 and Trigonometry Exam Chapter 15 Statistics 15.1 Gathering Data A2.S.1 Understand difference among studies S.IC.4 A2.S.2 Determine factors which affect outcome 15.2 Measures of Central Tendency A2.S.3 Calculate measures of central S.ID.2 tendency A2.S.4 Calculate measures of dispersion 15.3 Measures of Dispersion A2.S.4 Calculate measures of dispersion 15.4 Normal Distribution A2.S.5 Know and apply normal distribution S.ID Regression Models 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 A2.S.8 Use correlation coefficient Chapter 16 Probability 16.1 Probabilities A2.S.13 Calculate theoretical probabilities S.MD.3 A2.S.14 Calculate empirical probabilities S.MD Applying Probability 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...

9 16.3 Combinations and Permutations 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 A2.S.15 Apply the binomial probability formula 16.5 Normal Approximation of Binomial Probabilities A2.S.16 Use the normal distribution Chapter 16 Preparing for the New York Algebra 2 and Trigonometry Exam 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...