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The Bronx High School of Science Valerie Reidy, Principal Mathematics Department Rosemarie Jahoda, Assistant Principal MPS21 Precalculus Fundamentals: Sections 1.3, 1.6 1 2 Functions: Sections 2.1-2.4, 2.7, 3 2.8 4 5 6 7 8 Optimization: Sections 2.5, 2.6 Polynomials: Sections 3.1-3.5 Rational Functions: Sections 1.4, 3.6 Domains (Set and Interval Notation) Interpreting Graphs of Functions Piece-wise Functions Greatest Integer Function Increasing/Decreasing Functions (points of inflection will be included in both intervals) 9 Average Rate of Change 10 Transformations 11 Even and Odd Functions 12 Combining Functions 13 One-to-One Functions and their Inverses (Needed for Calculus AB/BC) 14 Quadratic Functions in Standard Form 15 Maximum/Minimum Values of Quadratic Functions 16- Modeling with Functions 19 20 End Behavior of Polynomial Graphs (Emphasis on Figure 1 on page 251 for Calculus) 21 Using Zeros and their Multiplicities to Graph Polynomials 22 Local Maxima/Minima of Polynomials 23 Polynomial Long Division and Division Algorithm 24 Synthetic Division (Emphasis for Calculus) 25 Remainder and Factor Theorems 26- Rational Zeros Theorem 27 28- Descartes’ Rule of Signs and Upper and Lower 29 Bounds Theorem 30 Operations with Complex Numbers 31 3233 34 3536 3739 Exponential and Logarithmic Fall Term Special Product Formulas, Special Factoring Formulas Modeling with Equations Evaluating Functions 40 Complex Zeros of Quadratics Complex Zeros of Polynomials Rational Expressions Finding Asymptotes of Rational Functions Graphing Rational Functions (points of discontinuity* and limit concepts introduced) (Emphasis for Calculus) Exponential Functions 1 The Bronx High School of Science Valerie Reidy, Principal Mathematics Department Rosemarie Jahoda, Assistant Principal Functions: Chapter 4 (including yellow pages) 41 42 43 44 Trigonometric Functions of Real Numbers: Chapter 5 MPS22 Precalulus Trigonometric Functions of Angles: Topics from 6.1-6.3 Analytic Trigonometry: Sections 7.1, 7.4 Natural Exponential Function (Emphasis for Calculus) Compound Interest Logarithmic Functions Common and Natural Logarithmic Functions (Emphasis for Calculus) 45 Laws of Logarithms 46 Exponential Equations 47 Logarithmic Equations 48 Modeling with Exponential Functions 49 Modeling with Logarithmic Functions 50 Focus on Modeling: Fitting Exponential and Power Curves to Data 51- The Unit Circle (full understanding of radian measure 52 for Calculus) 53 Evaluating Trigonometric Functions (Emphasis for Calculus) 54 Fundamental Trigonometric Identities 55 Graphing Sine and Cosine Functions 56- Graphing Transformations of Sine and Cosine 57 58 Graphing Tangent and Cotangent Functions 59 Graphing Transformations of Tangent and Cotangent 60 Graphing Secant and Cosecant Functions 61 Graphing Transformations of Secant and Cosecant 62- Simple Harmonic Motion 63 64 Damped Harmonic Motion Spring Term 1 Degrees and Radians Conversions 2 3 4 5 6-7 Arc Length and Area of a Sector Linear and Angular Speed Solving a Right Triangle Area of a Triangle Proving Trigonometric Identities (to reinforce the Pythagorean, reciprocal, and quotient identities – emphasis for Calculus) 8-9 Inverse Trigonometric Functions* Inverse Cosecant , 0 0, 2 2 Inverse Secant 0, , 2 2 2 The Bronx High School of Science Valerie Reidy, Principal Mathematics Department Rosemarie Jahoda, Assistant Principal Polar Coordinates: Sections 8.1- 10 8.3 11 Inverse Tangent 0, Plotting Points in Polar Coordinates Converting Between Polar and Rectangular Coordinates 12 Graphing Circles and Lines 13 Graphing Limacons 14 Graphing Roses 15 Using Symmetry to Graph a Polar Equation 16 Graphing Complex Numbers and Moduli 17 Polar Form of Complex Numbers 18 DeMoivre’s Theorem 19- The nth Roots of Complex Numbers 20 Vectors: Sections 8.4, 8.5 21 Component Form, Magnitude, and Operations of Vectors 22 Properties and Horizontal/Vertical Components of a Vector 23 Vector Applications 24 Dot Product: Definition, Properties, Dot Product Theorem, Angle between Two Vectors, Orthogonal Vectors 25 Work Conics: Sections 10.1-10.4, 26- Parabolas 10.6, 10.7 27 28- Ellipses 29 30- Hyperbolas 31 32- Shifted Conics 33 34 Degenerate Conics 35- Polar Equations of Conics 36 37- Parametric Equations 38 Matrices: Section 9.4 (including 39 Converting a System of Equations to a Matrix yellow pages) 40 Elementary Row Operations 41 Gaussian Elimination 42 Gauss-Jordan Elimination 43 Independent and Dependent Systems 44 Matrices on a Calculator 45 Focus on Modeling: Linear Programming Sequences and Series: Sections 46 Sequences, Recursive Sequences, and Partial Sums 3 The Bronx High School of Science Valerie Reidy, Principal Mathematics Department Rosemarie Jahoda, Assistant Principal 11.1-11.3, 11.5 Limits: Sections 12.1, 12.2, 12.4 47 48 49 50 51 52 53 54 Summation Arithmetic Sequences Geometric Sequences Infinite Geometric Sequences Summation Mathematical Induction Proofs Inequality Mathematical Induction Proofs Divisibility Mathematical Induction Proofs Finding Limits Numerically 55 Finding Limits Graphically 56 Finding Limits Algebraically 57 Limits at Infinity 58 Limits of Sequences *Either not in the textbook or incorrect in the textbook. Use alternate resourses. 4