Download MPS21-MP22 Course Outline - The Bronx High School of Science

The Bronx High School of Science
Valerie Reidy, Principal
Mathematics Department
Rosemarie Jahoda, Assistant Principal
MPS21 Precalculus
Fundamentals: Sections 1.3, 1.6
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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
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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 
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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
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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.
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