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Topic outline

 

PreCalculus H

Created by Paul Prencis


  
1

Functions

1.1 Lines in the Plane
1.2 Functions
1.5 Combinations of Functions
1.6 Inverse Functions

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2

Transformations of Functions

1.1 Lines in the Plane
1.3 Graphs of Functions
1.4 Shifting, Reflecting, and Stretching Graphs

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3

Polynomial Functions


2.1 Quadratic Functions
2.2 Polynomial Functions of Higher Degree
2.3 Real Zeros of Polynomial Functions
2.4 Complex Numbers
2.5 The Fundamental Theorem of Algebra

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4

Rational Functions and Limits

2.6 Rational Functions and Asymptotes
2.7 Graphs of Rational Functions
11.1 Introduction to Limits
11.2 Techniques for Evaluating Limits
11.4 Limits at Infinity and Limits of Sequences
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5

A Review of Exponential, Logarithmic and Trigonometric Functions

3.1 Exponential Functions and Their Graphs
3.2 Logarithmic Functions and Their Graphs
3.3 Properties of Logarithms
3.4 Solving Exponential and Logarithmic Equations
4.1 Radian and Degree Measure
4.2 Trigonmetric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
4.7 Inverse Trigonometric Functions
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This topic 6

Analytic Trigonometry

4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
6.1 Law of Sines
6.2 Law of Cosines
5.1 Using Fundamental Identities
5.2 Verifying Trigonometric Identities
5.3 Solving Trigonometric Equations
5.4 Sum and Difference Formulas

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7

Data and Modeling

1.7 Exploring Data: Linear Models and Scatter Plots
2.8 Exploring Data: Quadratic Models
3.5 Exponential and Logarithmic Models
3.6 Exploring Data: Nonlinear Models
4.8 Applications and Models
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8

Applications of Trigonometry

6.3 Vectors in the Plane
6.4 Vectors and Dot Products
6.5 Trigonometric (Polar) Form of a Complex Number

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9

Polar Coordinates

9.5 Parametric Equations
9.6 Polar Coordinates
9.7 Graphs of Polar Equations

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10

The Conic Sections

9.1 Introduction to Conics: Parabolas
9.2 Ellipses
9.3 Hyperbolas
9.4 Rotation and Systems of Quadratic Equations

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11

Series and Sequence

8.1 Sequences and Series
8.2 Arithmetic Sequences and Partial Sums
8.3 Geometric Sequences and Series
8.4 Mathematical Induction

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12

Limits and Continuity

1.2 Finding Limits Graphically and Numerically
1.3 Evaluating Limits Analytically
1.4 Continuity and One-Sided Limits
1.5 Infinite Limits
3.5 Limits at Infinity

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13

The Derivative

2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 Product and Quotient Rules and Higher-Order Derivatives
2.4 The Chain Rule
2.5 Implicit Differentiation

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