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Pre-Calculus Curriculum Map with CCS
Pre-Calculus Curriculum Map
Unit 0 - Preparing for Pre-Calculus
0-1 Sets
0-2 Operations with Complex Numbers
0-3 Quadratic Functions and Equations
0-4 nth Roots and Real Exponents
0-5 Systems of Linear Equations and Inequalities
0-6 Matrix Operations
0-7 Probability with Permutations and Combinations
0-8 Statistics
Unit 1 - Functions and Relations
1-1 Functions
1-2 Analyzing Graphs of Functions and Relations
1-3 Continuity, End Behavior, and Limits
1-4 Extrema and Average Rates of Change
1-5 Parent Functions and Transformations
1-6 Function Operations and Composition of Functions
1-7 Inverse Relations and Functions
Unit 2 - Power, Polynomial, and Rational Functions
2-1 Power and Radical Functions
2-2 Polynomial Functions
2-3 The Remainder and Factor Theorems
2-4 Zeros of Polynomial Functions
2-5 Rational Functions
2-6 Nonlinear Inequalities
Unit 3 - Exponential and Logarithmic Functions
3-1 Exponential Functions
3-2 Logarithmic Functions
3-3 Properties of Logarithms
3-4 Exponential and Logarithmic Equations
3-5 Modeling with Nonlinear Regression
Unit 4 - Trigonometric Functions
4-1 Right Triangle Trigonometry
4-2 Degrees and Radians
4-3 Trigonometric Functions on the Unit Circle
4-4 Graphing Sine and Cosine Functions
4-5 Graphing Other Trigonometric Functions
4-6 Inverse Trigonometric Functions
4-7 The Law of Sines and the Law of Cosines
Unit 5 - Trigonometric Identities and Equations
5-1 Trigonometric Identities
5-2 Verifying Trigonometric Identities
5-3 Solving Trigonometric Equations Exercises
5-4 Sum and Difference Formulas
5-5 Multiple-Angle and Product-to-Sum Identities
Unit 6 - Systems of Equations and Matrices
6-1 Multivariable Linear Systems and Row Operations
6-2 Matrix Multiplication, Inverses, and Determinants
6-3 Solving Linear Systems Using Inverses and Cramer's Rule
6-4 Partial Fractions
6-5 Linear Optimization
Unit 7 - Conic Sections and Parametric Equations
7-1 Parabolas
7-2 Ellipses and Circles
7-3 Hyperbolas
7-4 Rotations of Conic Sections
7-5 Parametric Equations
Unit 8 – Vectors
8-1 Introduction to Vectors
8-2 Vectors in the Coordinate Plane
8-3 Dot Products and Vector Projections
8-4 Vectors in Three-Dimensional Space
8-5 Dot and Cross Products of Vectors in Space
Unit 9 - Polar Coordinates and Complex Numbers
9-1 Polar Coordinates
9-2 Graphs of Polar Equations
9-3 Polar and Rectangular Forms of Equations
9-4 Polar Forms of Conic Sections
9-5 Complex Numbers and DeMoivre's Theorem
Unit 10 - Sequences and Series
10-1 Sequences, Series, and Sigma Notation
10-2 Arithmetic Sequences and Series
10-3 Geometric Sequences and Series
10-4 Mathematical Induction
10-5 The Binomial Theorems
10-6 Functions as Infinite Series
Unit 11 - Inferential Statistics
11-1 Descriptive Statistics
11-2 Probability Distributions
11-3 The Normal Distribution
11-4 The Central Limit Theorem
11-5 Confidence Intervals
11-6 Hypothesis Testing
11-7 Correlation and Linear Regression
Unit 12 - Limits and Derivatives
12-1 Estimating Limits Graphically
12-2 Evaluating Limits Algebraically
12-3 Tangent Lines and Velocity
12-4 Derivatives
12-5 Area Under a Curve and Integrations
12-6 The Fundamental Theorem of Calculus
