# UnLock Math Curriculum

Pre-Calculus is the direct successor to Algebra II. It builds on the concepts of Algebra II and prepares students for Calculus.

## Pre-Calculus

Pre-Calculus plays a crucial role in preparing students for calculus and post-secondary mathematics. This course focuses on more abstract and theoretical concepts, allowing students to improve their critical thought processes. The primary goal of this course is for students to own a thorough understanding of all types of functions and prepare them for Calculus. Includes 120 video lessons taught by acclaimed math teacher Alesia Blackwood, detailed solutions for each question, unlimited practice, just the right amount of review, continual support, live math help & tutoring with expert teachers, automated grading, and much, much more. This is the online Pre-Calculus curriculum that checks ALL your dream curriculum boxes

Unit 1

### Review of Functions and Quadratics

- 1.1 Introduction to Functions
- 1.2 Domain of a Function and Interval Notation
- 1.3 Range of a Function and Interval Notation
- 1.4 Composition of Functions
- 1.5 Inverse of Functions
- 1.6 Introduction to Quadratic Functions
- 1.7 Graphing Quadratic Functions in Vertex Form
- 1.8 Solving Quadratic Equations with Square Roots
- 1.9 Solving Quadratics by Completing the Square
- 1.10 Converting to Vertex Form by Completing the Square
- 1.11 Graphing Quadratic Inequalities

Unit 2

### Polynomial Functions

- 2.1 Introduction to Polynomials
- 2.2 Finding a Polynomial Given the Roots
- 2.3 Dividing Polynomials Using Long Division
- 2.4 Dividing Polynomials Using Synthetic Division
- 2.5 Remainder Theorem/Factor Theorem
- 2.6 Location principle & Multiplicity of Zeros
- 2.7 Rational Root Theorem
- 2.8 Complex Conjugate Root Theorem
- 2.9 Fundamental Theorem of Algebra & Descartes Rule of signs
- 2.10 Graphing Polynomials

Unit 3

### Rational Functions

- 3.1 Introduction to Rational Functions
- 3.2 Graphing Rational Functions
- 3.3 Graphing Rational Functions Part II
- 3.4 Slant Asymptotes
- 3.5 Parabolic Asymptotes
- 3.6 Multiplying and Dividing Rational Expressions
- 3.7 Solving Rational Equations

Unit 4

### Exponential & Logarithmic Functions

- 4.1 Introduction to Exponential & Logarithmic Functions
- 4.2 Graphing Exponential Functions
- 4.3 Logarithmic Functions and Change of Base Formula
- 4.4 Properties of Logarithms
- 4.5 Exponential/Logarithmic Inverse Property
- 4.6 Natural Exponentials & Logarithms
- 4.7 Solving Exponential Equations
- 4.8 Solving Logarithmic Equations
- 4.9 Fitting Log Functions to Data

Unit 5

### Vectors

- 5.1 Introduction to Vectors
- 5.2 Vectors in Two Dimensions
- 5.3 Adding & Subtracting Vectors
- 5.4 Multiplying Vectors by a Scalar
- 5.5 Vector Components
- 5.6 Vector Notation
- 5.7 Operations in Vector Noation
- 5.8 Dot Product

Unit 6

### Matrices

- 6.1 Introduction to Matrices
- 6.2 Basic Matrix Operations
- 6.3 Matrix Multiplication
- 6.4 Determinant of 2x2 Matrices
- 6.5 Determinant of 3x3 Matrices
- 6.6 Inverse of Matrices
- 6.7 Elementary Row Operations & Augmented Matrices
- 6.8 Using Matrices to Solve 2x2 Systems
- 6.9 Using Matrices to Solve 3x3 Systems

Unit 7

### Complex Numbers

- 7.1 Introduction to Complex
- 7.2 Adding and Subtracting Complex Numbers
- 7.3 Multiplying Complex Numbers
- 7.4 Complex Conjugate & Dividing
- 7.5 The Complex Plane
- 7.6 Modulus of Complex Numbers
- 7.7 Distance in the Complex Plane
- 7.8 Midpoint in the Complex Plane

Unit 8

### Trigonometric Functions

- 8.1 Introduction to Trigonometric Functions
- 8.2 Radian Measure
- 8.3 Standard Position & Reference Angles
- 8.4 Special Triangles and Exact Ratios
- 8.5 Graphing the Sine and Cosine Functions
- 8.6 Graphing the Tangent and Cotangent Functions
- 8.7 Graphing the Secant and Cosecant Functions
- 8.8 Applications of Trigonometric Functions
- 8.9 Modelling Trigonometric Functions
- 8.10 Inverse Trigonometric Functions

Unit 9

### Analytic Trigonometry

- 9.1 Introduction to Analytic Trigonometry
- 9.2 Cofunction, Periodicity and Negative Angle Identities
- 9.3 Addition and Subtraction Identities
- 9.4 Double and Half-Angle Identities
- 9.5 Product to Sum Identities
- 9.6 Solving Trigonometric Equations Algebraically
- 9.7 Solving Trigonometric Equations with Identities

Unit 10

### Conic Sections

- 10.1 Introduction to Conic Sections
- 10.2 Parabolas
- 10.3 Parabolas Part II
- 10.4 Circles
- 10.5 Circles Part II
- 10.6 Ellipses
- 10.7 Ellipses Part II
- 10.8 Hyperbolas
- 10.9 Hyperbolas Part II
- 10.10 Solving Non Linear Systems
- 10.11 Parametric Equations
- 10.12 Parametric Equations of Conic Sections

Unit 11

### Polar Coordinates

- 11.1 Introduction to Polar Coordinates
- 11.2 Converting Rectangular to Polar Coordinates
- 11.3 Converting Polar to Rectangular Coordinates
- 11.4 Polar Equations and Graphs
- 11.5 Eccentricity of Conic Sections
- 11.6 Polar Equations of Conic Sections
- 11.7 Complex Numbers in Polar Notation
- 11.8 Multiplication and Division with Polar Notation
- 11.9 DeMoivre's Theorem

Unit 12

### Sequence & Series

- 12.1 Introduction to Sequences and Series
- 12.2 Sequences & Series
- 12.3 Arithmetic Sequences
- 12.4 Arithmetic Series
- 12.5 Geometric Sequences
- 12.6 Finite Geometric Series
- 12.7 Infinite Geometric Series
- 12.8 Permutations and Combinations
- 12.9 Pascal's Triangle
- 12.10 Binomial Theorem

Unit 13

### Introduction to Calculus

- 13.1 Introduction to Calculus
- 13.2 Limits and Continuity
- 13.3 Limits Involving Infinity
- 13.4 Slope of a Tangent Line
- 13.5 The Power Rule
- 13.6 The Product and Quotient Rules
- 13.7 The Chain Rule
- 13.8 Applications of Derivatives
- 13.9 Antiderivatives
- 13.10 Integrals and the Area Under a Curve