# Start Precalculus Early

# Precalculus

This summer program will give students a head start in Calculus 1. In 25 live sessions, students will learn about transformation of functions and modeling with function, complex numbers, polynomials, composite and inverse functions, trigonometry, vectors and matrices, probabilities and combinatorics, series, and conic sections.

### Complex Numbers

*Lesson 1*

-The imaginary unit i

-Complex number introduction

### Complex Numbers

*Lesson 2*

-The Complex plane

-Quiz 1

-Adding and Subtracting complex numbers

-Multipying complex numbers
Quadratic equations with complex solutions

-Quiz 2

### Polynomials

*Lesson 3*

-Adding and subtracting polynomials

-Quiz 1

-Multiplying binomials by polynomials

-Special products of polynomials

-Quiz 2

### Polynomials

*Lesson 4*

-Factorizing higher degree polynomial

-Factorizing using structure

-Zeros of polynomials

### Polynomials

*Lesson 5*

-Quiz 3

-Dividing polynomials by x

-Dividing quadratics by linear factors

### Polynomials

*Lesson 6*

-Dividing polynomials by linear factors

-Quiz 3

### Composite and Inverse functions

*Lesson 7*

-Shifting functions

-Reflecting functions

-Scaling functions

### Composite and Inverse functions

*Lesson 8*

-Identifying function transformations

-Quiz 1

-Intro to domain and range of a function

### Composite and Inverse functions

*Lesson 9*

-Intro to inverse functions

-Quiz 2

### Trigonometry

*Lesson 10*

-Unit circle introduction

-Radians

### Trigonometry

*Lesson 11*

-The Pythagorean identity

-Trigonetric values of special angles

-Quiz 1

### Trigonometry

*Lesson 12*

-Graphing sinusoidal functions

-Sinusoidal models

-Quiz 2

### Vectors and Matrices

*Lesson 13*

-Equivalent systems of equations and the elimination method 1) elimination and manipulation

### Vectors and Matrices

*Lesson 14*

-Equivalent systems of equations and the elimination method 2

-Quiz 1

### Vectors and Matrices

*Lesson 15*

-Dilations

-Quiz 2

-Solving triangles using the trigonometric ratios

### Vectors and Matrices

*Lesson 16*

-Unit circle introduction

-Distance formula

-Quiz 3

### Series

*Lesson 17*

-Intro to sequences

-Quiz 1

### Series

*Lesson 18*

-Constructing arithmetic sequences

-Constructing geometric sequences

### Series

*Lesson 19*

-Modeling with sequences

-Quiz 2

-General sequences

-Geometric series

-Quiz 3

### Conic Sections

*Lesson 20*

-Graphs of circles intro

-Quiz 1

-Standard equation of a circle

### Conic Sections

*Lesson 21*

-Expanded equation of a circle

-Quiz 2

-Focus and Directrix of a parabola

### Probabilities and Combinatorics

*Lesson 22*

-Basic theoretical probability

### Probabilities and Combinatorics

*Lesson 23*

-Probability using sample spaces

-Basic set operation

### Probabilities and Combinatorics

*Lesson 24*

-Quiz 1

-Experimental probability

### Probabilities and Combinatorics

*Lesson 25*

-Randomness, probability, and simulation

-Addition rule

-Quiz 2