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