# Start AP Calculus Early

This summer program will give students a head start in AP Calculus. In 33 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. ### Limits and Continuity

Lesson 1
-Evaluating functions
-Inputs and outputs of a function
-Composing functions
-Quiz 1

### Limits and Continuity

Lesson 2
-Piecewise functions
-Quiz 2
-Introduction to factoring

Lesson 3

### Limits and Continuity

Lesson 4
-Factoring by grouping
-Quiz 3
-Factoring quadratics with difference of squares

### Polynomials

Lesson 5
-Factoring higher degree polynomial
-Quiz 4

### Polynomials

Lesson 6
-Introduction to the trigonometric ratios
-The reciprocal trigonometric ratios

### Composite and Inverse functions

Lesson 7
-The Pythagorean identity
-Quiz 5
-Special trigonometric values in the first quadrant
-Trigonometric identities on the unit circle

### Composite and Inverse functions

Lesson 8
-Quiz 6
-Reducing rational expressions to lowest terms

### Composite and Inverse functions

Lesson 9
-End behaviour of rational functions
-Discontinuities of rational functions
-Multiplying and dividing rational expressions
-Quiz 7

### Differentiation:definition and basic derivative rules

Lesson 10
-Intro to slope-intercept form
-Writing slope-intercept equations

### Differentiation:definition and basic derivative rules

Lesson 11
-Point-slope form
-Average rate of change
-Quiz 1
-Rational exponents Properties of exponents

### Differentiation:definition and basic derivative rules

Lesson 12
-Quiz 2
-Introduction to logarithm
-Quiz 3

### Differentiation:definition and basic derivative rules

Lesson 13
-Composing functions
-Quiz 1
-Linear equations with unknown coefficients

### Differentiation:definition and basic derivative rules

Lesson 14
-Intro to inverse functions
-Quiz 2
-Invertible functions

### Differentiation:definition and basic derivative rules

Lesson 15
-Invertible functions

### Differentiation:definition and basic derivative rules

Lesson 16
-Inverse trigonometric functions

### Differentiation:definition and basic derivative rules

Lesson 17
-Quiz 3
-Inverse functions in graphs and tables
-Verifying inverse functions by composition
-Quiz 4

### Contextual application of differentiation

Lesson 18
-Word problems with multiple units
-Linear equations word problems
-Interpreting function notation
-Average rate of change word problems
-Modelling with composite functions

### Contextual application of differentiation

Lesson 19
-Quiz 1
-Modelling with right triangles
-Volume and surface area
-Quiz 2

### Applying derivatives to analyze functions

Lesson 20
-Maximum and Minimum points
-Intervals where a function is positive, negative, increasing or decreasing
-Interpreting features of graphs
-Quiz 1
-Distance formula

### Applying derivatives to analyze functions

Lesson 21
-Square root equations
-Quiz 2

### Applying derivatives to analyze functions

Lesson 22
-Zero of polynomials
-Positive and negative of polynomials
-Quiz 3

### Integration and accumulation of change

Lesson 23
-Completing the square
-Quiz 1

### Integration and accumulation of change

Lesson 24
-Dividing polynomials by linear factors
-Quiz 2

### Integration and accumulation of change

Lesson 25
-Partial fraction expansion
-Summation notation

### Applications of integration

Lesson 26
-Rational equations
-Square-root equations
-Extraneous solutions

### Applications of integration

Lesson 27
-Sinusoidal equations
-Manipulating formulas
-Quiz 1
-Solving equations by graphing

### Probabilities and Combinatorics

Lesson 28
-Basic theoretical probabilityQuiz 2 2D vs. 3D objects
-Cavalieri’s principle and dissection method
-Quiz 3

### Parametric equations, polar coordinates and vector-valued functions (BC only)

Lesson 29
-Sector
-Vectors introduction
-Vector components
-Magnitude of vectors

### Parametric equations, polar coordinates and vector-valued functions (BC only)

Lesson 30
-Scalar multiplication
-Direction of vectors
-Vector components from Magnitude and direction

### Parametric equations, polar coordinates and vector-valued functions (BC only)

Lesson 31
-Arithmetic sequences
-Geometric sequences
-Quiz 1
-Summation notation

### Parametric equations, polar coordinates and vector-valued functions (BC only)

Lesson 32
-Arithmetic series

### Parametric equations, polar coordinates and vector-valued functions (BC only)

Lesson 33
-Geometric series( geometric series formula, finite series word problems, finite geometric series)
-Quiz 2
-End behaviour of rational functions