# Start AP Calculus Early

### 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

### Limits and Continuity

*Lesson 3*

-Factoring quadratics intro

### Limits and Continuity

*Lesson 4*

-Factoring by grouping

-Quiz 3

-Factoring quadratics with difference of squares

### Polynomials

*Lesson 5*

-Factoring quadratics with perfect squares

-Factoring higher degree polynomial

-Quiz 4

### Polynomials

*Lesson 6*

-Introduction to the trigonometric ratios

-The reciprocal trigonometric ratios

-Unit circle introduction Radians

### 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*

-Angle addition identities

-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 quadratics by linear factors

-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