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