AP® Precalculus practice

Independent practice matched to the topics of this course. It is not official course material, so check your own course outline for exactly what your teacher covers.

Functions

• Functions: notation, domain, range and the vertical line test
• Inverse functions
• Composite functions f(g(x))
• Parent functions and their key features
• Transformations: y = a f(k(x − d)) + c
• Odd and even functions
• Absolute value equations and inequalities

Quadratic Functions

• Quadratic inequalities

Polynomial and Rational Functions

• Polynomial functions: degree and end behaviour
• Zeros and multiplicity
• The remainder theorem
• The factor theorem: factor cubics
• Rational functions: asymptotes and holes
• Rational functions: zeros, intercepts and end behaviour
• Average rate of change
• Choose a model: linear, quadratic or exponential

Exponential and Logarithmic Functions

• Exponential functions: graphs and transformations
• Exponential growth and decay models
• Logarithmic functions and their graphs
• Log laws and change of base
• Solve exponential and logarithmic equations
• Exponential and logarithmic inequalities
• Semi-log plots and linearizing exponential data

Sequences and Series

• Arithmetic sequences: general term
• Geometric sequences: general term
• Infinite geometric series

Trigonometry

• Angles in standard position and the CAST rule
• Exact values for special angles up to 360°
• Find all angles from 0° to 360° with a given ratio
• Reciprocal ratios: csc, sec and cot
• Radians and the unit circle
• Trigonometric identities
• Double-angle and compound-angle formulas
• Solve trigonometric equations
• Inverse trigonometric functions

Periodic and Sinusoidal Functions

• Periodic functions: period, amplitude and axis
• Graphs of y = sin x and y = cos x
• Transformations: amplitude, period, phase shift and axis
• Write the equation of a sinusoidal function
• Sinusoidal models: Ferris wheels, tides and daylight
• The tangent function and its graph
• Polar coordinates

Complex Numbers, Counting and Proof

• Complex numbers: add, subtract, multiply and divide
• Quadratics with complex roots
• Complex numbers in polar form and De Moivre's theorem

Vectors, Matrices and Conics

• Vectors: magnitude, addition and scalar multiples
• The dot product and the angle between vectors
• Vector and parametric equations of lines
• Matrices: add, multiply and use in context
• Determinant and inverse of a 2 × 2 matrix
• Matrices as transformations
• Parametric equations and planar motion
• Conic sections: circles and parabolas
• Conic sections: ellipses and hyperbolas

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