Grade 11 Functions (MCR3U) 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
• Parent functions and their key features
• Transformations: y = a f(k(x − d)) + c
• Multiply, divide, add and subtract rational expressions
• Simplify polynomial and radical expressions

Quadratic Functions

• Maximum or minimum of a quadratic function
• Roots, zeros and x-intercepts
• Where a line meets a parabola
• Write a quadratic from its zeros, vertex or a family

Polynomial and Rational Functions

• Average rate of change

Exponential and Logarithmic Functions

• Rational exponents
• Simplify with the exponent laws
• Exponential functions: graphs and transformations
• Exponential growth and decay models

Sequences and Series

• Recursive sequences
• Arithmetic sequences: general term
• Geometric sequences: general term
• Arithmetic series
• Geometric series
• Pascal's triangle and the binomial theorem

Financial Mathematics

• Compound interest
• Present value
• Annuities: future value and present value

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
• Trigonometric identities
• The sine law: the ambiguous case (SSA)
• Trigonometry in 3D and with bearings

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

Course codes are those used in Ontario secondary schools. The Math Meridian is an independent practice site and is not affiliated with the Ontario Ministry of Education.