Pre-Calculus Mathematics, Grade 11 (30S)

Unit 1: Algebra and Number

Absolute value of real numbers, radicals and radical equations, and rational expressions and equations with non-permissible values.

• Absolute value of real numbers
• Simplifying and operating on radicals
• Rationalizing denominators
• Radical equations

• Equivalent rational expressions and non-permissible values
• Multiplying and dividing rational expressions
• Adding and subtracting rational expressions
• Rational equations

Unit 2: Trigonometry

Angles in standard position from 0 to 360 degrees, the primary trigonometric ratios beyond right triangles, and the sine and cosine laws with the ambiguous case.

• Angles in standard position
• Trig ratios from a terminal-arm point
• Exact values and solving trig equations

• Deriving and applying the sine and cosine laws
• The ambiguous case

Unit 3: Relations and Functions

Advanced factoring, absolute value functions, quadratic functions and equations, systems and inequalities, arithmetic and geometric sequences and series, and reciprocal functions.

• Factoring trinomials and differences of squares
• Factoring quadratic patterns

• Graphing absolute value functions
• Solving absolute value equations

• Transformation effects in vertex form
• Sketching and analyzing from vertex form
• Completing the square
• Analyzing and modelling with general form

• Solving quadratics by factoring and completing the square
• The quadratic formula and the discriminant
• Linear-quadratic and quadratic-quadratic systems graphically
• Solving quadratic systems algebraically
• Linear and quadratic inequalities in two variables
• Quadratic inequalities in one variable

• Arithmetic sequences
• Arithmetic series
• Geometric sequences
• Geometric series and convergence
• Reciprocal functions