Mathematics 20-1

Unit 1: Algebra and Number

General outcome: develop algebraic reasoning and number sense. Absolute value, operations on radicals with variable radicands, radical equations, and the algebra of rational expressions and equations.

• Absolute value as distance
• Evaluating and ordering with absolute value

• Radicals with variable radicands
• Adding and subtracting radicals
• Multiplying, dividing and rationalizing

• Solving radical equations
• Problems with radical equations

• Non-permissible values
• Simplifying rational expressions

• Multiplying and dividing
• Adding and subtracting

• Solving rational equations
• Problems with rational equations

Unit 2: Trigonometry

General outcome: develop trigonometric reasoning. Angles in standard position from 0° to 360°, the three primary ratios beyond acute angles, and the sine and cosine laws including the ambiguous case.

• Standard position
• Reference angles

• Ratios from a terminal-arm point
• Signs by quadrant
• Finding angles from ratios

• The sine law
• The cosine law
• The ambiguous case

Unit 3: Relations and Functions

General outcome: develop algebraic and graphical reasoning through the study of relations. Advanced factoring, absolute value functions, quadratic functions and equations, systems, inequalities, sequences and series, and reciprocal functions.

• Trinomials and differences of squares
• Factoring in function form

• Graphing y = |f(x)|
• Solving with absolute value graphs

• Reading y = a(x − p)² + q
• The roles of a, p and q

• Analyzing y = ax² + bx + c
• Completing the square

• Roots by factoring and graphing
• The quadratic formula and the discriminant

• Solving systems graphically
• Solving systems algebraically

• Linear inequalities
• Quadratic inequalities

• Solving with the graph
• Solving with roots and sign analysis

• Arithmetic sequences
• Arithmetic series

• Geometric sequences
• Geometric series

• Reciprocals of linear functions
• Reciprocals of quadratic functions