Pre-Calculus 11

Unit 1: Algebra and Number

Absolute value, operations on radicals and radical equations, and equivalent forms of and operations on rational expressions and equations.

• Absolute value of real numbers

• Simplifying and operating on numerical radicals
• Radicals with variable radicands

• Solving radical equations

• Equivalent forms of rational expressions
• Multiplying and dividing rational expressions
• Adding and subtracting rational expressions
• Solving rational equations

Unit 2: Relations and Functions

Factoring polynomials, absolute value and quadratic functions, quadratic equations, systems and inequalities, arithmetic and geometric sequences and series, and reciprocal functions.

• Factoring trinomials
• Factoring differences of squares

• Absolute value of linear functions
• Absolute value of quadratic functions

• Vertex and direction of opening from vertex form
• Domain, range and axis of symmetry from vertex form
• Intercepts from vertex form

• Vertex and axis from general form
• Intercepts, domain and range from general form
• Solving problems with quadratic functions

• Solving quadratic equations by factoring
• Solving quadratic equations with the quadratic formula

• Non-linear systems graphically
• Non-linear systems algebraically
• Linear and quadratic inequalities in two variables
• Quadratic inequalities in two variables
• Quadratic inequalities in one variable

• Arithmetic sequences
• Arithmetic series
• Geometric sequences
• Geometric series

• Reciprocals of linear functions

Unit 3: Trigonometry

Angles in standard position, the primary trigonometric ratios from 0° to 360°, and the cosine and sine laws including the ambiguous case.

• Angles in standard position

• Trig ratios from the terminal arm
• Solving problems with the ratios over 0° to 360°

• Applying the cosine and sine laws
• The ambiguous case of the sine law