Mathematics: Provincial Level—Algebra and Trigonometry
Mathematics: Provincial Level—Algebra and Trigonometry
Goal Statement
The goals of the Provincial Algebra and Trigonometry are to prepare adult learners with the knowledge and skills in algebra and trigonometry necessary for entry to technical, vocational and career programs that require Math 12 equivalency as a prerequisite and for future study in higher-level math courses at college/university.
Learning Outcomes
1. Algebra Review
Note: the following outcomes are suggested, but not required. It is expected that learners will be able to:
- recognize subsets and identify properties of real numbers
- use interval notation to write a set of numbers
- evaluate absolute value of a real number and find the distance between two real numbers
- use rules for order of operations and properties of exponents to simplify expressions
- add, subtract, and multiply polynomials and factor a polynomial completely
- determine the domain of a rational expression, simplify rational expressions, perform operations with rational expressions and simplify complex rational expressions
- use properties of exponents to simplify radical expressions
- rationalize the denominator or numerator in a rational expression
- use properties of radicals to simplify and combine radicals
- define imaginary and complex numbers, express them in standard form, and perform operations with complex numbers
- solve linear equations, equations with absolute value, quadratic equations, radical equations, and equations reducible to a quadratic form
- solve linear inequalities, combined inequalities, and absolute value inequalities and graph the solutions on a number line
- solve applied problems using linear and quadratic equations
- solve equations of variation and applied problems involving variation
- solve systems of linear equations in two variables and in three variables
- distinguish between consistent/inconsistent and dependent/independent systems
- use systems of linear equations to solve applied problems
2. Functions and Graphs
It is expected that learners will be able to:
- find the distance between two points in the plane and find the midpoint of a segment
- apply the distance formula and mid-point formula to solve problems
- recognize graphs of common functions: linear, constant, quadratic, cubic, square root, absolute value, reciprocal
- use the vertical line test to identify functions
- graph functions and analyze graphs of functions, identifying: domain and range; intervals on which the function is increasing, decreasing or constant
- write formulas or functions to model real life applications
- determine whether a graph is symmetric with respect to the x-axis, y-axis, and the origin
- identify even or odd functions and recognize their symmetries
- graph transformations of functions: translations, reflections, stretchings and shrinkings
- graph functions defined piecewise
- find the sum, difference, product and quotient of two functions and determine their domains
- find the compo