Mathematics: Advanced Level—Algebraic
Goal Statement
The goals for Advanced Algebraic Mathematics are (1) to provide students with sufficient mathematical knowledge for academic, career, and technical programs whose admission requirements include Math 11 equivalence and (2) to prepare students to enter Provincial Level mathematics courses.
Learning Outcomes
It is expected that learners will use a scientific calculator to evaluate complex expressions with emphasis on using special keys to perform a variety of functions. The use of a graphing calculator or other technology is optional.
1. Basic Algebraic Skills Review
Note: A review of the following basic algebraic skills is suggested but not required. It is expected that learners will be able to:
- perform operations with real numbers including absolute value and exponential notation
- simplify expressions using rules for order of operations including nested parentheses and properties of exponents
- translate common language into algebraic expressions
- evaluate algebraic expressions by substitution
2. Solving Linear Equations and Inequalities
It is expected that learners will be able to:
- solve first degree/linear equations in one variable
- manipulate simple formulas to isolate a specified variable
- solve and graph linear inequalities in one variable
- write set-builder and/or interval notation for the solution set or graph of an inequality
- use linear equations, formulas and linear inequalities to solve applied problems
- find the union (disjunction) and intersection (conjunction) of sets
- solve and graph compound inequalities
- solve absolute value equations
3. Graphing Relations and Functions
It is expected that learners will be able to:
- write linear equations in slope-intercept form
- graph linear equations using a table of values
- graph linear equations using the y-intercept and slope and using x- and y-intercepts
- graph horizontal and vertical lines
- find the slope of a line given two points on the line
- find the equation of a line given graphic data: the slope and y-intercept, the slope and one point, or two points on the line
- determine whether a pair of lines is parallel, perpendicular or neither
- find the equation of a line parallel or perpendicular to a given line and through a given point
- use the definition of function and the vertical line test to distinguish between functions and non-functions
- use and interpret function notation to evaluate functions for given x-values and find x-values for given function values
- determine the domain and range of a function
- use a table of values to graph linear functions and non-linear functions such as quadratic, cubic, square root, reciprocal, and absolute value functions
Optional Outcomes:
- graph exponential functions
- analyze functions to determine line of symmetry, vertices, asymptotes, and intercepts
- understand and demonstrate transformations in graphs resulting from the following changes in the defining equation: trans