Mathematics: Advanced Level—Developmental
Goal Statement
The goal of Advanced Developmental Mathematics is to provide students with sufficient algebra, geometry, and trigonometry to satisfy grade 11 prerequisites for some vocational, career, technical, and/or further academic programs.
Learning Outcomes
1. Operations with Real Numbers
It is expected that learners will be able to:
- write fractions as decimals and repeating decimals as fractions
- add, subtract, multiply and divide rational numbers
- evaluate powers with rational bases and integer exponents
- demonstrate the order of operations with rational numbers
- evaluate radicals with rational radicands and distinguish between exact answers and approximate answers
- simplify, add, subtract, multiply and divide square roots
2. First Degree Equations and Inequalities
It is expected that learners will be able to:
- solve first degree equations, in one variable, including those involving parentheses
- solve formulas for a given variable when other variables are known
- solve formulas for a given variable
- solve first degree inequalities in one variable
- solve practical problems that can be solved using a first degree equation
3. Polynomials
It is expected that learners will be able to:
- distinguish between monomials, binomials, trinomials and other polynomials (in one variable only)
- apply the laws of exponents to variable expressions with integral exponents
- evaluate polynomials by substitution
- add, subtract, and multiply polynomials
- factor polynomials by removing the largest common factor
- factor binomials of the form a²x² – b²y² and trinomials of the form x² + bx + c
- solve quadratic equations using the law of zero products
Optional Outcomes:
- factor trinomials of the form ax² + bx + c
4. Rational Expressions and Equations
It is expected that learners will be able to:
- simplify, by factoring, rational expressions consisting of polynomial numerators and either monomial, binomial, or trinomial denominators
- determine values for which a rational expression is undefined
- multiply and divide rational expressions
- add and subtract rational expressions consisting of monomial and/or binomial denominators
- solve simple rational equations and check solutions
5. Linear Equations
It is expected that learners will be able to:
- graph a linear equation including the forms x = a and y = b
- given a linear equation or its graph, determine its
- slope
- x– and y-intercepts
- determine the equation of a line, y = mx + b, given
- its graph
- its slope and a point on the line
- two points on the line
6. Systems of Linear Equations
It is expected that learners will be able to:
- solve a system of first degree equations in two unknowns by graphing, substitution, and elimination methods
- solve practical problems that can be solved using a system of equations
7. Radical Expressions and Equations
It is expected that learners will be able to:
- simplify square roots with variable radicands
- add, sub