## MATH 040 - Advanced Mathematics

As an equivalent to Principles of Math 11 and Pre-Calculus 11, this course satisfies the requirements for Grade 11 mathematics. MATH 040 is designed to meet the entrance requirements for further academic, career, or technical training. Topics include: basic algebraic review; linear equations and inequalities; graphing, relations, and functions; polynomials and polynomial functions; rational expressions and equations; radical expressions and equations; quadratic equations; and trigonometry. MATH 040 is recommended for students requiring Grade 11 math for academic post-secondary studies.

Hours: 120 (Lecture: 120)

Total Weeks: 20

Prerequisites:
“C” or higher in MATH030 or MATH10 or equivalent or Advanced Level Placement on the CCP Math Assessment

Non-Course Prerequisites:

None

Co-Requisites:

None

Course Content:
Core Topics:
- Basic Algebraic Skills Review
- Solving Linear Equations and Inequalities
- Graphing, Relations, and Functions
- Systems of Linear Equations and Inequalities
- Polynomials and Polynomial Functions
- Rational Expressions, Rational Equations and Variation
- Trigonometry
Optional Topics:
- Geometry
- Data Analysis

Learning Outcomes:
1. Basic Algebraic Skills Review: Upon successful completion of this course, learners will be able to:
- perform operations with real numbers including absolute value and exponential notation
- simplify expressions using rules for order of operations and properties of exponents
- translate common language into algebraic expressions
- evaluate algebraic expressions by substitution
- simplify algebraic expressions with nested parentheses
2. Linear Equations and Inequalities: Upon successful completion of this course, learners will be able to:
- solve first degree/linear equations in one variable
- solve simple formulas for a given 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 or intersection of two sets
- solve and graph compound inequalities (conjunctions and disjunctions)
- solve absolute value equations
3. Graphing, Relations, and Functions:Upon successful completion of this course, learners will be able to:
- write linear equations in slope-intercept form
- graph linear equations and non-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
- graph linear inequalities in two variables
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: translation, reflection, dilation
- use a graphing calculator or other appropriate technology to graph equations
- identify an appropriate graph for a given relation
- develop a model function from a given graph or set of data
- perform linear regression using a graphing calculator to fit a linear function to data
4. Systems of Linear Equations and Inequalities: Upon successful completion of this course, learners will be able to:
- solve systems of linear equations in two variables by graphing, substitution and elimination methods
- determine if a system of equations will have no, one or an infinite number of solutions
- use systems of equations to solve applied problems
Optional Outcomes:
- solve systems of equations in three variables and applied problems using such systems
- graph the solution for a system of linear inequalities in two variables
- use a graphing calculator or other appropriate technology to solve systems of equations and inequalities
5. Polynomials and Polynomial Functions: Upon successful completion of this course, learners will be able to:
- determine the degree of a polynomial
- distinguish between monomials, binomials, trinomials, and other polynomials
- add, subtract, multiply polynomials
- divide polynomials by monomials
- factor polynomials using an appropriate strategy or a combination of techniques: common factors, difference of squares, difference and sum of cubes, perfect square trinomials, trial/error, or grouping
- solve polynomial equations using the principle of zero products
- solve applied problems using polynomial equations/ functions
Optional Outcomes:
- divide polynomials and binomials using long division
- divide polynomials and binomials using synthetic division
6. Rational Expressions, Rational Equations and Variation: Upon successful completion of this course, learners will be able to:
- identify situations and find values for which a rational expression will be undefined
- simplify rational expressions
- add, subtract, multiply and divide rational expressions
- solve rational equations and check
- solve formulas involving rational expressions for a given variable
- solve applied problems that can be modeled with rational equations
- simplify complex fractions
- express variations in the form of equations (direct, inverse, joint, combined)
- solve problems involving direct, inverse, joint and combined variation
7. Radical Expressions Radical and Equations: Upon successful completion of this course, learners will be able to:
- identify situations and find values for which a radical expression will be undefined
- write radicals as powers with rational exponents and vice versa
- use rational exponents to simplify radical expressions
- simplify, add, subtract, multiply and divide radical expressions (numeric or algebraic)
- rationalize denominators in fractional expressions containing radicals (including the use of conjugates)
- solve equations involving radical expressions or powers with rational exponents and check for extraneous roots
- solve formulas involving powers and square roots for a given variable
- solve applied problems which can be modeled by radical equations, and determine if solutions are reasonable given the context of the problem
Optional Outcomes:
- identify imaginary and complex numbers and express them in standard form
- add, subtract, multiply, and divide complex numbers
8. Quadratic Equations and Quadratic Functions: Upon successful completion of this course, learners will be able to:
- solve quadratic equations by factoring, principle of square roots, completing the square and the quadratic formula
- use the discriminant to identify the number and type of solutions of a quadratic equation
- write a quadratic equation given its solutions
- solve rational and radical equations reducible to a quadratic pattern and check that answers are reasonable
- solve selected polynomial equations that can be factored simplifying to linear and/or quadratic factors
- graph quadratic functions of the form f(x) = a(x -h)² + k and demonstrate translations, reflections and stretching/shrinking resulting from changes in the function equation
- find the vertex, line of symmetry, minimum or maximum values, x- and y-intercepts, domain and range, given the function f(x) = a(x -h)² + k
- rewrite f(x) = ax² + bx + c as f(x) = a(x -h)² + k by completing the square
- solve problems that can be modeled using quadratic equations such as maximum and minimum problems
Optional Outcomes:
- solve quadratic equations having complex number solutions
- use a graphing calculator or other appropriate technology to graph and solve quadratic equations
- solve quadratic inequalities by graphing
- solve polynomial and rational inequalities algebraically
9. Trigonometry: Upon successful completion of this course, learners will be able to:
- label the sides of a right triangle with respect to a given angle
- determine sine, cosine, and tangent ratios of an angle in a right triangle using the side lengths
- use a scientific calculator to find the trigonometric value for a given angle and to find an angle given its trigonometric value
- solve right triangles and applied problems using the basic trigonometric ratios, the Pythagorean theorem, and sum of the angles (180°)
- use the Law of Sines and the Law of Cosines to solve non-right (oblique) triangles and applied problems
Optional Outcomes:
- use 1/2 bcsinA formula to find the area of a triangle
- determine the quadrant for positive and negative angles in standard position
- identify coterminal angles
- determine primary trigonometric function values for angles in standard position
- identify reference angles
- evaluate primary trigonometric functions for any angle in a variety of conditions
- solve trigonometric equations involving the primary functions over a specific domain
- use the trigonometric definitions to deduce unknown trigonometric values from given values
10. Optional Topics
Learners may also wish to complete either A or B but these outcomes are not required.
A. Geometry
- recall the properties of parallel lines, similar and congruent figures, polygons, angle relationships, angle measurements, and basic compass and straightedge construction
- demonstrate an understanding of the following properties of a circle:
- the perpendicular bisector of a chord passes through the centre of the circle
- the line joining the midpoint of a chord to the centre is perpendicular to the chord
- the line through the centre, perpendicular to a chord, bisects the chord
- central angles containing equal chords or arcs are equal (the converse is also true)
- inscribed angles containing the same or equal chords (on the same side of chord) or arcs are equal
- an inscribed angle equals half the central angle containing the same or equal chords (on the same side of chord) or arcs are equal
- an inscribed angle in a semicircle measures 90°
- opposite angles of a cyclic (inscribed) quadrilateral are supplementary
- a tangent is perpendicular to the radius at the point of contact (the converse is also true)
- tangents from an external point are equal
- the angle between a chord and tangent equals the inscribed angle of the opposite side of the chord (the converse is also true)
- demonstrate and clearly communicate deductive reasoning in the solution of applied problems
B. Data Analysis
- explain the uses and misuses of statistics
- demonstrate an understanding of mean, median, mode, range, quartiles, percentiles, standard deviation, the normal curve, z-scores, sampling error and confidence intervals
- graphically present data in the form of frequency tables, line graphs, bar graphs, and stem and leaf plots
- design and conduct statistics project, analyze the data, and communicate the outcomes
- See Detailed Course Content, Topics, and Sequence Covered (Above)