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

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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

- Additional study of Radical Expressions, Radicals, and Equations

- Quadratic Equations and Quadratic Functions

- Trigonometry

Optional Topics:

- Geometry

- Data Analysis

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)

**Grading System:** Letters

**Passing Grade:** D (50%)

**Percentage of Individual Work:** 100