Grade 11 Pre-Calculus Mathematics (30S) Outcomes by Unit

Unit A: Quadratic Functions
Unit B: Trigonometry
Unit C: Algebra
Unit D: Analytic Geometry
Unit E: Geometry
Unit F: Consumer Math
Unit G: Logic/Proof
Unit H: Functions

 

Unit A: Quadratic Functions

Represent and analyze quadratic, polynomial, and rational functions using technology as appropriate

Use interval notation (A-1)

Plot and describe data of quadratic form using appropriate scales (A-2)

Determine the following characteristics of a graph of a quadratic function: Vertex Domain and range Axis of symmetry Intercepts (A-3)

Connect algebraic and graphical transformations of quadratic functions, using completing the square as required (A-4)

Model real-world situations, using quadratic functions (A-5)

 

Unit B: Trigonometry

Solve problems involving triangles including those found in 3-D and 2-D applications

Sketch the graph of and (B-1a)

Extend the definitions of trigonometric functions to include all quadrants (B-1b)

Solve trigonometric equations 0° £ q £ 360° (B-1c)

Solve problems involving ambiguous case triangles (B-2)

 

Unit C: Algebra

Represent and analyze quadratic, polynomial, and rational functions using technology as appropriate

Solve quadratic equations, and relate the solutions to the zeros of a corresponding quadratic function using: Graphing The quadratic formula Factoring (C-1a)

Solve non-linear equations By factoring Graphically Graphically with a graphing calculator's built in function [zeros, intersect, equation solver] (C-1b)

Determine the character of the real and non-real roots of a quadratic equation, using The discriminant in the quadratic formula Graphing (C-2)

Represent and analyze situations that involve expressions, equations, and inequalities

Solve non-linear equations using a graphing tool (C-3)

Formulate and apply strategies to solve absolute value equations, radical equations, and rational equations (C-4)

 

Unit D: Analytic Geometry

Solve coordinate geometry problems involving lines and line segments and justify the solutions

Develop the coordinate equation of a circle (D-1)

Solve problems involving the distances between points and lines (D-2)>

Verify and prove assertions in plane geometry using coordinate geometry (D-3)

Represent and analyze situations that involve expressions, equations, and inequalities

Solve systems of linear equations in two variables: Graphically Algebraically (elimination and substitution) (D-4)

Solve systems of linear equations, in three variables: Algebraically With technology (D-5)

Determine the solution to a system of non-linear equations, using technology as appropriate (D-6)

Graph linear inequalities in two variables (D-7)

Formulate and apply strategies to solve quadratic, absolute value, radical, and rational inequalities (D-8)

 

Unit E: Geometry

Develop and apply the geometric properties of circles and polygons to solve problems

Use technology and measurement to confirm and apply the following properties to particular cases The perpendicular from the centre of a circle to a chord bisects the chord The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc Inscribed angles subtended by the same arc are congruent The angle inscribed in a semicircle is a right angle Opposite angles of a cyclic quadrilateral are supplementary A tangent to a circle is perpendicular to the radius at the point of tangency The tangent segments to a circle, from any external point, are congruent The angle between a tangent and a chord is equal to the inscribed angle on the opposite side of the chord The sum of the interior angles of an n-sided polygon is 180° (n-2) The measure of an arc is one half the measure of the inscribed angle subtended by the arc (E-1)

Verify the following general properties by providing reasons for each step in the solution The perpendicular bisector of a chord contains the centre of the circle The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc (for the case when the centre of the circle is in the interior of the inscribed angle) Inscribed angles subtended by the same arc are congruent The angle inscribed in a semicircle is a right angle Opposite angles of a cyclic quadrilateral are supplementary A tangent to a circle is perpendicular to the radius at the point of tangency The tangent segments to a circle from any external point are congruent The angle between a tangent and a chord is equal to the inscribed angle on the opposite side of the chord The sum of the interior angles of an n-sided polygon is (2n-4) right angles (E-2)

 

Unit F: Consumer Math

Solve consumer problems, using arithmetic operations

Solve consumer problems, including: Wages earned in various situations Property taxation Exchange rates Unit prices (F-1)

Reconcile financial statements including Chequebooks with bank statements cash register tallies with daily receipts (F-2)

Solve budget problems, using graphs and tables to communicate solutions (F-3)

Plot and describe data of exponential form, using appropriate scales (F-4)

Solve investment and credit problems involving simple and compound interest (F-5)

 

Unit G: Logic/Proof

Apply the principles of mathematical reasoning to solve problems and to justify solutions

Differentiate between inductive and deductive reasoning (G-1)

Explain and apply connecting words, such as "and" , "or", and "not" to solve problems (G-2)

Use examples and counterexamples to analyze conjectures (G-3)

Distinguish between an "if-then" proposition, its converse, and its contrapositive (G-4)

Prove assertions in a variety of settings, using direct and indirect reasoning (G-5)

 

Unit H: Functions

Examine the nature of relations with an emphasis on functions

Perform operations on functions and compositions of functions (H-1)

Determine the inverse of a function (H-2)

Represent and analyze situations that involve expressions, equations, and inequalities

Use the remainder theorem to evaluate polynomial expressions and the factor theorem to determine factors of polynomials (H-3)

Represent and analyze quadratic, polynomial, and rational functions using technology as appropriate

Describe, graph, and analyze polynomials and rational functions, using technology (H-4)