Grade 11 Principles of Mathematics MathUSee
BC Learning Outcomes

Problem Solving
It is expected that students will use a variety of methods to solve reallife, practical, technical, and theoretical problems
It is expected that students will:

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 solve problems that involve a specific content area such as geometry, algebra, trigonometry, statistics, probability
 solve problems that involve more than one content area
 solve problems that involve mathematics within other disciplines
 analyse problems and identify the significant elements
 develop specific skills in selecting and using an appropriate problemsolving strategy or combination of strategies chosen from, but not restricted to, the following:
 guess and check
 look for a pattern
 make a systematic list
 make and use a drawing or model
 eliminate possibilities
 work backward
 simplify the original problem
 develop alternative original approaches
 analyse keywords
 demonstrate the ability to work individually and cooperatively to solve problems
 determine that their solutions are correct and reasonable
 clearly explain the solution to a problem and justify the processes used to solve it
 use appropriate technology to assist in problem solving



Number (Number Operations)
It is expected that students will solve consumer problems, using arithmetic operations.
It is expected that students will: 
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Some of these are covered in texts or Honors Supplements Others will be included in projected “Consumer math” text. 
 solve consumer problems, including:
 wages earned in various situations
 property taxation
 exchange rates
 unit prices
 reconcile financial statements including:
 cheque books with bank statements
 cash register tallies with daily receipts
 solve budget problems, using graphs and tables to communicate solutions
 solve investment and credit problems involving simple and compound interest



Patterns and Relations (Patterns)
It is expected that students will apply the principles of mathematical reasoning to solve problems and to justify solutions.
It is expected that students will: 
Geometry Honors 
 differentiate between inductive and deductive reasoning

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 explain and apply connecting words, such as and, or, and not, to solve problems
 use examples and counterexamples to analyse conjectures

Geometry Honors 
 distinguish between an if–then proposition, its converse and its contra positive

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 prove assertions in a variety of settings, using direct and indirect reasoning



Patterns and Relations (Variables and Equations)
It is expected that students will represent and analyse situations that involve expressions, equations and inequalities.
It is expected that students will: 
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 graph linear inequalities, in two variables
 solve systems of linear equations, in two variables:
 algebraically (elimination and substitution)
 graphically
 solve systems of linear equations, in three variables:
 algebraically
 with technology
 solve nonlinear equations, using a graphing tool
 solve nonlinear equations:

Algebra 1Honors 
 use the Remainder Theorem to evaluate polynomial expressions, the Rational Zeros Theorem, and the Factor Theorem to determine factors of polynomials

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 determine the solution to a system of nonlinear equations, using technology as appropriate



Patterns and Relations (Relations and Functions)
It is expected that students will:

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 represent and analyze quadratic, polynomial and rational functions, using technology as appropriate
 examine the nature of relations with an emphasis on functions

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 determine the following characteristics of the graph of a quadratic function:
 vertex
 domain and range
 axis of symmetry
 intercepts
 perform operations on functions and compositions of functions
 determine the inverse of a function
 connect algebraic and graphical transformations of quadratic functions, using completing the square as required
 model realworld situations, using quadratic functions
 solve quadratic equations, and relate the solutions to the zeros of a corresponding quadratic function, using:
 factoring
 the quadratic formula
 graphing
 determine the character of the real and nonreal roots of a quadratic equation, using:
 the discriminate in the quadratic formula
 graphing
 describe, graph, and analyze polynomial and rational functions, using technology
 formulate and apply strategies to solve absolute value equations, radical equations, rational equations, and inequalities



Shape and Space (Measurement)
It is expected that students will:

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 solve problems involving triangles, including those found in 3D and 2D applications.
 solve coordinate geometry problems involving lines and line segments, and justify the solutions.

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 solve problems involving ambiguous case triangles in 3D and 2D
 solve problems involving distances between points and lines
 verify and prove assertions in plane geometry, using coordinate geometry



Shape and Space (3D Objects and 2D Shapes)
It is expected that students will develop and apply the geometric properties of circles and polygons to solve problems.
It is expected that students will: 
These are addressed in Geometry or Geometry Honors without using technology. 
 use technology with dynamic geometry software to confirm and apply the following properties:
 the perpendicular from the center 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
 the inscribed angles subtended by the same arc are congruent
 the angle inscribed in a semicircle is a right angle
 the 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 nsided polygon is 180(n2)
 prove the following general properties, using established concepts and theorems:
 the perpendicular bisector of a chord contains the center 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 center of the circle is in the interior of the inscribed angle)
 the inscribed angles subtended by the same arc are congruent
 the angle inscribed in a semicircle is a right angle
 the 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 nsided polygon is 180(n2)

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 solve problems, using a variety of circle properties, and justify the solution strategy used
