Pure Math 20

Course name and abbreviation:

Pure Mathematics 20 (PM 20)

Grade Level:

Grade 11

Summary of course content and activities:

PM 20 is the second course in the Pure Math 10-20-30 sequence.

This course includes the following strands:

• Finance
• Quadratic Functions
• Polynomial and Rational Functions
• Equations and Inequalities
• Circle Geometry
• Coordinate Geometry

Who should be taking this course? For whom is this course designed and intended?

This is an academic course for the grade11 student who:

• Has successfully completed Pure Math 10.
• Is intending to graduate from NorthStar Academy, or any other high school, with an academic diploma
• Is intending to pursue university, college, or vocational training upon graduation from high school.

Philosophy statement for and/or behind teaching this course:

Pure mathematics emphasizes mathematical theory and the testing of mathematical hypotheses. The pure mathematics approach, which is often deductive and symbolic, endeavors to show that concepts are valid all the time, or valid within a well-defined set of restrictions. Real-life problems are then presented in order for students to apply previously learned mathematical concepts and procedures. Students will make use of algebra and graphing to solve problems.

Students are required to demonstrate effective communication skills. This includes understanding, using, and interpreting various mathematical concepts and processes. Students will be expected to explain, to illustrate, to reason and to make connections. Multiple solution strategies to problems and problem contexts will be expected as students work through both routine and non-routine problems. Tasks vary from short procedural items that help students develop skills in the language of mathematics, to longer tasks that require students to test either subtle conjectures or apply mathematical knowledge to real-life problems.

 Technology is a part of pure mathematics. The graphing calculator is the primary technological tool used by students for mathematical exploration, modeling and problem solving. The use of spreadsheets, with functions defined by the student, can be profitable in many contexts.

Major course goals:

Students will be able to:

Personal Finance

It is expected that students will solve consumer problems, using arithmetic operations.

It is expected that students will:

•  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

Linear and Non-Linear Systems

It is expected that students will represent and analyze situations that involve expressions, equations and inequalities.

It is expected that students will:

• 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 non-linear equations, using a graphing tool
• solve non-linear equations:
  • by factoring
  • graphically
• use the Remainder Theorem to evaluate polynomial expressions, the Rational Zeros Theorem, and the Factor Theorem to determine factors of polynomials 
• determine the solution to a system of nonlinear equations, using technology as appropriate

Quadratic & Polynomial Functions

It is expected that students will:

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

It is expected that students will:

• 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 real-world 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 non-real 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

Circle Geometry, Coordinate Geometry & Trigonometry

It is expected that students will:

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

It is expected that students will:

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

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:

• 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 n-sided polygon is 180(n-2)
• 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)
  • he 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 n-sided polygon is 180(n-2)
• solve problems, using a variety of circle properties, and justify the solution strategy used

 Pre-requisite(s):

Students taking PM 20 are presumed to have reached the acceptable standard or better in Pure Math 10.

Number of credits that this course is worth:

5

Materials and resources provided by NSA, purchased by student, and/or recommended:

Provided by NSA:

Purchased by student:

Recommended but not required:

Forecasted amount of time required to complete each week's lesson:

Semester students can expect to complete the course in about 8 hours per week over twenty weeks. Full year students will complete the course in about 4 hours per week over forty weeks.

Description of student evaluations, quizzes, and tests:

Exams and assignments throughout the course are worth 70% of the final mark.  The final exam is worth 30% of the final mark.

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