Pure Mathematics 30

Course name and abbreviation:

Pure Mathematics 30 (PM30)

Grade Level:

Grade 12

Summary of course content and activities:

This course includes the following strands:

• Transformations of Functions
• Exponents, Logarithms, and Geometric Series
•  Trigonometry
• Permutations and Combinations
• Statistics
• Conic Sections

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

Pure Mathematics 30 is the third course in the Pure Mathematics 10-20-30 sequence. Pure Mathematics 30 is designed to follow Pure Mathematics 20. This is an academic course for the grade 12 student who:

• Is intending to graduate 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:

• Transformations of Functions
  • Represent and analyze quadratic, polynomial and rational functions, using technology as appropriate
  • Perform, analyze, and create transformations of functions and relations that are described by equations or graphs.
• Exponents, Logarithms, and Geometric Series  -
  • Generate and analyze exponential patterns  
  • Solve exponential and logarithmic equations and identities
  • Represent and analyze exponential and logarithmic functions, using technology as appropriate
• Trigonometry
  • Represent and analyze trigonometric functions, using technology as appropriate
  • Solve trigonometric equations and identities
• Permutations and Combinations
  • Solve problems based on the counting of sets, using techniques such as the fundamental counting principle, permutations, and combinations
  • Model the probability of a compound event, and solve problems based on the combining of simpler probabilities
• Statistics
  • Use normal and binomial probability distributions to solve problems involving uncertainty.
• Conic Sections
  • Classify conic sections, using their shapes and equations 

Pre-requisite(s):

Students taking PM30 are presumed to have reached the acceptable standard or better in Pure Mathematics 20

Number of credits that this course is worth:

5 credits

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

Provided by NSA:

 Mathematics 12 textbook, Western Canadian Edition, published by Addison Wesley Longman (1998)
The Learning Equation Disk (TLE disk)
Addison Wesley Math 12 Independent Study Guide
Learning Equation Math 12 Refresher Text
Pure Math 30 Workbook

Purchased by student:

Microsoft Office (greater than 97) especially Word and Excel
A graphing calculator. The textbook and my lesson examples will use a TI-83 but a TI-83 Plus is very similar.

Recommended but not required:

A geometry set (compass, protractor, ruler and triangles)
Notebook for pencil and paper assignments.

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

Semester students can expect to complete the course in about 8-10 hours per week over eighteen weeks. Full year students will complete the course in about 4-5 hours per week over thirty-six weeks.

Description of student evaluations, quizzes, and tests:

School Based Mark (50% of the final mark)

Assignments	40%
Quizzes	15%
Exams	25%
In Class Project	10%
Final Exam	10%

Provincial Final Exam Mark (50% of the final mark)