Mathematics


Portage Collegiate Institute offers all three streams of mathematics after the completion of Math 10F.  Each of the three streams is provided in some detail below as well as advanced placement calculus.  It must be noted that a math credit from each grade from S1 to S4 must be attained to graduate from the school.

Final exams in all math courses are mandatory

Transitional Math (MTT10F)

Grade 9 Transitional Mathematics is comprised of a series of units designed to address gaps in students’ mathematical understanding as they transition from grade 8 to grade 9 Mathematics.  The curriculum for grade 9 Transitional Mathematics allows students to earn an optional credit within Senior Years graduation requirements.  Grade 9 Mathematics (Math 10F) will remain as the compulsory core credit for Grade 9 Mathematics.

Transitional Math

Optional Course at S1 Level

Learning to Learn           Investigations in Algebra
Smart Math                      Nutrition and Fitness
Investigations                  Probability and Sampling
Skill Development          Scheme - A - Team
Money Management

Timetabling for this new curriculum is a local decision as is determining the students for whom it is appropriate.  Some students may require this program while other students will not require Grade 9 Transitional Mathematics in order to transition satisfactorily to Grade 9 Mathematics (10F).


Math 10F (MAT10F)

This course is arranged by topics which will be used to help students become engaged in making connections among concepts and thus make mathematical experiences meaningful.  The focus of student learning should be on developing a conceptual and procedural understanding of mathematics.  Students’ conceptual understanding and procedural understanding must be directly related.


Topics in Senior 1 Mathematics (10F)

Compulsory Course at S1 Level
• Number
• Patterns and Relations (Number)
• Patterns and Relations (Variables and Equations)
• Shape and Space (Measurement)
• Shape and Space (2D and 3D Shapes)
• Shape and Space (Transformations)
• Statistics and Probability (Data Analysis)
• Statistics and Probability (Chance and Uncertainty)

Intro to Pre-Calculus and Applied math 20S (MAT20S)

Introduction to Applied and Pre-calculus Mathematics (20S) is intended for students considering post-secondary studies that require a math pre-requisite. This pathway provides students with the mathematical understanding and critical-thinking skills that have been identified for specific post-secondary programs of study. The topics studied form the foundation for topics to be studied later in both Grade 11 Applied Mathematics and Grade 11 Pre-calculus Mathematics.  Components of the curriculum are both context driven and algebraic in nature. Students will engage in experiments and activities that include the use of technology, problem solving, mental mathematics, and theoretical mathematics to promote the development of mathematical skills. These experiences will provide opportunities for students to make connections between symbolic mathematical ideas and the world around us.

Topics in Intro to Pre-Calculus and Applied Mathematics

Prerequisite: Math 10F with a suggested mark of 75%
• Graphs, Relations and Functions
• Number Sense
• Measurement, Areas and Volumes
• Right Angle Trigonometry
• Co-ordinate Geometry
• Linear Equation and Systems
• Polynomials


Essential Mathematics (MAE 20S/ MAE 30S/ MAE 40S)


(20S) is intended for students whose post-secondary planning does not include a focus on mathematics and science-related fields. Essential Mathematics is a one-credit course emphasizing consumer applications, problem solving, decision making, and spatial sense. Students are expected to work both individually and in small groups on mathematical concepts and skills encountered in everyday life in a technological society.

Topics in Essential Mathematics 20S

Prerequisite: Math 10F
• Analysis of Games and Numbers
• Personal Finance
• Measurement
• Geometry
• Right Angle Trigonometry
• Consumer Decisions
• Angle Construction
• Transformations

Topics in Essential Mathematics 30S

Prerequisite: Any 20S Mathematic Credit
• Analysis of Games and Numbers
• Managing Money
• Relations, Formulas and Patterns
• Trigonometry (Right Triangle)
• Design Modeling
• Interest and Credit
• 3D Geometry
• Statistics


Topics in Essential Mathematics 40S
Prerequisite: Any 30S Math Credit (Except Accounting)
• Analysis of Games and Numbers
• Vehicle Finance
• Statistics
• Precision Measurement
• Career Life Project
• Home Finance
• Geometry and Trig
• Business Finance
• Probability


Pre-Calculus Mathematics (MAP 30S/ MAP 40S)


Pre-calculus Mathematics is designed for students who intend to study calculus and related mathematics as part of post-secondary education including fields such as engineering, sciences, medicine, management and agriculture. Pre-Calculus 30S will build on concepts studied in grade 10 Intro to Applied and Pre-Calculus and Pre-Calculus 40S will develop concepts that are needed in Calculus and other university math courses. The course comprises a high-level study of theoretical mathematics and algebra with an emphasis on problem solving and mental mathematics.  Students can expect at least an hour of homework each night, with limited class time to complete assignments.


Topics in Pre-Calculus 30S


Prerequisite: Introduction to Applied and Pre-Calculus 20S with a suggested mark of 75% with strong aptitude in all forms of algebra, graphing equations, trigonometry, theoretical mathematics and mental mathematics.
• Quadratic Equations
• Solving Radicals
• Quadratic Functions
• Sequences and Series
• Rational Expressions
• Trigonometry
• Systems of Equations
• Inequalities

Topics in Pre-Calculus 40S


Prerequisite: Pre-Calculus 30S with strong aptitude in all forms of algebra, graphing equations, trigonometry, theoretical mathematics and mental mathematics.
• Transformations
• Trigonometric Functions
• Binomial Theorem
• Polynomial Functions
• Trigonometric Equations and Identities
• Exponents and Logarithms
• Radicals and Rational Equations


Applied Mathematics (MAA 30S/ MAA 40S)


Applied Mathematics is intended for students considering post-secondary studies that do not require a study of theoretical calculus. It is context driven and promotes the learning of numerical and geometrical problem-solving techniques as they relate to the world around us. Grade 11 Applied will build on concepts studied in grade 10 Introduction to Applied and Pre-Calculus to prepare students for Grade 12 Applied Math. Primary goals of Applied Mathematics are to have students develop critical-thinking skills through problem solving and model real-world situations mathematically to make predictions.  There will be a strong technology component in the program and students can expect at least an hour of homework each night.  Students must note that 30S Applied Mathematics will be a pre-requisite for grade 12 Applied Mathematics.

Topics in Applied Mathematics 30S


Prerequisite: Introduction to Applied and Pre-Calculus 20S with a suggested mark of 70% with strong aptitude in graphing, trigonometry, problem solving and basic algebra (such as solving for a variable).
• Quadratic Equations
• Solving Radicals
• Quadratic Functions
• Sequences and Series
• Rational Expressions
• Trigonometry
• Systems of Equations
• Inequalities


Topics in Applied Mathematics 40S


Prerequisite: Applied Math 30S
• Sinusoidal Functions
• Compound Interest
• Probability
• Polynomial Functions
• Permutations and Combinations
• Investments
• Design and Measurement
• Research Project
• Exponential Logarithmic Functions


Calculus 42S (CAL42S)


Calculus 42S is designed to prepare students for the Advanced Placement Calculus AB examination. Pre-Calculus 40S is a prerequisite and this course continues the study of calculus with integration, the fundamental theorem of calculus and application problems. There will be a thorough review of all topics from 41G as well as the material that is new in this semester. The outline for this course is determined by the College Board and is available at their web site http://www.collegeboard.com/ap/students/index.html or at the AP web site http://apcentral.collegeboard.com. Graphing technology continues to be an integral tool for this course and graphing calculators may be used daily. Students who are successful in completing this course and passing the AP exam will be eligible for credit or advanced standing at many universities in Canada and around the world.