## 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 Grade 9 to 12 must be attained to graduate.

*Final exams in all math courses are mandatory*

**In Grade 9, Math is taken all year long. **

Two Grade 9 credits - MTT10F and MAT10F. Course descriptions are below.

**Transitional Math 10F (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. Topics will include basic skills development on fractions, decimals, integers and working with rational numbers. All of these skills will be worked on as students start the Math 10F course and work through Grade 9 outcomes all year long.

The curriculum for Grade 9 Transitional Mathematics allows students to earn an optional credit within Senior Years graduation requirements. Grade 9 Mathematics (MAT10F) will remain as the compulsory core credit for Grade 9 Mathematics.

**Mathematics 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 include: rational numbers, exponents, polynomials, algebra, linear relations, transformations, symmetry and surface area, circle properties, inequalities, probability and statistics.

**Grade 10 Options: A student can take either or both MAE20S and MAT20S. ****Descriptions are below.**

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

*Prerequisite: MAT10F with a suggested mark of 65% or higher with a strong work ethic.*

Introduction to Applied and Pre-calculus Mathematics 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 include: graphs, relations and functions; number sense; measurement, areas and volumes; right angle trigonometry; co-ordinate geometry; linear equation and systems; and polynomials.

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

These courses are intended for students whose post-secondary planning does not include a focus on mathematics and science-related fields. 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****/ MAP40S)**

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 65% or higher with **strong work ethic and 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 (MAA30S/ MAA40S)**

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. The 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 Applied Mathematics 30S will be a prerequisite for Applied Mathematics 40S.

**Topics in Applied Mathematicsâ€Ż30S**

*Prerequisite: Introduction to Applied and Pre-Calculus 20S with a suggested mark of 65 percent or higher 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 Mathematicsâ€Ż40S**

*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 limits, derivatives, integration and application problems. 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 calculators continue to be a tool for this course and they will be handed out for use by the students in April. 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.