Welcome to Mackenzie Mathematics Department!

The Math Office is located on the second floor in the Art hallway.

Contact us at 416 395 3330 x20080

ACL: Ms. Spiliopoulos

**Math Exam Review**

Find the review packages for all math courses in this google drive folder.

**Courses Offered:**

### Grade 9 Courses

Course Title: **Principles of Mathematics, Academic **

Course Code: **MPM1D1**

Description: This course enables students to develop generalizations of mathematical ideas and methods through the exploration of applications, the effective use of technology, and abstract reasoning. Students will investigate relationships to develop equations of straight lines in analytic and surface area of objects in measurement, and apply extended algebraic skills in problem solving. Students will engage in abstract extensions of core learning that will deepen their mathematical knowledge and enrich their understanding. *Prerequisite: None*

Course Title: **Foundations of Mathematics, Applied**

Course Code: **MFM1P1**

Description: This course enables students to develop mathematical ideas and methods through exploration of applications, the effective use of technology, and extended experiences with hands-on activities. Students will investigate relationships of straight lines in analytic geometry, solve problems involving the measurement of 3-dimensional objects and 2-dimensional ﬁgures, and apply key numeric and algebraic skills in problem solving. Students will also have opportunities to consolidate core skills and deepen their understanding of key mathematical concepts. *Prerequisite: None*

Course Title: **Mathematics, Locally Developed Compulsory Credit Course**

Course Code: **MAT1L1****
**

Description: This course emphasizes further development of mathematical knowledge and skills to prepare students for success in their everyday lives, in the workplace, in the Grade 10 Locally Developed Compulsory Credit course and in the Mathematics Grade 11 and Grade 12 Workplace Preparation courses. The course is organized by three strands related to money sense, measurement, and proportional reasoning. In all strands, the focus is on developing and consolidating key foundational mathematical concepts and skills by solving authentic, everyday problems. Students have opportunities to further develop their mathematical literacy and problem-solving skills and to continue developing their skills in reading, writing, and oral language through relevant and practical math activities. *Prerequisite: None*

### Grade 10 Courses

Course Title: **Principles of Mathematics, Academic**

Course Code: **MPM2D1****
**

Description: This course enable students to broaden their understanding of relations, extend their skills in multi-step problem solving, and continue to develop their abilities in abstract reasoning. Students will pursue investigations of quadratic functions and their applications; solve and apply linear systems; solve multistep problems in analytic geometry to verify properties of geometric ﬁgures; investigate the trigonometry of right and acute triangles; and develop supporting algebraic skills. *Prerequisite: Principles of Mathematics, Grade 9, Academic. NOTE: Students who have completed Foundations of Mathematics Grade 9, Applied (MFM1P) will need to take a transfer course to take MPM2D*

Course Title: **Foundations of Mathematics, Applied**

Course Code: **MFM2P1**

Description: This course enables students to consolidate their understanding of key mathematical concepts through hands-on activities and to extend their problem-solving experiences in a variety of applications. Students will solve problems involving proportional reasoning and the trigonometry of right triangles; investigate applications of piecewise linear functions; solve and apply systems of linear functions; solve and apply systems of linear equations; and solve problems involving quadratic functions. The effective use of technology in learning and solving problems will be a focus of the course. *Prerequisite: Foundations of Mathematics, Grade 9, Applied*

Course Title: **Mathematics, Locally Developed Compulsory Credit Course**

Course Code: **MAT2L1**

Description: This course emphasizes the extension of mathematical knowledge and skills to prepare students for success in their everyday lives, in the workplace, and in the Mathematics Grade 11 and Grade 12 Workplace Preparation courses. This course is organized by three strands related to money sense, measurement, and proportional reasoning. In all strands, the focus is on strengthening and extending key foundational mathematical concepts and skills by solving authentic, everyday problems. Students have opportunities to extend their mathematical literacy and problem-solving skills and to continue developing their skills in reading, writing and oral language through relevant and practical math activities. *Prerequisite: A grade 9 Mathematics credit*

### Grade 11 Courses

Course Title: **Functions, University Preparation**

Course Code: **MCR3U1**

Description: This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; and develop facility in simplifying polynomial and rational expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems. *Prerequisite: Principles of Mathematics, Grade 10, Academic*

Course Title: **Functions and Applications, University/College Preparation**

Course Code: **MCF3M1**

Description: This course introduces basic features of the function by extending students’ experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modelling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to ﬁnancial and trigonometric applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems. *Prerequisite: Principles of Mathematics, Grade 10, Academic, or Foundations of Mathematics, Grade 10, Applied*

Course Title: **Foundations for College Mathematics, ****College Preparation**

Course Code: **MBF3C1**

Description: This course enables students to broaden their understanding of mathematics as a problem-solving tool in the real world. Students will extend their understanding of quadratic relations, as well as of measurement and geometry; investigate situations involving exponential growth; solve problems involving compound interest; solve ﬁnancial problems connected with vehicle ownership; and develop their ability to reason by collecting, analysing, and evaluating data involving one and two variables. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. *Prerequisite: Foundations of Mathematics, Grade 10, Applied*

Course Title: **Mathematics for Work & Everyday Life, Workplace Preparation**

Course Code: **MEL3E1**

Description: This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. *Prerequisite: Principles of Mathematics, Grade 9, Academic, or Foundations of Mathematics, Grade 9, Applied, or a ministry-approved locally developed Grade 10 mathematics course*

### Grade 12 Courses

Course Title: **Advanced Functions, University Preparation or Advanced Placement**

Course Code: **MHF4U1, MHF4U0**

Description: This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also reﬁne their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students who plan to study mathematics in university and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs. *Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation*

Course Title: **Foundations for College Mathematics, College Preparation**

Course Code: **MAP4C1**

Description: This course enables students to broaden their understanding of real world applications of mathematics. Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades. *Prerequisite: Foundations for College Mathematics, Grade 11, College Preparation*

Course Title: **Mathematics of Data Management, University Preparation**

Course Code: **MDM4U1**

Description: This course broadens students’ understanding of mathematics as it relates to managing data. Students will apply methods for organizing large amounts of information; solve problems involving probability and statistics; and carry out a culminating project that integrates statistical concepts and skills. Students will also reﬁne their use of the mathematical processes necessary for success in senior mathematics. Students planning to enter university programs in business, the social sciences, and the humanities will ﬁnd this course of particular interest. *Prerequisite: Functions and Applications, Grade 11, University/College Preparation, or Functions, Grade 11, University Preparation*

Course Title: **Calculus and Vectors, University Preparation or Advanced Placement**

Course Code: **MCV4U1, MCV4U0**

Description: This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors, and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, rational, exponential, and sinusoidal functions; and apply these concepts and skills to the modelling of real world relationships. Students will also reﬁne their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who plan to study mathematics in university and who may choose to pursue careers in ﬁelds such as physics and engineering. *Recommended preparation: Advanced Functions, Grade 12 University Preparation. Note: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U).*
*To take Advanced Placement Calculus and Vectors, Advanced Functions must also be taken in Advanced Placement.*

**Teachers:**

## Ms. Elena Balland

*Started teaching at Mackenzie in 2016.*

Education

- Diplom, Leningrad Polytechnical Institute, U.S.S.R.
- B.Ed. Faculty of Education, Queen’s University, Ontario

**Office Location: Mathematics Office**

## Ms. Tanya Chevannes

*Started teaching at Mackenzie in 2005.*

Education

- B.A. at York University
- B.Ed. at OISE, University of Toronto

**Office Location: Mathematics Office**

## Mr. Youssef Daoud

*Started teaching at Mackenzie in 2014*

Education

- B.Eng. at Cairo University, Egypt
- B.Ed. at OISE, University of Toronto

**Office Location: Math Office **

## Mr. Anatoli Fourmanovskis

*Started teaching at Mackenzie in 2011.*

Education

- Graduate of Vilnius State University, Lithuania
- B.Ed. at Commonwealth of Independent States Teacher Training

**Office Location: Mathematics Office**

## Mr. Jaime Galo Arcia

*Started teaching at Mackenzie in 1998.*

Education

- Licence, Nicaragua Teacher Training
- M.A. at York University

**Office Location: Mathematics Office**

## Ms. Iulia Gugoiu

**ACL of Numeracy & Advanced Placement**

*Started teaching at Mackenzie in 2005.*

Education

- B.Sc. at University of Bucharest
- M.Sc. Physics
- B.Ed. at UOIT
- Honour Specialist Physics

**Office Location: Mathematics Office**

## Mr. Robert Onizuka

*Started teaching at Mackenzie in 1998.*

Education

- B.A. at York University
- M.B.A. at York University
- B. Ed. at OISE, University of Toronto

**Office Location: Mathematics Office**

## Mr. Ben Segev

*Started teaching at Mackenzie in 2007.*

Education

- B.A.Sc. at University of Toronto
- B.Ed. at OISE, University of Toronto

**Office Location: Mathematics Office**

## Ms. Anna Spiliopoulos

**ACL of Mathematics**

*Started teaching at Mackenzie in 2002.*

Education

- Spec. Hon. B.Sc. at York University
- B.Ed. at OISE, University of Toronto

**Office Location: Mathematics Office**

## Ms. Stephanie White

*Started teaching at Mackenzie in 2007.*

Education

- Hon.B.Sc. at University of Toronto
- PEP at D’Youville College
- M.T.S. at Tyndale University

**Office Location: Mathematics Office**