# Grade 10 Mathematics

PREREQUISITE: Principles of Mathematics, Grade 9, Academic or Mathematics Transfer Course

AVAILABILITY: Full-time, Part-time, Private and Online

Grade 10 Mathematics enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry, and investigate the trigonometry of right and acute triangles. In Grade 10 Mathematics, students will reason mathematically and communicate their thinking as they solve multi-step problems.

### UNIT ONE

Linear Systems

Essential Question: How can mathematical expressions be analyzed to help us understand our world?

• In this unit, students will investigate how to determine the point of intersection of two lines algebraically and graphically. students will apply their knowledge to examine real-world scenarios that can be modelled using a linear system of equations and interpret the meaning of a point of intersection through the lens of the real-world application.

### UNIT TWO

Analytic Geometry

Essential Question: How can Geometry be used to analyze relationships between variables?

• In this unit, students will investigate a series of tools that are useful in geometric problem-solving scenarios. Students will apply their understanding of analytic geometry tools to classify quadrilaterals based on their determined properties. Students will also combine their understanding of analytic geometry tools with their understanding of linear relations to solve complex geometry problems.

### UNIT THREE

Similar Triangles and Trigonometry

Essential Question: How do effective problem-solvers approach problems that involve multiple steps?

• In this unit, students will learn to analyze and classify triangles as similar or congruent. Students will also investigate the relationship between sides and angles in both right and non-right triangles. Students will apply their understanding of trigonometric ratios to determine unknown sides and angles, as well as solve problems that are encountered in the real-world.

### Unit Four

Essential Question: How does representing expressions in different ways help to solve problems?

• In this unit, students will develop strategies for representing trinomial expressions in different forms. Students will learn to select the appropriate strategy for any given problem. These skills are important and considered foundational for the remainder of this course and future mathematics studies.

### UNIT FIVE

Quadratic Equations (Part I)

Essential Question: How can models be used to make predictions in real-world scenarios?

• In this unit, students will investigate the properties of the vertex form of a quadratic relation and apply these properties to graph quadratic relations. Students will also develop the skills necessary for converting standard form to vertex form. Students will apply these skills to solve real-world problems involving maximums and minimums of quadratic models.

### UNIT SIX

Quadratic Equations (Part II)

Essential Question: How can observed patterns be summarized in order to make informed predictions?

• In this unit, students will develop an understanding of how factoring can be used to determine the x-intercepts of a quadratic relation. Students will investigate how the quadratic formula can be used to determine the x-intercepts when factoring is not possible. Students will make connections between the x-intercepts of a quadratic and real-world context, while also applying their new skills to solve real-world problems involving maximums and minimums of quadratic models.

### CULMINATING PROJECT

10% of Final Grade

• This project is one of the final evaluations of this course. The culminating activity will make up 10% of the final mark. It is designed so that students can work on it throughout the course.

### FINAL EXAM

20% of Final Grade

• This exam is the final evaluation of this course. Students need to arrange their final exam 10 days in advance. All coursework should be completed and submitted before writing the final exam, please be advised that once the exam is written, any outstanding coursework will be given a grade of zero. The exam will be 1.5 hours.