MPM2D – Principles of Mathematics – Grade 10
This course 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. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
₹450.00
*Course outline is subject to change
Overall Curriculum Expectations
By the end of this course, students will :
Quadratic Relations of the Form y = ax2+ bx+ c
By the end of this course, students will:
- determine the basic properties of quadratic relations;
- relate transformations of the graph of y = x2 to the algebraic representation y = a(x– h)2 + k;
- solve quadratic equations and interpret the solutions with respect to the corresponding relations;
- solve problems involving quadratic relations.
Analytic Geometry
By the end of this course, students will:
- model and solve problems involving the intersection of two straight lines;
- solve problems using analytic geometry involving properties of lines and line segments;
- verify geometric properties of triangles and quadrilaterals, using analytic geometry.
Trigonometry
By the end of this course, students will:
- use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
- solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
- solve problems involving acute triangles, using the sine law and the cosine law.
Outline of Course Content
Linear systems play a crucial role in both everyday decision-making and advanced mathematical applications. They allow us to understand relationships between variables, such as the connection between distance and time when calculating speed or analyzing rates of change in business and economics.
This unit builds on the foundational concepts of linear algebra introduced in Grade 9, deepening students’ understanding of equations, graphs, and problem-solving techniques. Students will explore multiple representations of linear relationships, develop strategies to manipulate and solve equations, and apply these skills to real-world scenarios. By the end of this unit, students will be able to confidently represent, analyze, and solve linear systems using both algebraic and graphical methods.
Expanding upon the foundation built in the previous unit, students will explore the equations of lines and line segments through analytic geometry. This unit will focus on developing mathematical methods for determining line segment length, midpoint, slope, and perpendicular bisectors. Students will use equations and coordinate geometry to analyze and verify geometric properties, deepening their understanding of the relationships between points, lines, and shapes. The application of these concepts to real-world contexts, such as engineering, design, and navigation, will be emphasized to demonstrate their practical significance.
In this unit, students will explore quadratic functions, a fundamental class of second-order functions that extend beyond linear relationships. Quadratic functions model real-world scenarios such as projectile motion, economics, and engineering. Students will analyze key characteristics, including domain, range, vertex, and intercepts, and examine how transformations affect their graphs. They will also develop algebraic skills in factoring, completing the square, and solving quadratic equations, gaining a deeper understanding of the mathematical relationships that govern quadratic behavior. By the end of this unit, students will be able to apply these concepts to problem-solving and real-world applications.
In this unit, students will transition from the graphical representations of quadratic functions to algebraic methods for solving quadratic equations. They will explore different techniques, including factoring, completing the square, and using the Quadratic Formula, which are essential for solving real-world problems and will be extensively applied in future math courses. By the end of this unit, students will develop a deeper understanding of how quadratic relations are used to model motion, optimization problems, and structural designs in various fields such as physics, engineering, and economics.
In this unit, students will explore the concepts of similarity and congruence in triangles and how they apply to geometric reasoning. They will investigate the relationships between corresponding sides and angles in both right and non-right triangles, developing strategies to determine unknown measurements. Through the use of trigonometric ratios (sine, cosine, and tangent), the Pythagorean theorem, and proportional reasoning, students will learn to solve real-world problems involving indirect measurement, scaling, and angle calculations. By the end of this unit, students will have a strong foundation in applying trigonometry to various practical and mathematical contexts.
Triangles play a fundamental role in mathematics, appearing in physics, engineering, and real-world problem-solving. In this unit, students will explore how right and acute triangles can be analyzed using trigonometric ratios (sine, cosine, and tangent) and extended to more complex problems with the Sine Law and Cosine Law. The unit begins with a review of the Pythagorean Theorem, reinforcing its connection to trigonometry. Students will develop the ability to apply these mathematical tools to determine unknown angles and side lengths in both theoretical and real-world contexts, such as navigation, architecture, and physics.
Students will have time to review and then they will have a student/teacher conference and write their final exam. The exam will cover all curriculum expectations.