MPM2D, Foundations of Mathematics,
Grade 10, Applied, ( 1 credit)

What You Will Learn:
This course enables 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 model linear and quadratic relationships arising from a variety of contexts.

Using trigonometric ratios and analytic geometry techniques, students will learn how to find exact measures in geometric contexts, as opposed to the approximate measures they have found using scale drawings and measurement tools.

Geometric relationships investigated in Grade 9 will be confirmed, analytically, in specific cases, and students will be introduced to proof in general. Algebraic skills will be extended to generate factored, expanded, and completed square forms of quadratic expressions, and to solve linear systems and quadratic equations.

Fundamental mathematical ideas of modeling, patterning, optimization, and superimposing a grid onto a geometric situation are reinforced. Connections among the various strands of the course are intentionally developed.

Course Outline:

Units:

• Similar Triangles and Trigonometry: Primary trigonometric ratios, Sine and Cosine Laws are used to solve problems that are modeled by right-angled or acute triangles. Students investigate how the tangent ratio for the angle of inclination is connected to the slope of a line.

• Analytic Geometry: Formulas for midpoint, distance between points, and circles centred at the origin. Geometric relationships investigated in Grade 9 mathematics are confirmed through the use of the Cartesian system and formulas. Properties of triangles and quadrilaterals are investigated analytically

• Linear Systems: This unit focuses on the use of two linear equations to model a problem. In some cases, both lines are graphical models where the point of intersection of the lines has meaning in the context of the problem. Points of intersection will be found through numerical, graphical, and algebraic analysis. In other cases, only parts of two lines are needed to model a single situation. These result in consideration of a range of values for solution to an optimization problem through linear programming analysis. This unit also contains multi-step problems in analytic geometry which require solution of a linear system

• Quadratic functions: This unit enables 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 gather, organize, manipulate, and analyze data from primary and secondary sources to model and communicate results about quadratic situations. A variety of problems help students gain depth of understanding of quadratics through meeting the same specific expectations in different contexts. Students conduct investigations to verify or refute their own conjectures about relationships, using lines or curves of best fit, tables, and pattern descriptions. Students communicate their findings and describe trends.

Resources/ materials used:

• Class handouts, textbook.

Related Courses:

• Successful completion of MPM2D will prepare students for the MCF3M, Grade 11 Functions.

Further information