OntarioGrade 10
ON Grade 10 Math Curriculum (MPM2D)
Video lessons and practice for every Grade 10 math topic. Aligned to Ontario's Principles of Mathematics, Academic (MPM2D) curriculum. Study at your own pace.
ON Grade 10 Math Curriculum (MPM2D) | StudyPugHelp
OE_ID | Expectations | StudyPug Topic |
|---|---|---|
ON.OE.10P.1.1 | 1.1 Investigating the Basic Properties of Quadratic Relations: Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology, or from secondary sources; graph the data and draw a curve of best fit, if appropriate, with or without the use of technology; determine, through investigation with and without the use of technology, that a quadratic relation of the form y = ax^2 + bx + c (a ? 0) can be graphically represented as a parabola, and that the table of values yields a constant second difference; identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum value), and use the appropriate terminology to describe them; compare, through investigation using technology, the features of the graph of y = x^2 and the graph of y = 2^x, and determine the meaning of a negative exponent and of zero as an exponent |
ON.OE.10P.1.2 | 2.1 Relating the Graph of y = x^2 and Its Transformations: Identify, through investigation using technology, the effect on the graph of y = x^2 of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k; explain the roles of a, h, and k in y = a(x ? h)^2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry; sketch, by hand, the graph of y = a(x ? h)^2 + k by applying transformations to the graph of y = x^2; determine the equation, in the form y = a(x ? h)^2 + k, of a given graph of a parabola |
ON.OE.10P.1.3 | 3.1 Solving Quadratic Equations: Expand and simplify second-degree polynomial expressions; factor polynomial expressions involving common factors, trinomials, and differences of squares; determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts of the graph of the corresponding quadratic relation; interpret real and non-real roots of quadratic equations, through investigation using graphing technology, and relate the roots to the x-intercepts of the corresponding relations; express y = ax^2 + bx + c in the form y = a(x ? h)^2 + k by completing the square in situations involving no fractions; sketch or graph a quadratic relation whose equation is given in the form y = ax^2 + bx + c, using a variety of methods; explore the algebraic development of the quadratic formula; solve quadratic equations that have real roots, using a variety of methods |
ON.OE.10P.2.1 | 1.1 Using Linear Systems to Solve Problems: Solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination; solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method |
ON.OE.10P.2.2 | 2.1 Solving Problems Involving Properties of Line Segments: Develop the formula for the midpoint of a line segment, and use this formula to solve problems; develop the formula for the length of a line segment, and use this formula to solve problems; develop the equation for a circle with centre (0, 0) and radius r, by applying the formula for the length of a line segment; determine the radius of a circle with centre (0, 0), given its equation; write the equation of a circle with centre (0, 0), given the radius; and sketch the circle, given the equation in the form x^2 + y^2 = r^2; solve problems involving the slope, length, and midpoint of a line segment |
ON.OE.10P.2.3 | 3.1 Using Analytic Geometry to Verify Geometric Properties: Determine, through investigation, some characteristics and properties of geometric figures; verify, using algebraic techniques and analytic geometry, some characteristics of geometric figures; plan and implement a multi-step strategy that uses analytic geometry and algebraic techniques to verify a geometric property |
ON.OE.10P.3.1 | 1.1 Investigating Similarity and Solving Problems Involving Similar Triangles: Verify, through investigation, the properties of similar triangles; describe and compare the concepts of similarity and congruence; solve problems involving similar triangles in realistic situations |
ON.OE.10P.3.2 | 2.1 Solving Problems Involving the Trigonometry of Right Triangles: Determine, through investigation, the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios; determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem; solve problems involving the measures of sides and angles in right triangles in real-life applications |
ON.OE.10P.3.3 | 3.1 Solving Problems Involving the Trigonometry of Acute Triangles: Explore the development of the sine law within acute triangles; explore the development of the cosine law within acute triangles; determine the measures of sides and angles in acute triangles, using the sine law and the cosine law; solve problems involving the measures of sides and angles in acute triangles |
Ontario Grade 10 Academic Math (MPM2D) — Full Curriculum Coverage
MPM2D, Principles of Mathematics Grade 10 Academic, is one of Ontario's core math courses. It introduces three major strands: quadratic relations, analytic geometry, and trigonometry. Students who master MPM2D are well prepared for MCR3U (Grade 11 Functions) and MBF3C.
Quadratic Relations
Students begin by exploring quadratic relations through data collection and graphing. They learn to identify key features of a parabola — the vertex, axis of symmetry, y-intercept, zeros, and maximum or minimum value. The course then moves into transformations using y = a(x − h)² + k, factoring, completing the square, the quadratic formula, and solving real-world problems involving quadratic equations.
Analytic Geometry
The analytic geometry strand develops formulas for midpoint, length of a line segment, and the equation of a circle. Students apply these tools to verify properties of geometric figures, solve problems involving linear systems using substitution and elimination, and explore similarity and congruence in geometric shapes.
Trigonometry
The trigonometry strand starts with primary trig ratios (sine, cosine, tangent) and the Pythagorean theorem in right triangles, then extends to the sine law and cosine law for acute triangles. Students solve real-life problems involving angles and side lengths in both right and non-right triangles.
How StudyPug Supports MPM2D Students
- Video lessons broken into short, focused segments for each MPM2D topic
- Practice problems with step-by-step solutions after every lesson
- Content organized by MPM2D unit so students can find exactly what they need
- Available on any device — computer, tablet, or phone
Whether your child is preparing for a unit test, catching up after missing class, or working ahead, StudyPug covers every MPM2D topic aligned to the Ontario math curriculum.