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Grade 10 Math Courses - Ontario Curriculum
Discover Ontario's Grade 10 Math options: Academic (MPM2D) and Applied (MFM2P). Learn key concepts, develop problem-solving skills, and prepare for future math studies in this crucial year.
Ontario Grade 10 Math Curriculum - Academic and Applied Topics
OE_ID | Expectations | StudyPug Topic |
|---|---|---|
1. Quadratic Relations of the Form y = ax^2 + bx + c : 1. Determine the basic properties of quadratic relations | ||
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 |
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 |
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 |
2. Analytic Geometry : 1. Model and solve problems involving the intersection of two straight lines | ||
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 |
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 |
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 |
3. Trigonometry : 1. Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity | ||
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 |
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 |
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 |
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