What's the difference between Grade 10 Academic and Applied Math?

Academic Math (MPM2D) focuses on abstract concepts and theory, while Applied Math (MFM2P) emphasizes practical applications. Academic is more challenging and prepares for university-level math.

How can I choose between Academic and Applied Math in Grade 10?

Consider your math performance in Grade 9, future educational goals, and career aspirations. Consult with your teacher or guidance counselor for personalized advice on the best fit for you.

What support is available for struggling Grade 10 Math students?

Schools often offer extra help sessions, peer tutoring, and online resources. Additionally, private tutoring and educational platforms provide targeted support for challenging topics.

What are the key topics covered in Grade 10 Academic Math (MPM2D)?

MPM2D covers quadratic relations, analytic geometry, trigonometry, and linear systems. Students learn to analyze and graph functions, solve equations, and apply geometric and trigonometric concepts.

How is Grade 10 Applied Math (MFM2P) assessed?

MFM2P assessment includes quizzes, tests, assignments, and a final exam. It focuses on practical problem-solving, measurement skills, and understanding of linear and quadratic relationships.

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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

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	Characteristics of quadratic functions Transformations of quadratic functions Quadratic function in general form: y = ax^2 + bx + c Converting from general to vertex form by completing the square Shortcut: Vertex formula Graphing quadratic functions: General form VS. Vertex form Finding the quadratic functions for given parabolas Applications of quadratic functions

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

Combining transformations of functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Quadratic function in vertex form: y = a(x-p)^2 + q

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

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares: $x^2 - y^2$

Factoring trinomials

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Completing the square

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

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

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

Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$

Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

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

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Parallel and perpendicular lines in linear functions

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

Similar triangles

Similar polygons

Isosceles and equilateral triangles

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

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

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

Law of sines

Law of cosines

Applications of the sine law and cosine law

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