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Master Grade 10 Academic Math (MPM2D)

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Find the right Ontario Grade 10 course

Principles of Mathematics, Grade 10, Academic (MPM2D)

Foundations of Mathematics, Grade 10, Applied (MFM2P)

Grade 10 Math Help Ontario: Master MPM2D ConceptsHelp

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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
Complete Ontario Principles of Mathematics, Grade 10, Academic (MPM2D) Coverage

Principles of Mathematics, Grade 10, Academic (MPM2D) Lessons

69

Video Explanations

363

Practice Problems

568

Ontario Standards

100% Aligned

Why Ontario Principles of Mathematics, Grade 10, Academic (MPM2D) Students Love StudyPug

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Success Stories

Factoring trinomials was impossible. The step-by-step videos made it click. Raised my grade from 68% to 82% in three months.

Jordan Lee

The sine law confused me forever. Photo search found the exact lesson I needed. Aced my trigonometry unit test.

Taylor Singh

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Frequently Asked Questions

Everything you need to know about mastering Grade 10 Academic Math with StudyPug

What does MPM2D coverage include?

Complete Grade 10 Academic Math curriculum with video lessons on quadratic relations, analytic geometry, and trigonometry. Includes practice problems, step-by-step solutions, and progress tracking for every Ontario MPM2D topic.

How does photo search work for math problems?

Take a photo of any MPM2D problem, and StudyPug finds the exact lesson teaching that concept. It's like having a personal tutor who knows exactly what you need for quadratics, trig, or analytic geometry.

Are the teachers certified Ontario educators?

Yes! Our teachers are Canadian certified Ontario educators who understand MPM2D curriculum and create lessons specifically for Ontario Grade 10 Academic Math standards.

Can I use StudyPug on my phone or tablet?

Absolutely! StudyPug works on desktop, tablet, and mobile. Your progress syncs automatically so you can study for MPM2D anywhere, whether at school, home, or on the go.

How will StudyPug help me prepare for university preparation?

MPM2D builds essential foundations for Grade 11 and 12 university math courses. We cover all Ontario curriculum expectations and help you master concepts needed for future success in mathematics.

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