Will this help with my child's Grade 10 math homework?

Yes. StudyPug covers every MPM2D strand, so when your child is stuck on quadratic equations, analytic geometry, or trigonometry, they can find a clear worked example and practice problem that matches exactly what was assigned.

How long are the video lessons?

Most video lessons are short and focused, typically running between five and fifteen minutes. Your child can pause, rewind, and rewatch each one as many times as needed until the concept is clear.

Is there an Ontario test for Grade 10 math?

Grade 10 is not a standard EQAO math assessment year in Ontario. EQAO assesses math in Grades 3, 6, and 9. Students in Grade 10 may encounter school-based assessments and the OSSLT literacy test, but there is no provincial math exam at this level.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, and computers, so your child can study at home, on the go, or wherever is most convenient for them.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can see the content before committing. There is also a 30-day money-back guarantee if you are not satisfied after subscribing.

ON Grade 10 Math Curriculum

Give your child the support they need for Grade 10 Academic Math in Ontario. Every strand from MPM2D is covered with clear lessons and practice problems that match what their teacher is doing in class.

ON Grade 10 Math Curriculum

OE_IDExpectationsStudyPug Topic

ON.OE.10P.1.1Collect 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.1.2Identify, 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.1.3Expand 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.2.1Solve 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.2.2Develop 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.2.3Determine, 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
- Triangles
- Rectangles
- Parallelograms
- Trapezoids, rhombi, and kites
- Polygons
- Complex polygons
ON.OE.10P.3.1Verify, 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.3.2Determine, 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.3.3Explore 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

Grade 10 Academic Math (MPM2D)

About Grade 10 Ontario math

Ontario's Grade 10 Academic Math course (MPM2D) follows the Ontario Curriculum and covers five major areas: quadratic relations, analytic geometry, trigonometry, linear systems, and similar triangles. Students work with parabolas, transformations, factoring, the quadratic formula, the sine and cosine laws, and coordinate geometry. StudyPug provides step-by-step lessons and practice problems for every strand in MPM2D, so students can keep pace with class and prepare for EQAO.

Strands: Quadratic Relations, Analytic Geometry, Linear Systems, Similar Triangles, Trigonometry
Step-by-step lessons and worked examples for every MPM2D topic
Practice problems with instant feedback, aligned to the Ontario Curriculum
Video lessons for math concepts so students can review at their own pace

Curriculum topics by strand

Find lessons and practice for every strand in Ontario Grade 10 Academic Math (MPM2D), aligned to the Ontario Curriculum.

Topic includes:

Practice

Video

Quiz

OE_ID

Expectations

StudyPug Topic

Ontario Grade 10 Math Topics

Quadratic Relations - Data and Graphs: Collecting data that forms a quadratic pattern, graphing parabolas, identifying key features such as the axis of symmetry, vertex, zeros, and maximum or minimum values, and comparing quadratic and exponential relations.
Quadratic Relations - Transformations: Investigating the effect of parameters a, h, and k on the graph of y = a(x - h)^2 + k, applying translations, reflections, and vertical stretches or compressions, and determining equations of parabolas from their graphs.
Quadratic Relations - Solving: Expanding and simplifying polynomial expressions, factoring using common factors, trinomials, and differences of squares, completing the square, and solving quadratic equations using a variety of methods including the quadratic formula.
Quadratic Relations - Applications: Determining zeros and maximum or minimum values from graphs or equations, and solving problems arising from realistic situations modeled by quadratic relations.
Linear Systems: Solving systems of two linear equations using substitution and elimination, and applying these methods to problems described in words or represented graphically.
Analytic Geometry - Line Segments and Circles: Developing and applying the midpoint formula, the length formula, and the equation of a circle centered at the origin, and solving problems involving slope, length, and midpoint.
Analytic Geometry - Geometric Properties: Investigating and verifying characteristics of geometric figures using algebraic techniques, and planning multi-step strategies to verify geometric properties.
Similar Triangles: Verifying properties of similar triangles, comparing similarity and congruence, and solving problems involving similar triangles in realistic situations.
Trigonometry - Right Triangles: Defining and using the sine, cosine, and tangent ratios, applying the Pythagorean theorem, and solving right triangle problems in real-life applications.
Trigonometry - Acute Triangles: Exploring and applying the sine law and cosine law to determine measures of sides and angles in acute triangles, and solving related problems.

How StudyPug Helps Ontario Grade 10 Math Students

When a student hits a wall on completing the square or gets confused applying the sine law, StudyPug lets them pull up a focused video lesson on that exact concept, watch a worked example at their own pace, and then try a practice problem with instant feedback. There is no need to wait until the next class or hope the textbook explanation clicks.

Parents can track which strands their child has visited, so it is easy to spot where extra practice is needed before a unit test. Every lesson is built around the MPM2D course expectations, meaning the language and sequence match what Ontario teachers use in class.

Aligned to Ontario Grade 10 Math Curriculum

All StudyPug content for this course is built from the Ontario Curriculum expectations for Principles of Mathematics, Grade 10, Academic (MPM2D). Each strand - from quadratic relations through analytic geometry and trigonometry - follows the sequence and terminology of the Ontario Curriculum, so students are always practicing what their school expects them to know.

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Jump into practice questions for every Ontario Grade 10 topic - with instant feedback and step-by-step video solutions when you get stuck.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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