Courses

Ontario · Grade 10

Foundations of Mathematics, Grade 10 (Applied)

  • MFM2P

Ontario’s Grade 10 math course, from Measurement and Trigonometry to Quadratic Relations.

Learn thisPractice test
Units
3
Lessons
9
Skills
34
Provincial exam
None
Official curriculum
Ontario Ministry of Education

Unit by unit

Every skill in the course, numbered by unit.

Unit 1 · 12 skills

Measurement and Trigonometry

Similar Triangles

Right-Triangle Trigonometry

Surface Area and Volume, Imperial and Metric

The official wording · 12 outcomes
1.1
verify, through investigation (e.g., using dynamic geometry software, concrete materials), properties of similar triangles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides);
1.2
determine the lengths of sides of similar triangles, using proportional reasoning;
1.3
solve problems involving similar triangles in realistic situations (e.g., shadows, reflec- tions, scale models, surveying)
1.4
determine, through investigation (e.g., using dynamic geometry software, con- crete materials), 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
1.5
determine the measures of the sides and angles in right triangles, using the primary opposite hypotenuse trigonometric ratios and the Pythagorean theorem;
1.6
solve problems involving the measures of sides and angles in right triangles in real- life applications
1.7
describe, through participation in an activity, the application of trigonometry in an occupation
1.8
use the imperial system when solving measurement problems (e.g., problems involving dimensions of lumber, areas of carpets, and volumes of soil or concrete);
1.9
perform everyday conversions between the imperial system and the metric system (e.g., millilitres to cups, centimetres to inches) and within these systems
1.10
determine, through investigation, the rela- tionship for calculating the surface area of a pyramid (e.g., use the net of a square- based pyramid to determine that the sur- face area is the area of the square base plus the areas of the four congruent triangles);
1.11
solve problems involving the surface areas of prisms, pyramids, and cylinders, and the volumes of prisms, pyramids, cylinders, cones, and spheres, including problems involving combinations of these figures, using the metric system or the imperial system, as appropriate
1.12
develop the formula for the volume of a sphere, using concrete materials and the volume relationships between cylinders, cones, and spheres.

Key ideas

  1. Similar triangles have exactly the same angles, just possibly at a different size.

  2. In similar right triangles, the ratio between two sides stays the same for a given angle.

  3. The imperial system uses units like feet, inches, and yards — still common in construction and lumber sales in Canada.

  4. In similar triangles, matching (corresponding) sides all have the same scale factor between them.

  5. Sine, cosine, and tangent are named ratios: for example, sin A = opposite/hypotenuse.

Watch out for

  • Assuming any two triangles that 'look similar' actually are, without checking angles or side ratios.
  • Mixing up which side is opposite versus adjacent depending on which angle is chosen.
  • Mixing imperial and metric units within the same calculation without converting first.

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Unit 2 · 12 skills

Modelling Linear Relations

Solving First-Degree Equations

  • Solving first-degree equations, including fractional coefficients

    I can solve first-degree equations, including ones with fractional coefficients.

    2.1

    Learn itPractice testActivities

  • Finding the value of a variable using a formula

    I can find the value of a variable using a formula.

    2.2

    Learn itPractice testActivities

  • Rewriting a line's equation in y = mx + b form

    I can rewrite a line's equation from general form into y = mx + b form.

    2.3

    Learn itPractice testActivities

Graphing and Writing Equations of Lines

Solving and Interpreting Systems of Linear Equations

The official wording · 12 outcomes
2.1
solve first-degree equations involving one variable, including equations with frac- tional coefficients
2.2
determine the value of a variable in the first degree, using a formula (i.e., by isolating the variable and then substituting known values; by substituting known values and then solving for the variable)
2.3
express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0.
2.4
connect the rate of change of a linear rela- tion to the slope of the line, and define the slope as the ratio m =
2.5
identify, through investigation, y = mx + b as a common form for the equation of a straight line, and identify the special cases x = a, y = b;
2.6
identify, through investigation with tech- nology, the geometric significance of m and b in the equation y = mx + b;
2.7
identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism), using graphing technology to facilitate investiga- tions, where appropriate;
2.8
graph lines by hand, using a variety of techniques (e.g., graph using the y-intercept and slope; graph 2x + 3y = 6 using the x- and y-intercepts);
2.9
determine the equation of a line, given its graph, the slope and y-intercept, the slope and a point on the line, or two points on the line.
2.10
determine graphically the point of inter- section of two linear relations (e.g., using graph paper, using technology)
2.11
solve systems of two linear equations involving two variables with integral coefficients, using the algebraic method of substitution or elimination
2.12
solve problems that arise from realistic sit- uations described in words or represented by given linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method

Key ideas

  1. Whatever you do to one side of an equation, you must do to the other side, to keep it balanced.

  2. Rate of change describes how fast one quantity changes compared to another — like speed (distance per time).

  3. The point where two lines cross is the ONE point that satisfies both equations at once.

  4. Fractional coefficients can be cleared early by multiplying every term by the denominator.

  5. Slope is the same idea applied to a graph: rise (vertical change) over run (horizontal change).

Watch out for

  • Applying an operation to only one side of the equation instead of both.
  • Calculating run over rise instead of rise over run.
  • Reading the intersection point's coordinates in the wrong order (mixing up x and y).

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Unit 3 · 10 skills

Quadratic Relations

Identifying Characteristics of Quadratic Relations

Graphing Quadratic Relations

  • Collecting and graphing quadratic data

    I can collect data that forms a quadratic relation and graph a curve of best fit.

    3.5

    Learn itPractice testActivities

  • Recognizing a parabola from a table of second differences

    I can use technology to show a quadratic relation makes a parabola with constant second differences.

    3.6

    Learn itPractice testActivities

  • Identifying the key features of a parabola

    I can identify a parabola's key features from a graph.

    3.7

    Learn itPractice testActivities

  • Comparing standard-form and factored-form graphs

    I can compare graphs of a quadratic relation in standard and factored form.

    3.8

    Learn itPractice testActivities

Solving Problems by Interpreting Graphs of Quadratic Relations

  • Solving quadratic problems by interpreting a graph

    I can solve quadratic problems by interpreting a graph.

    3.9

    Learn itPractice testActivities

  • Interpreting key features from an experimental quadratic graph

    I can interpret the key features of a graph made from experimental data.

    3.10

    Learn itPractice testActivities
The official wording · 10 outcomes
3.1
expand and simplify second-degree polyno- mial expressions involving one variable that consist of the product of two binomials [e.g., (2x + 3)(x + 4)] or the square of a binomial [e.g., (x + 3)2], using a variety of tools
3.2
factor binomials (e.g., 4x2 + 8x) and trino- mials (e.g., 3x2 + 9x – 15) involving one variable up to degree two, by determining a common factor using a variety of tools
3.3
factor simple trinomials of the form x2 + bx + c (e.g., x2 + 7x + 10, x2 + 2x – 8), using a variety of tools
3.4
factor the difference of squares of the form x2 – a2 (e.g., x2 – 16).
3.5
collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology (e.g., concrete materials, scientific probes, graphing calculators), or from secondary sources (e.g., the Internet, Statistics Canada); graph the data and draw a curve of best fit
3.6
determine, through investigation using technology, that a quadratic relation of the form y = ax2 + bx + c (a ≠ 0) can be graph- ically represented as a parabola, and deter- mine that the table of values yields a con- stant second difference
3.7
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), using a given graph or a graph generated with technology from its equation, and use the appropriate terminol- ogy to describe the features;
3.8
compare, through investigation using tech- nology, the graphical representations of a quadratic relation in the form y = x2 + bx + c and the same relation in the factored form y = (x – r)(x – s)
3.9
solve problems involving a quadratic rela- tion by interpreting a given graph or a graph generated with technology from its equation
3.10
solve problems by interpreting the signifi- cance of the key features of graphs obtained by collecting experimental data involving quadratic relations

Key ideas

  1. Expanding (2x + 3)(x + 4) means multiplying every term in the first bracket by every term in the second.

  2. Rolling a can, bouncing a ball, or other simple experiments can produce quadratic-shaped data.

  3. Real quadratic situations (like a ball's height over time) can be understood by reading specific features of the graph.

  4. Squaring a binomial, like (x + 3)², means multiplying it by itself, not just squaring each term separately.

  5. A curve of best fit smooths out experimental scatter to reveal the underlying quadratic shape.

Watch out for

  • Treating (x + 3)² as x² + 9, forgetting the middle term.
  • Connecting data points with straight segments instead of a smooth curve.
  • Reading the wrong axis when looking for a height versus a time value.

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Which course?

Ontario has 2 math courses for Grade 10. Here they are side by side.

What a university, college or program asks for is theirs to say: check its admission page, and your school’s course guide.

The official curriculum

This page follows Ontario’s own curriculum for Foundations of Mathematics, Grade 10 (Applied).

The Ontario Curriculum, Grades 9 and 10: MathematicsOntario Ministry of Education · dcp.edu.gov.on.ca · Read July 27, 2026

Textbooks

The textbooks Ontario Ministry of Education lists for Foundations of Mathematics, Grade 10 (Applied):

  • Foundations of Mathematics 10McGraw-Hill Ryerson · 2007
  • Addison Wesley Foundations of Mathematics 10Pearson Education Canada · 2000
  • MATHEMATICS: Applying the Concepts 10McGraw-Hill Ryerson · 2000

From the Trillium List, read October 27, 2026. ontario.ca

Study it in MapleMind

MapleMind teaches Foundations of Mathematics, Grade 10 (Applied) one skill at a time. Each skill gets a short lesson, practice as you go and a check worth up to three stars. It remembers where you stopped.

Geography of Canada, Grade 9 in the MapleMind app on a tablet: its units, Unit 2 open, and the skills done so far with their starsGeography of Canada, Grade 9 in the MapleMind app on a phone: its units, Unit 2 open, and the skills done so far with their stars
Pictured: Geography of Canada, Grade 9, another Ontario course, partway through Unit 2.

Practise it

Course Companion

Your year in one workbook

A fun way to keep Foundations of Mathematics, Grade 10 (Applied) organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.

Pages
26
Fillable fields
1,424
Price
$4.99
See the Course Companion

Questions about Foundations of Mathematics, Grade 10 (Applied)

What is Foundations of Mathematics, Grade 10 (Applied)?

Ontario’s Grade 10 math course: 3 units and 34 skills, from Measurement and Trigonometry to Quadratic Relations.

What units are in Foundations of Mathematics, Grade 10 (Applied)?

1. Measurement and Trigonometry, 2. Modelling Linear Relations and 3. Quadratic Relations.

Is there a provincial exam for Foundations of Mathematics, Grade 10 (Applied)?

No. Ontario gives no provincial exam for Foundations of Mathematics, Grade 10 (Applied).

What textbook does Foundations of Mathematics, Grade 10 (Applied) use?

The textbooks Ontario Ministry of Education lists for Foundations of Mathematics, Grade 10 (Applied): Foundations of Mathematics 10, McGraw-Hill Ryerson, Addison Wesley Foundations of Mathematics 10, Pearson Education Canada and MATHEMATICS: Applying the Concepts 10, McGraw-Hill Ryerson.

What comes after Foundations of Mathematics, Grade 10 (Applied)?

Functions, Grade 11 (University), Functions and Applications, Grade 11 (University/College), Foundations for College Mathematics, Grade 11 (College) and Mathematics for Work and Everyday Life, Grade 11 (Workplace).

Can MapleMind help with Foundations of Mathematics, Grade 10 (Applied)?

Yes. MapleMind teaches every skill of Foundations of Mathematics, Grade 10 (Applied), step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.

Before this course

After this course

Get ready for Foundations of Mathematics, Grade 10 (Applied)

Practise every skill of Foundations of Mathematics, Grade 10 (Applied) in MapleMind, free with daily limits.