Grade 10 math practice
Both Grade 10 pathways — Academic (MPM2D) and Applied (MFM2P): quadratics, analytic geometry, trigonometry and linear systems with full worked solutions.
Grade 10 Applied (MFM2P)
Geometry Trigonometry · MFM2P
6 question sets · 10 questions each, easiest to hardest
Similar Triangles and Proportional Reasoning
Geometry Trigonometry · 30 questions, easiest to hardest
Right Triangle Trigonometry — Primary Ratios (SOH CAH TOA)
Geometry Trigonometry · 30 questions, easiest to hardest
Solving for Sides and Angles in Right Triangles
Geometry Trigonometry · 30 questions, easiest to hardest
Applications — Angle of Elevation and Depression
Geometry Trigonometry · 30 questions, easiest to hardest
Applications — Indirect Measurement (Similar Triangles and Trigonometry Together)
Geometry Trigonometry · 30 questions, easiest to hardest
Optimization and Real-World Geometry Problems (Perimeter/Area)
Geometry Trigonometry · 30 questions, easiest to hardest
Measurement · MFM2P
6 question sets · 10 questions each, easiest to hardest
Surface Area of 3D Objects
Measurement · 30 questions, easiest to hardest
Volume of 3D Objects
Measurement · 30 questions, easiest to hardest
Composite 2D Shapes (Area/Perimeter)
Measurement · 30 questions, easiest to hardest
Composite 3D Objects (Surface Area/Volume)
Measurement · 30 questions, easiest to hardest
Unit Conversions (Metric/Imperial) and Scale Drawings
Measurement · 30 questions, easiest to hardest
Optimization Problems Involving Measurement (Real-World Packaging/Design)
Measurement · 30 questions, easiest to hardest
Mathematical Models · MFM2P
6 question sets · 10 questions each, easiest to hardest
Linear Relations — Rate of Change and Initial Value
Mathematical Models · 30 questions, easiest to hardest
Solving Linear Equations in Applied Contexts
Mathematical Models · 30 questions, easiest to hardest
Systems of Linear Equations — Graphing and Applications
Mathematical Models · 30 questions, easiest to hardest
Introduction to Quadratic Relations — Tables, Graphing, Basic Properties
Mathematical Models · 30 questions, easiest to hardest
Quadratic Applications (Using Given Formulas)
Mathematical Models · 30 questions, easiest to hardest
Direct and Partial Variation — Real-World Modelling
Mathematical Models · 30 questions, easiest to hardest
Endless practice · MFM2P
Generated fresh every time — adaptive difficulty, never runs out
Solve linear equations
Solve linear equations for x, from two-step equations up to equations with brackets on both sides.
Slope as a rate of change
Find the slope (rate of change) between two data points in a real context, and interpret its sign.
Write the equation of a linear model
Write the equation (y = mx + b) of a linear relation from a described fixed value and rate of change.
Solve a linear system in context — break-even point
Solve a linear system algebraically to find where two plans (each a fixed fee plus a rate) cost the same.
Similar triangles — indirect measurement
Use similar-triangle proportions (equal height-to-shadow ratios) to find a missing height or shadow length.
Right-triangle trig — find a missing side
Use SOH-CAH-TOA to find a missing side of a right triangle given one angle and one side, in a real context.
Right-triangle trig — find a missing angle
Use inverse trig ratios to find a missing angle of a right triangle given two sides, in a real context.
Convert between imperial and metric measurements
Convert a length, weight, or volume between imperial and metric units using a given conversion factor.
Surface area and volume of prisms and cylinders
Find the volume or total surface area of a rectangular prism or a cylinder.
Expand and simplify a product of two binomials
Expand and simplify a product of two binomials, such as the area of a rectangle with binomial side lengths.
Factor a simple trinomial
Factor a trinomial of the form x^2 + bx + c into two binomials.
Identify the vertex and axis of symmetry
Identify the vertex, axis of symmetry, and direction of opening of a quadratic relation given in vertex form.
Interpret a quadratic height model
Use a quadratic height model h(t) = -5t^2 + vt + h0 to find a maximum height or the time an object lands.
Grade 10 Academic (MPM2D)
Analytic Geometry · MPM2D
6 question sets · 10 questions each, easiest to hardest
Slope, Length, and Midpoint of a Line Segment
Analytic Geometry · 30 questions, easiest to hardest
Equations of Lines
Analytic Geometry · 30 questions, easiest to hardest
Parallel and Perpendicular Lines
Analytic Geometry · 30 questions, easiest to hardest
Systems of Linear Equations — Solving by Substitution and Elimination
Analytic Geometry · 30 questions, easiest to hardest
Applications of Linear Systems
Analytic Geometry · 30 questions, easiest to hardest
Circle Equations and Verifying Shape Properties Using Analytic Geometry
Analytic Geometry · 30 questions, easiest to hardest
Quadratics · MPM2D
6 question sets · 10 questions each, easiest to hardest
Table of Values and Finite Differences — identifying quadratic relations
Quadratics · 30 questions, easiest to hardest
Vertex Form and Transformations
Quadratics · 30 questions, easiest to hardest
Factored Form and Zeros/X-intercepts
Quadratics · 30 questions, easiest to hardest
Standard Form, Expanding and Simplifying
Quadratics · 30 questions, easiest to hardest
Completing the Square
Quadratics · 30 questions, easiest to hardest
Solving Quadratic Equations and Applications
Quadratics · 30 questions, easiest to hardest
Trigonometry · MPM2D
6 question sets · 10 questions each, easiest to hardest
Primary Trigonometric Ratios (SOH CAH TOA)
Trigonometry · 30 questions, easiest to hardest
Solving Right Triangles
Trigonometry · 30 questions, easiest to hardest
Angle of Elevation/Depression and Applications
Trigonometry · 30 questions, easiest to hardest
Sine Law
Trigonometry · 30 questions, easiest to hardest
Cosine Law
Trigonometry · 30 questions, easiest to hardest
Applications Combining the Sine Law and Cosine Law
Trigonometry · 30 questions, easiest to hardest
Endless practice · MPM2D
Generated fresh every time — adaptive difficulty, never runs out
Solve a linear system by substitution or elimination
Solve a system of two linear equations algebraically, using substitution when one equation isolates a variable and elimination otherwise.
Linear systems word problems
Set up and solve a system of two linear equations from a real-world word problem involving two ticket or item prices.
Midpoint and length of a line segment
Find the midpoint of a line segment, its length using the distance formula, or a missing endpoint given the midpoint.
Equation of a circle centred at the origin
Write the equation of a circle centred at the origin, and verify whether a given point lies inside, on, or outside the circle.
Expand and simplify a product of binomials
Expand and simplify a product of two binomials, such as (2x+3)(x-4), into standard trinomial form.
Factor by common factor and simple trinomials
Factor a trinomial x^2+bx+c into two binomials, including trinomials that share a common factor.
Factor a difference of squares or a complex trinomial
Factor a difference of squares, or a trinomial ax^2+bx+c where a is not 1, using the decomposition method.
Vertex form: vertex, axis of symmetry, and transformations
Identify the vertex, axis of symmetry, and direction of opening of a parabola in vertex form, and describe its transformations from y = x^2.
Solve quadratic equations by factoring
Solve a quadratic equation by factoring to find its roots, including a projectile word problem.
Complete the square to find a maximum or minimum value
Complete the square to convert a quadratic to vertex form and find its maximum or minimum value, including a fencing-optimization word problem.
Solve quadratic equations with the quadratic formula
Solve a quadratic equation using the quadratic formula, and use the discriminant to determine the number of real roots.
Similar triangles
Use similar-triangle ratios to find a missing side, both in abstract triangle notation and in an indirect-measurement word problem.
Primary trig ratios — find a missing side
Use SOH-CAH-TOA to find a missing side of a right triangle given one angle and one side, in a real context.
Primary trig ratios — find a missing angle
Use inverse trig ratios to find a missing angle of a right triangle given two sides, in a real context.
Sine law
Use the sine law to find a missing side or angle in an acute triangle, including surveying-style word problems.
Cosine law
Use the cosine law to find a missing side or angle in an acute triangle, including a surveying word problem.
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