Grade 10 math exam: MPM2D practice questions, answers and exam rules

The daily Grade 10 Math paper has 8 original questions worth 25 to 35 marks. It is practice for quadratics, linear systems (simultaneous equations), straight-line and quadratic graphs, similar triangles and trigonometry. Its circle theorems, vectors, histograms and probability questions go beyond MPM2D, so skip those.

How the Grade 10 math exam counts in 2026-27

In Grades 9 and 10 in Ontario, your final mark is now 65% classroom work, a 20% written exam, and 15% attendance and participation. In mathematics the whole 20% is the written exam, set by your school and written in your board's exam period. Excused absences don't lower your attendance mark. These figures come from the Ministry of Education's September 2026 update to Growing Success.

What's on the MPM2D exam

• Quadratic relations: factoring, completing the square, graphs and applications.
• Linear systems: solving and applying systems of two linear equations.
• Analytic geometry: midpoint, length of a line segment, equations of lines and circles, and verifying properties of shapes on the coordinate plane.
• Trigonometry: similar triangles, right-triangle trigonometry, and the sine and cosine laws for acute triangles.

Grade 10 math practice questions with answers

We wrote these for this page. Use a calculator in degree mode for questions 4 and 5.

1. Linear systems. Solve 2x + 3y = 12 and x − y = 1. Answer: from the second equation, x = y + 1. Substitute: 2(y + 1) + 3y = 12, so 5y = 10, y = 2 and x = 3. The solution is (3, 2), where the two lines cross. Try a systems question from our Algebra course, then press Mark.

2. Analytic geometry. For A(−2, 3) and B(4, −5), find the midpoint and length of AB. Does B lie on the circle x² + y² = 41? Answer: midpoint = ((−2 + 4) ÷ 2, (3 − 5) ÷ 2) = (1, −1). Length = √(6² + 8²) = 10. For B, 16 + 25 = 41, so yes. Check with the Midpoint and Distance Calculator.

3. Quadratics. Write y = 2x² + 8x + 3 in vertex form and give the vertex. Answer: factor 2 from the first two terms: 2(x² + 4x) + 3. Complete the square: 2(x² + 4x + 4 − 4) + 3 = 2(x + 2)² − 8 + 3 = 2(x + 2)² − 5. The vertex is (−2, −5), a minimum because the 2 is positive.

Here x is the input and y is the value of 2x² + 8x + 3. The parabola is symmetric about the line x = −2.

4. Right-triangle trigonometry. From 25 m away, the angle of elevation to the top of a flagpole is 32°. How tall is the flagpole? Answer: the height is opposite the angle and 25 m is adjacent, so h = 25 tan 32° ≈ 15.6 m.

5. Acute triangles. In triangle ABC, a = 12 cm, ∠A = 40° and ∠B = 65°. Find b. Then, in another triangle, two sides of 8 cm and 11 cm meet at 50°: find the third side. Answer: by the sine law, b = 12 sin 65° ÷ sin 40° ≈ 16.9 cm. By the cosine law, c² = 8² + 11² − 2(8)(11) cos 50° ≈ 71.87, so c ≈ 8.48 cm. The Trigonometry Calculator solves triangles step by step.

Use the daily paper as a practice exam

1. Open today's Grade 10 Math paper and work to the suggested time, 35 to 40 minutes.
2. Skip the circle theorem, vector, histogram and probability questions.
3. Show each step: your teacher's exam will give marks for method.
4. Mark it and note the topic behind each lost mark.

Common Grade 10 math mistakes

• Forgetting to multiply back when completing the square with a leading coefficient.
• Getting the vertex sign wrong: (x + 2)² gives a vertex at x = −2.
• Using the sine law when you know two sides and the angle between them: that needs the cosine law.
• Calculator in radian mode.
• Stopping at x in a linear system without finding y.

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