MHF4U exam review: Grade 12 Advanced Functions practice questions and exam rules

The daily Advanced Functions (MHF4U) paper has 8 original questions worth 25 to 35 marks. It is practice for the exponential, logarithmic, trigonometric and polynomial parts of MHF4U, plus combining and transforming functions. It has no rational functions, and its binomial expansion, partial fractions and proof questions go beyond MHF4U, so skip those.

How the MHF4U exam counts in 2026-27

Ontario's rules changed for the 2026-27 school year. In Grade 12 mathematics, your final mark is 65% classroom work through the course, a 25% written exam, and 10% attendance and participation. The exam is written on official exam days in your board's exam period, and your board sets the dates. Excused absences don't lower your attendance mark. These figures come from the Ministry of Education's September 2026 update to Growing Success.

The prerequisite for MHF4U is Functions, Grade 11 (MCR3U), or Mathematics for College Technology, Grade 12. Your teacher sets the exam's length and format, so ask about both.

What's on the MHF4U exam: the four strands

MHF4U practice questions with answers

We wrote these for this page, one or more from each strand. Try each before reading the working.

1. Exponential and logarithmic equations

Question: Solve 3^{2x − 1} = 81, then solve log₂(x + 3) + log₂(x − 3) = 4.

81 = 3⁴, so 2x − 1 = 4 and x = 2.5. For the second, combine the logs: log₂((x + 3)(x − 3)) = 4, so x² − 9 = 2⁴ = 16 and x² = 25. Reject x = −5, because log₂(x − 3) needs x > 3. The answer is x = 5. Check: log₂ 8 + log₂ 2 = 3 + 1 = 4. The Logarithm Calculator checks values like these.

2. Radians and trig equations

Question: Convert 135° to radians, then solve 2 sin x − 1 = 0 for 0 ≤ x ≤ 2π.

Multiply by π/180: 135° = 3π/4. Then sin x = 1/2. Sine is positive in the first and second quadrants, and the reference angle is π/6, so x = π/6 or x = 5π/6. Finding only the calculator's answer, π/6, loses half the marks.

3. Compound angle formulas

Question: Find the exact value of sin 75°.

Put in the exact values √2/2, √3/2 and 1/2, and the answer is (√6 + √2)/4, about 0.9659. "Exact" means leave the roots in. Try an identity question from our Trigonometry course, then press Mark.

4. Polynomial inequalities and rational functions

Question: Solve (x + 2)(x − 1)(x − 4) > 0. Then give the asymptotes of f(x) = (2x + 1)/(x − 3).

The zeros are −2, 1 and 4. Test a value in each interval: the product is negative for x < −2, positive between −2 and 1, negative between 1 and 4, and positive above 4. So −2 < x < 1 or x > 4. For f, the denominator is zero at x = 3, giving a vertical asymptote x = 3, and the leading coefficients give a horizontal asymptote y = 2.

Here x is the input and y is the value of the product. The answer is where the curve sits above the axis.

5. Rates of change

Question: For f(x) = x³, find the average rate of change from x = 1 to x = 3, and estimate the instantaneous rate of change at x = 2.

Average rate = (f(3) − f(1)) ÷ (3 − 1) = (27 − 1) ÷ 2 = 13. For the instantaneous rate, use a very small interval around 2: (2.001³ − 1.999³) ÷ 0.002 is about 12. That is the slope of the tangent at x = 2, which you'll find exactly with derivatives in MCV4U.

Use the daily paper as a practice exam

1. Open today's MHF4U paper and work to the suggested time, 35 to 45 minutes.
2. Skip any binomial expansion, partial fractions or proof questions.
3. Mark it and note which strand each lost mark belongs to.
4. Practise rational functions separately, because the paper doesn't include them.

Common MHF4U mistakes

• Keeping a solution that makes a log undefined.
• Giving one angle when a trig equation has two in the interval.
• Using degrees when the question is in radians.
• Splitting log(a + b) into log a + log b.
• Forgetting to test each interval in a polynomial inequality.

Read next

Canada · Grade 12SCH4U Practice Exam: Grade 12 Chemistry Questions, AnswersAn SCH4U practice exam: free Grade 12 Chemistry questions on organic, structure, calorimetry, equilibrium and cells, and how the 2026-27 exam counts.