MDM4U exam review: Grade 12 Data Management practice questions and exam rules

The daily Data Management (MDM4U) paper has 8 original questions worth 25 to 35 marks. It is practice for probability, conditional probability, the binomial and normal distributions, sampling, measures of centre and spread, data displays and correlation. Its hypothesis tests go beyond MDM4U, and it has few counting questions, so practise permutations and combinations separately.

How the MDM4U exam counts in 2026-27

In Grade 12 mathematics in Ontario, your final mark is now 65% classroom work, a 25% written exam, and 10% attendance and participation, with the exam written in your board's exam period. MDM4U also has a culminating data management investigation as one of its strands, so ask your teacher how that is marked. The prerequisite is Functions (MCR3U) or Functions and Applications (MCF3M). These figures come from the Ministry of Education's September 2026 update to Growing Success.

What's on the MDM4U exam: the strands

MDM4U practice questions with answers

We wrote these for this page. Try each before reading the working.

1. Permutations and combinations

Question: A club has 10 members. How many ways can it choose a committee of 4, and how many ways can it choose a president, vice-president and treasurer?

A committee has no order, so use combinations: C(10, 4) = 210. The three officer roles are different, so order matters: P(10, 3) = 10 × 9 × 8 = 720. Ask "does order matter?" every time. The Permutations and Combinations Calculator checks these.

2. The binomial distribution

Question: 15% of parts from a machine are faulty. In a random batch of 20, what is the probability that exactly 2 are faulty, and what is the expected number of faulty parts?

The expected value is np = 20 × 0.15 = 3 faulty parts. The binomial fits because there is a fixed number of independent trials with the same probability each time.

3. The hypergeometric distribution

Question: A bag holds 6 red and 4 blue marbles. Three are drawn without replacement. What is the probability that exactly 2 are red?

Choose 2 of the 6 red and 1 of the 4 blue, out of all ways to choose 3 of 10: C(6, 2) × C(4, 1) ÷ C(10, 3) = 15 × 4 ÷ 120 = 0.5. Without replacement, the draws are dependent, which is why this is hypergeometric rather than binomial. Try a question on dependent events from our Probability course, then press Mark.

4. The normal distribution

Question: Test marks are normally distributed with mean 68 and standard deviation 8. What percentage of students scored above 84?

z = (84 − 68) ÷ 8 = 2. The area above z = 2 is about 0.0228, so roughly 2.3% of students. That fits the 68-95-99.7 rule: 95% lie within 2 standard deviations, leaving about 2.5% in each tail.

5. Correlation

Question: The correlation between hours of screen time and hours of sleep in a sample is r = −0.85. Interpret it.

It is a strong negative linear relationship: students with more screen time tend to sleep less. It doesn't prove that screen time causes less sleep; a third factor could affect both. Fit and plot a line in the Linear Regression Calculator.

Use the daily paper as a practice exam

1. Open today's MDM4U paper and work to the suggested time, 35 to 45 minutes.
2. Treat the hypothesis test questions as extra.
3. Mark it and note which strand each lost mark belongs to.
4. Practise counting problems separately, because the paper has few.

Common MDM4U mistakes

• Using permutations when order doesn't matter, or combinations when it does.
• Using the binomial for draws without replacement: that is hypergeometric.
• Reading correlation as causation.
• Forgetting to standardize before using a normal table.
• Calling a convenience sample random.

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