Ontario Grade 12 University Preparation math (MDM4U)

Probability concepts, permutations, combinations, and counting.

• A1.1 · Interpret likelihood and probability (written lesson not published)
• A1.2 · Describe discrete and continuous sample spaces (written lesson not published)
• A1.3 · Calculate theoretical probabilities (written lesson not published)
• A1.4 · Estimate probability through experiments and simulations (written lesson not published)
• A1.5 · Analyze events, complements, and mutually exclusive events (written lesson not published)
• A1.6 · Analyze independence, dependence, and conditional probability (written lesson not published)
• A2.1 · Use permutations and combinations as counting strategies (written lesson not published)
• A2.2 · Calculate simple permutations and combinations (written lesson not published)
• A2.3 · Apply additive and multiplicative counting principles (written lesson not published)
• A2.4 · Connect Pascal’s triangle with combinations (written lesson not published)
• A2.5 · Calculate probabilities using counting methods (written lesson not published)

Discrete, binomial, hypergeometric, continuous, and normal distributions.

• B1.1 · Represent discrete random-variable distributions (written lesson not published)
• B1.2 · Calculate and interpret expected value (written lesson not published)
• B1.3 · Create and interpret probability histograms (written lesson not published)
• B1.4 · Recognize and calculate binomial probabilities (written lesson not published)
• B1.5 · Recognize and calculate hypergeometric probabilities (written lesson not published)
• B1.6 · Compare discrete probability distributions (written lesson not published)
• B1.7 · Solve applications involving discrete distributions (written lesson not published)
• B2.1 · Interpret continuous random variables (written lesson not published)
• B2.2 · Calculate mean and standard deviation for grouped data (written lesson not published)
• B2.3 · Recognize challenges in continuous frequency distributions (written lesson not published)
• B2.4 · Represent continuous data with tables, histograms, and polygons (written lesson not published)
• B2.5 · Connect interval probability with area (written lesson not published)
• B2.6 · Describe properties of the normal distribution (written lesson not published)
• B2.7 · Connect normal and discrete distributions (written lesson not published)
• B2.8 · Use z-scores and normal probabilities (written lesson not published)

Data types, sampling, bias, surveys, and ethical collection.

• C1.1 · Explain the role and applications of data (written lesson not published)
• C1.2 · Recognize inherent variability in data (written lesson not published)
• C1.3 · Classify types of data (written lesson not published)
• C2.1 · Apply principles of primary data collection (written lesson not published)
• C2.2 · Distinguish populations, samples, and sampling methods (written lesson not published)
• C2.3 · Identify and reduce bias (written lesson not published)
• C2.4 · Design ethical and effective surveys (written lesson not published)
• C2.5 · Collect and organize primary and secondary data (written lesson not published)

One-variable and two-variable analysis, interpretation, and evaluation.

• D1.1 · Calculate one-variable numerical summaries (written lesson not published)
• D1.2 · Use quartiles, percentiles, and z-scores (written lesson not published)
• D1.3 · Create one-variable graphical summaries (written lesson not published)
• D1.4 · Interpret margin of error and confidence (written lesson not published)
• D1.5 · Interpret and compare one-variable data (written lesson not published)
• D2.1 · Measure relationships with a correlation coefficient (written lesson not published)
• D2.2 · Distinguish correlation, causation, and common cause (written lesson not published)
• D2.3 · Create two-variable graphical summaries (written lesson not published)
• D2.4 · Use regression, residuals, and goodness of fit (written lesson not published)
• D2.5 · Interpret and compare two-variable data (written lesson not published)
• D3.1 · Interpret statistics reported in the media (written lesson not published)
• D3.2 · Assess sources, methods, and bias (written lesson not published)
• D3.3 · Investigate data-management careers and programs (written lesson not published)

Plan, conduct, report, and defend a statistical investigation.

• E1.1 · Pose a significant investigation question (written lesson not published)
• E1.2 · Create an investigation plan (written lesson not published)
• E1.3 · Gather and organize investigation data (written lesson not published)
• E1.4 · Analyze and summarize investigation data (written lesson not published)
• E1.5 · Draw evidence-based conclusions and identify limitations (written lesson not published)
• E2.1 · Write a clear investigation report (written lesson not published)
• E2.2 · Present investigation findings (written lesson not published)
• E2.3 · Defend methods and conclusions (written lesson not published)
• E2.4 · Critique another statistical investigation (written lesson not published)

How many committees of 3 can be chosen from 8 students?

Worked method: Order does not matter, so use a combination: C(8,3) = 56.

A game pays CAD 10 with probability 0.2 and CAD 0 otherwise. Find the expected payout.

Worked method: E(X) = 10(0.2) + 0(0.8) = CAD 2.

How many ways can 5 different books be arranged?

For a normal value with x = 72, mean 60, and standard deviation 6, find z.