Will this help with my child's Grade 12 math homework?

Yes, StudyPug covers every strand in MDM4U, including probability distributions, statistical analysis, and data management, so your child can find step-by-step explanations for the exact topics assigned in class.

How long are the video lessons for Grade 12 math?

Most video lessons are short and focused on a single concept, typically a few minutes each, so your child can watch one lesson at a time without losing track of where they are in the MDM4U course.

Is there a provincial test for Grade 12 math in Ontario?

Grade 12 MDM4U is not an EQAO assessment year. Ontario's EQAO assessments cover Grades 3, 6, and 9. Grade 12 students are evaluated through their school's course assessments and the culminating investigation.

Can my child use StudyPug on a tablet or phone?

Yes, StudyPug works on tablets, phones, and computers, so your child can review MDM4U lessons and practice problems at home, on the go, or wherever they study best.

Can I try StudyPug before paying?

Yes, StudyPug offers free sample lessons so you can explore the MDM4U content before subscribing. There is also a 30-day money-back guarantee if the course is not the right fit for your child.

ON Grade 12 Math Curriculum

Support your child through Ontario's Grade 12 Mathematics of Data Management course with lessons and practice problems covering probability, statistics, and data analysis, all matched to what their school teaches.

ON Grade 12 Math Curriculum

OE_IDExpectationsStudyPug Topic

ON.OE.12DM.A1.1Recognize and describe how probabilities are used to represent the likelihood of a result of an experiment and the likelihood of a real-world event
- Introduction to probability
ON.OE.12DM.A1.2Describe a sample space as a set that contains all possible outcomes of an experiment, and distinguish between a discrete sample space and a continuous sample space
- Organizing outcomes
ON.OE.12DM.A1.3Determine the theoretical probability of each outcome of a discrete sample space, recognize that the sum of the probabilities of the outcomes is 1, recognize that the probabilities form the probability distribution associated with the sample space, and solve related problems
- Comparing experimental and theoretical probability
ON.OE.12DM.A1.4Determine, through investigation using class-generated data and technology-based simulation models, the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases
- Probability of independent events
ON.OE.12DM.A1.5Recognize and describe an event as a set of outcomes and as a subset of a sample space, determine the complement of an event, determine whether two or more events are mutually exclusive or non-mutually exclusive, and solve related probability problems
- Reading and drawing Venn diagrams
ON.OE.12DM.A1.6Determine whether two events are independent or dependent and whether one event is conditional on another event, and solve related probability problems
- Conditional probability
- Probability with Venn diagrams
ON.OE.12DM.A2.1Recognize the use of permutations and combinations as counting techniques, distinguish between situations that involve the use of permutations and those that involve the use of combinations, and make connections between, and calculate, permutations and combinations
- Permutation vs. Combination
ON.OE.12DM.A2.2Solve simple problems using techniques for counting permutations and combinations, where all objects are distinct, and express the solutions using standard combinatorial notation
- Permutations
- Combinations
- Problems involving both permutations and combinations
ON.OE.12DM.A2.3Solve introductory counting problems involving the additive counting principle and the multiplicative counting principle
- Fundamental counting principle
ON.OE.12DM.A2.4Make connections, through investigation, between combinations and Pascal's triangle
- Pascal's triangle
ON.OE.12DM.A2.5Solve probability problems using counting principles for situations involving equally likely outcomes
- Binomial theorem
- Probability involving permutations and combinations
ON.OE.12DM.B1.1Recognize and identify a discrete random variable, generate a probability distribution by calculating the probabilities associated with all values of a random variable, and represent a probability distribution numerically using a table
- Probability distribution - histogram, mean, variance & standard deviation
ON.OE.12DM.B1.2Calculate the expected value for a given probability distribution, interpret the expected value in applications, and make connections between the expected value and the weighted mean of the values of the discrete random variable
- Properties of expectation
ON.OE.12DM.B1.3Represent a probability distribution graphically using a probability histogram, and make connections between the frequency histogram and the probability histogram
- Reading and drawing histograms
ON.OE.12DM.B1.4Recognize conditions that give rise to a random variable that follows a binomial probability distribution, calculate the probability associated with each value of the random variable, represent the distribution numerically using a table and graphically using a probability histogram, and make connections to the algebraic representation
- Binomial distribution
- Negative binomial distribution
ON.OE.12DM.B1.5Recognize conditions that give rise to a random variable that follows a hypergeometric probability distribution, calculate the probability associated with each value of the random variable, and represent the distribution numerically using a table and graphically using a probability histogram
- Hypergeometric distribution
ON.OE.12DM.B1.6Compare, with technology and using numeric and graphical representations, the probability distributions of discrete random variables
- Geometric distribution
ON.OE.12DM.B1.7Solve problems involving probability distributions, including problems arising from real-world applications
- Mean and standard deviation of binomial distribution
- Poisson distribution
ON.OE.12DM.B2.1Recognize and identify a continuous random variable, and distinguish between situations that give rise to discrete frequency distributions and situations that give rise to continuous frequency distributions
- Introduction to normal distribution
ON.OE.12DM.B2.2Recognize standard deviation as a measure of the spread of a distribution, and determine, with and without technology, the mean and standard deviation of a sample of values of a continuous random variable
- Spread of a data set - standard deviation & variance
ON.OE.12DM.B2.3Describe challenges associated with determining a continuous frequency distribution, and recognize the need for mathematical models to represent continuous frequency distributions
- Normal distribution and continuous random variable
ON.OE.12DM.B2.4Represent, using intervals, a sample of values of a continuous random variable numerically using a frequency table and graphically using a frequency histogram and a frequency polygon
- Frequency polygons
ON.OE.12DM.B2.5Recognize that theoretical probability for a continuous random variable is determined over a range of values, that the probability that a continuous random variable takes any single value is zero, and that the probabilities of ranges of values form the probability distribution associated with the random variable
- Z-scores and random continuous variables
ON.OE.12DM.B2.6Recognize that the normal distribution is commonly used to model the frequency and probability distributions of continuous random variables, describe some properties of the normal distribution, and recognize and describe situations that can be modelled using the normal distribution
- Shapes of distributions
ON.OE.12DM.B2.7Make connections, through investigation using dynamic statistical software, between the normal distribution and the binomial and hypergeometric distributions for increasing numbers of trials of the discrete distributions
- Sampling distributions
ON.OE.12DM.B2.8Recognize a z-score as the positive or negative number of standard deviations from the mean to a value of the continuous random variable, and solve probability problems involving normal distributions using a variety of tools and strategies
- Measures of relative standing - z-score, quartiles, percentiles
ON.OE.12DM.C1.1Recognize and describe the role of data in statistical studies, describe examples of applications of statistical studies, and recognize that conclusions drawn from statistical studies of the same relationship may differ
- Classification of data
ON.OE.12DM.C1.3Distinguish different types of statistical data
- Frequency tables and dot plots
ON.OE.12DM.C2.1Determine and describe principles of primary data collection and criteria that should be considered in order to collect reliable primary data
- Sampling methods
ON.OE.12DM.C2.2Explain the distinction between the terms population and sample, describe the characteristics of a good sample, explain why sampling is necessary, and describe and compare some sampling techniques
- Census and bias
ON.OE.12DM.C2.3Describe how the use of random samples with a bias or the use of non-random samples can affect the results of a study
- Central limit theorem
ON.OE.12DM.C2.4Describe characteristics of an effective survey, and design questionnaires or experiments for gathering data
- Rare event rule
ON.OE.12DM.C2.5Collect data from primary sources, through experimentation, or from secondary sources, and organize data with one or more attributes to answer a question or solve a problem
- Frequency distribution and histograms
- Stem and leaf plots
ON.OE.12DM.D1.1Recognize that the analysis of one-variable data involves the frequencies associated with one attribute, and determine, using technology, the relevant numerical summaries
- Center of a data set: mean, median, mode
ON.OE.12DM.D1.2Determine the positions of individual data points within a one-variable data set using quartiles, percentiles, and z-scores, use the normal distribution to model suitable one-variable data sets, and recognize these processes as strategies for one-variable data analysis
- Box-and-whisker plots and scatter plots
ON.OE.12DM.D1.3Generate, using technology, the relevant graphical summaries of one-variable data based on the type of data provided
- Reading and drawing bar graphs
ON.OE.12DM.D1.4Interpret, for a normally distributed population, the meaning of a statistic qualified by a statement describing the margin of error and the confidence level, and make connections between the sample size, the margin of error, and the confidence level
- Confidence levels and critical values
- Margin of error
ON.OE.12DM.D1.5Interpret statistical summaries to describe the characteristics of a one-variable data set and to compare two related one-variable data sets; describe how statistical summaries can be used to misrepresent one-variable data; and make inferences, and make and justify conclusions, from statistical summaries of one-variable data
- Making a confidence interval
ON.OE.12DM.D2.1Recognize that the analysis of two-variable data involves the relationship between two attributes, recognize the correlation coefficient as a measure of the fit of the data to a linear model, and determine, using technology, the relevant numerical summaries
- Bivariate, scatter plots and correlation
ON.OE.12DM.D2.2Recognize and distinguish different types of relationships between two variables that have a mathematical correlation
- Regression analysis
ON.OE.12DM.D2.3Generate, using technology, the relevant graphical summaries of two-variable data based on the type of data provided
- Reading and drawing line graphs
ON.OE.12DM.D2.4Determine, by performing a linear regression using technology, the equation of a line that models a suitable two-variable data set, determine the fit of an individual data point to the linear model, and recognize these processes as strategies for two-variable data analysis
- Equation of the best fit line
ON.OE.12DM.D2.5Interpret statistical summaries to describe the characteristics of a two-variable data set and to compare two related two-variable data sets; describe how statistical summaries can be used to misrepresent two-variable data; and make inferences, and make and justify conclusions, from statistical summaries of two-variable data
- Confidence intervals to estimate population mean
ON.OE.12DM.D3.1Interpret statistics presented in the media, and explain how the media, the advertising industry, and others use and misuse statistics to promote a certain point of view
- Null hypothesis and alternative hypothesis
ON.OE.12DM.D3.2Assess the validity of conclusions presented in the media by examining sources of data, methods of data collection, and possible sources of bias, and by questioning the analysis of the data and conclusions drawn from the data
- Proving claims
ON.OE.12DM.D3.3Gather, interpret, and describe information about applications of data management in occupations, and about university programs that explore these applications
- Confidence levels, significance levels and critical values
ON.OE.12DM.E1.1Pose a significant problem of interest that requires the organization and analysis of a suitable set of primary or secondary quantitative data, and conduct appropriate background research related to the topic being studied
- Test statistics
ON.OE.12DM.E1.2Design a plan to study the problem
- Traditional hypothesis testing
ON.OE.12DM.E1.3Gather data related to the study of the problem and organize the data
- P-value hypothesis testing
ON.OE.12DM.E1.4Interpret, analyse, and summarize data related to the study of the problem
- Student's t-distribution
ON.OE.12DM.E1.5Draw conclusions from the analysis of the data, evaluate the strength of the evidence, specify any limitations of the conclusions, and suggest follow-up problems or investigations
- Mean hypothesis testing with t-distribution
ON.OE.12DM.E2.1Compile a clear, well-organized, and detailed report of the investigation
- Analysis of variance (ANOVA)
ON.OE.12DM.E2.2Present a summary of the culminating investigation to an audience of their peers within a specified length of time
- Chi-square goodness of fit test
ON.OE.12DM.E2.3Answer questions about the culminating investigation and respond to critiques
- Type 1 and type 2 errors
ON.OE.12DM.E2.4Critique the mathematical work of others in a constructive manner
- Chi-Squared hypothesis testing

Grade 12 Mathematics of Data Management (MDM4U)

About Grade 12 Ontario math

Ontario follows the Ontario Curriculum, organized around strands that develop mathematical reasoning through connected concepts. In MDM4U, students work across counting and probability, probability distributions, organization of data for analysis, statistical analysis, and a culminating data management investigation. StudyPug provides step-by-step lessons, worked examples, and practice problems for every strand in this course, helping students build the skills they need for university preparation.

Strands covered: counting and probability, probability distributions, organization of data for analysis, statistical analysis, and the culminating investigation
Step-by-step lessons and worked examples for every MDM4U topic
Practice problems and guided practice aligned to the Ontario Curriculum
University preparation support for the MDM4U course

Curriculum topics by strand

Find lessons and practice for every strand in Ontario's Grade 12 Mathematics of Data Management course, aligned to the Ontario Curriculum.

Topic includes:

Practice

Video

Quiz

OE_ID

Expectations

StudyPug Topic

Ontario Grade 12 Math Topics

Counting and Probability: Permutations, combinations, sample spaces, probability rules, independent and dependent events, and conditional probability.
Probability Distributions: Discrete and continuous random variables, expected value, binomial and hypergeometric distributions, and the normal distribution.
Organization of Data for Analysis: Primary and secondary data collection, sampling techniques, survey design, and organizing one-variable and two-variable data sets.
Statistical Analysis: One-variable and two-variable data analysis, measures of spread, z-scores, linear regression, correlation, margin of error, and confidence levels.
Culminating Investigation: Posing a data management problem, designing a study plan, gathering and analyzing data, drawing conclusions, and presenting findings.

How StudyPug Helps Ontario Grade 12 Math Students

When a student gets stuck on a probability distribution or a regression problem, StudyPug lets them go back to the exact concept causing difficulty. Each lesson breaks down one idea at a time with worked examples and practice problems, so students can work through MDM4U topics at their own pace without waiting for the next class.

Students preparing for their culminating investigation can use StudyPug to review data analysis methods and statistical summaries, building confidence in the skills they need to complete and present their study.

Aligned to Ontario Grade 12 Math Curriculum

All StudyPug content for MDM4U is built around the Ontario Curriculum for Grade 12 Mathematics of Data Management, University Preparation. Every strand - from counting and probability through to the culminating investigation - matches what Ontario students are expected to learn, so practice on StudyPug directly supports what is being taught in class.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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