How does Grade 12 math differ from Grade 11?

Grade 12 math in Ontario is more advanced, focusing on complex problem-solving and abstract thinking. It prepares students for university-level mathematics and specialized fields like engineering and sciences.

Which Grade 12 math course should I choose?

Your choice depends on your post-secondary goals. Advanced Functions and Calculus are essential for STEM programs, while Data Management is valuable for social sciences and business-related fields.

Are there online resources for Grade 12 math support?

Yes, there are numerous online platforms offering video lessons, practice problems, and personalized tutoring for Grade 12 math courses, aligned with the Ontario curriculum.

What are the main topics covered in Advanced Functions 12?

Advanced Functions 12 covers exponential and logarithmic functions, trigonometric functions, rational functions, and an introduction to mathematical reasoning and proof techniques.

How difficult is Calculus and Vectors 12?

Calculus and Vectors 12 is considered challenging, introducing fundamental calculus concepts like limits, derivatives, and integrals. It requires strong algebraic skills and abstract thinking abilities.

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Grade 12 Math Courses - Ontario Curriculum

Discover Ontario's Grade 12 math options, from Advanced Functions to Data Management. Prepare for university-level mathematics and explore diverse career pathways in STEM fields.

Advanced Functions 12

Calculus and Vectors 12

Mathematics of Data Management 12

Mathematics for College Technology 12

Foundations for College Mathematics 12

Mathematics for Work and Everyday Life 12

Ontario Grade 12 Math Curriculum - Advanced Functions & More

OE_ID	Expectations	StudyPug Topic
ON.OE.12WE.A1.1	1.1: Read and interpret graphs obtained from various sources	Classification of data Frequency distribution and histograms Stem and leaf plots Frequency polygons Shapes of distributions

ON.OE.12WE.A1.2

1.2: Explain the distinction between the terms population and sample, describe the characteristics of a good sample, and explain why sampling is necessary

Sampling methods

Census and bias

ON.OE.12WE.A1.3

1.3: Collect categorical data from primary sources, through experimentation involving observation or measurement, or from secondary sources, and organize and store the data using a variety of tools

Organizing data

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

ON.OE.12WE.A1.4

1.4: Represent categorical data by constructing graphs using a variety of tools

Reading and drawing Venn diagrams

Frequency tables and dot plots

ON.OE.12WE.A1.5

1.5: Make inferences based on the graphical representation of data, and justify conclusions orally or in writing using convincing arguments

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

ON.OE.12WE.A1.6

1.6: Make and justify conclusions about a topic of personal interest by collecting, organizing, representing, and making inferences from categorical data

Bivariate, scatter plots and correlation

Regression analysis

Equation of the best fit line

ON.OE.12WE.A1.7

1.7: Explain how the media, the advertising industry, and others use and misuse statistics to promote a certain point of view

Sampling distributions

Central limit theorem

Rare event rule

ON.OE.12WE.A1.8

1.8: Gather, interpret, and describe information about applications of data management in the workplace and in everyday life

Median and mode

Mean

Range and outliers

Application of averages

ON.OE.12WE.A2.1

2.1: Determine the theoretical probability of an event, and represent the probability in a variety of ways

Introduction to probability

Organizing outcomes

ON.OE.12WE.A2.2

2.2: Identify examples of the use of probability in the media and various ways in which probability is represented

Probability with Venn diagrams

ON.OE.12WE.A2.3

2.3: Perform simple probability experiments, record the results, and determine the experimental probability of an event

Probability of independent events

Comparing experimental and theoretical probability

ON.OE.12WE.A2.4

2.4: Compare, through investigation, the theoretical probability of an event with the experimental probability, and describe how uncertainty explains why they might differ

Addition rule for "OR"

Multiplication rule for "AND"

ON.OE.12WE.A2.5

2.5: Determine, 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

Conditional probability

Probability involving permutations and combinations

ON.OE.12WE.A2.6

2.6: Interpret information involving the use of probability and statistics in the media, and describe how probability and statistics can help in making informed decisions in a variety of situations

Law of total probability

Bayes' rule

ON.OE.12WE.B1.1

1.1: Identify the financial implications and the non-financial implications associated with living independently

Taxes, discounts, tips and more

Simple interest

ON.OE.12WE.B1.2

1.2: Gather and compare, through investigation, information about the costs and the advantages and disadvantages of different types of rental accommodation in the local community

Finance: Compound interest

Continuous growth and decay

ON.OE.12WE.B1.3

1.3: Gather and compare, through investigation, information about purchase prices of different types of owned accommodation in the local community

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

ON.OE.12WE.B1.4

1.4: Gather, interpret, and compare information about the different types of ongoing living expenses associated with renting and owning accommodation and related costs

Logarithmic scale: dB scale

Finance: Future value and present value

ON.OE.12WE.B1.5

1.5: Gather, interpret, and describe information about the rights and responsibilities of tenants and landlords

Ratios

Rates

ON.OE.12WE.B1.6

1.6: Generate a checklist of necessary tasks associated with moving, and estimate the total cost involved under various conditions

Proportions

Representing percents

ON.OE.12WE.B2.1

2.1: Categorize personal expenses as non-discretionary or discretionary

Percents, fractions, and decimals

Percent of a number

ON.OE.12WE.B2.2

2.2: Categorize personal non-discretionary expenses as fixed or variable

Adding and multiplying percents

ON.OE.12WE.B2.3

2.3: Read and interpret prepared individual or family budgets, identify and describe the key components of a budget, and describe how budgets can reflect personal values

Model and solve one-step linear equations: ax = b, x/a = b

ON.OE.12WE.B2.4

2.4: Design, explain, and justify a monthly budget suitable for an individual or family described in a given case study that provides the specifics of the situation, with technology and without technology

Solving two-step linear equations using addition and subtraction: ax + b = c

Solving two-step linear equations using multiplication and division: x/a + b = c

ON.OE.12WE.B2.5

2.5: Identify and describe factors to be considered in determining the affordability of accommodation in the local community

Solving linear equations using multiplication and division

Solving two-step linear equations using distributive property: a(x + b) = c

ON.OE.12WE.B2.6

2.6: Make adjustments to a budget to accommodate changes in circumstances, with technology

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

ON.OE.12WE.B3.1

3.1: Explain why most Canadians are expected to file a personal income tax return each year, and identify and describe the major parts of a personal income tax return

Solving linear equations with variables on both sides

Solving literal equations

ON.OE.12WE.B3.2

3.2: Gather, interpret, and describe the information and documents required for filing a personal income tax return, and explain why they are required

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

ON.OE.12WE.B3.3

3.3: Gather, interpret, and compare information about common tax credits and tax deductions

Solving multi-step linear inequalities

Compound inequalities

ON.OE.12WE.B3.4

3.4: Complete a simple personal income tax return, with or without tax preparation software

Squares and square roots

Pythagorean theorem

ON.OE.12WE.B3.5

3.5: Gather, interpret, and describe some additional information that a self-employed individual should provide when filing a personal income tax return

Estimating square roots

Using the pythagorean relationship

ON.OE.12WE.B3.6

3.6: Gather, interpret, and describe information about services that will complete a personal income tax return and resources that will help with completing a personal income tax return, and compare the services and resources

Square and square roots

Applications of pythagorean theorem

ON.OE.12WE.B3.7

3.7: Gather, interpret, and describe information about applications of the mathematics of personal finance in the workplace

Cubic and cube roots

Evaluating and simplifying radicals

ON.OE.12WE.C1.1

1.1: Measure, using a variety of tools, the lengths of common objects and the capacities of common containers, using the metric system and the imperial system

Metric systems

Imperial systems

ON.OE.12WE.C1.2

1.2: Estimate lengths, distances, and capacities in metric units and in imperial units by applying personal referents

Conversions between metric and imperial systems

Conversions involving squares and cubic

ON.OE.12WE.C1.3

1.3: Estimate quantities, and describe the strategies used

Converting radicals to mixed radicals

Converting radicals to entire radicals

ON.OE.12WE.C1.4

1.4: Convert measures within systems, as required within applications that arise from familiar contexts

Adding and subtracting radicals

Multiplying and dividing radicals

ON.OE.12WE.C1.5

1.5: Convert measures between systems, as required within applications that arise from familiar contexts

Rationalize the denominator

Product rule of exponents

ON.OE.12WE.C2.1

2.1: Construct accurate right angles in practical contexts, and explain connections to the Pythagorean theorem

Quotient rule of exponents

Solving for exponents

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

ON.OE.12WE.C2.2

2.2: Apply the concept of perimeter in familiar contexts

Power of a product rule

Power of a quotient rule

Surface area and volume of prisms

ON.OE.12WE.C2.3

2.3: Estimate the areas and volumes of irregular shapes and figures, using a variety of strategies

Power of a power rule

Negative exponent rule

ON.OE.12WE.C2.4

2.4: Solve problems involving the areas of rectangles, triangles, and circles, and of related composite shapes, in situations arising from real-world applications

Combining the exponent rules

Scientific notation

Surface area and volume of pyramids

Surface area and volume of cylinders

ON.OE.12WE.C2.5

2.5: Solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite figures, in situations arising from real-world applications

Convert between radicals and rational exponents

Surface area and volume of spheres

Relationship between two variables

ON.OE.12WE.C2.6

2.6: Construct a two-dimensional scale drawing of a familiar setting on grid paper or using design or drawing software

Understand relations between x- and y-intercepts

Domain and range of a function

ON.OE.12WE.C2.7

2.7: Construct, with reasonable accuracy, a three-dimensional scale model of an object or environment of personal interest

Identifying functions

Function notation

ON.OE.12WE.C2.8

2.8: Investigate, plan, design, and prepare a budget for a household improvement, using appropriate technologies

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Graphing from slope-intercept form y=mx+b

ON.OE.12WE.C3.1

3.1: Identify and describe applications of ratio and rate, and recognize and represent equivalent ratios and equivalent rates, using a variety of tools

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

ON.OE.12WE.C3.2

3.2: Identify situations in which it is useful to make comparisons using unit rates, and solve problems that involve comparisons of unit rates

Parallel and perpendicular lines in linear functions

Applications of linear relations

ON.OE.12WE.C3.3

3.3: Identify and describe real-world applications of proportional reasoning, distinguish between a situation involving a proportional relationship and a situation involving a non-proportional relationship in a personal and/or workplace context, and explain their reasoning

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

Slope equation:

m = \frac{y_2-y_1}{x_2- x_1}

ON.OE.12WE.C3.4

3.4: Identify and describe the possible consequences of errors in proportional reasoning

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

ON.OE.12WE.C3.5

3.5: Solve problems involving proportional reasoning in everyday life

Point-slope form: y - y_1 = m(x - x_1)

Rate of change

ON.OE.12WE.C3.6

3.6: Solve problems involving proportional reasoning in work-related situations

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

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