Manitoba · Grade 12
Applied Mathematics, Grade 12 (40S)
Manitoba’s Grade 12 math course, from Financial Mathematics to Design and Measurement.
- Units
- 6
- Lessons
- 13
- Skills
- 27
- Provincial exam
- 20% of the final mark
- Official curriculum
- Manitoba Education
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 6 skills
Financial Mathematics
Compound Interest
Compound versus simple interest
I can explain how compound interest grows and compare it with simple interest.
Official code: 12A.FM.1
Loan costs and credit options
I can find the total cost of a loan and compare credit options.
Official code: 12A.FM.1
Renting, Leasing, and Buying
Appreciation, depreciation, and comparing options
I can tell whether an asset appreciates or depreciates and compare renting, leasing, and buying.
Official code: 12A.FM.2
Justifying a rent, lease, or buy decision
I can justify a rent, lease, or buy decision for a real situation.
Official code: 12A.FM.2
Investment Portfolios
Investment value and the Rule of 72
I can find an investment's value over time and use the Rule of 72.
Official code: 12A.FM.3
Strategies and comparing portfolios
I can choose an investment strategy and compare portfolios.
Official code: 12A.FM.3
The official wording · 6 outcomes
- 12A.FM.1
- Solve problems that involve compound interest in financial decision making.
- 12A.FM.1
- Solve problems that involve compound interest in financial decision making.
- 12A.FM.2
- Analyze costs and benefits of renting, leasing, and buying.
- 12A.FM.2
- Analyze costs and benefits of renting, leasing, and buying.
- 12A.FM.3
- Analyze an investment portfolio in terms of Q Q interest rate Q Q rate of return Q Q total return
- 12A.FM.3
- Analyze an investment portfolio in terms of Q Q interest rate Q Q rate of return Q Q total return
Key ideas
Compound interest earns interest on previously earned interest; simple interest does not.
An appreciating asset gains value over time; a depreciating asset loses value.
Regular contributions add to the principal, so the investment grows faster.
More frequent compounding periods increase the total interest over time.
Renting, leasing, and buying each trade up-front cost against long-term ownership.
Watch out for
- Thinking simple and compound interest give the same total over many years.
- Assuming every large purchase appreciates.
- Treating the Rule of 72 as exact rather than an estimate.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 5 skills
Logical Reasoning
Puzzles and Games
Strategies for puzzles and games
I can find and verify a winning strategy for a puzzle or game.
Official code: 12A.L.1
Set Theory
Sets and Venn diagram operations
I can use Venn diagrams to find unions, intersections, and complements.
Official code: 12A.L.2
Solving problems with sets
I can solve a real problem using sets and a Venn diagram.
Official code: 12A.L.2
Conditional Statements
If-then statements and their forms
I can find the converse, inverse, and contrapositive of an if-then statement and judge each.
Official code: 12A.L.3
Biconditionals and truth tables
I can use biconditionals and truth tables to summarize logical arguments.
Official code: 12A.L.3
The official wording · 5 outcomes
- 12A.L.1
- Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies.
- 12A.L.2
- Solve problems that involve the application of set theory.
- 12A.L.2
- Solve problems that involve the application of set theory.
- 12A.L.3
- Solve problems that involve conditional statements.
- 12A.L.3
- Solve problems that involve conditional statements.
Key ideas
Strategies include guess-and-check, looking for a pattern, working backward, and eliminating possibilities.
A Venn diagram shows how sets overlap; the intersection is the shared region.
An if-then statement has a hypothesis and a conclusion.
A good strategy can be verified and explained, not just guessed.
The complement of a set is everything in the universal set that is not in it.
Watch out for
- Treating a lucky solution as a reliable strategy.
- Confusing union and intersection.
- Assuming the converse of a true statement is also true.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 7 skills
Probability
Odds and Probability
Interpreting odds and probability
I can convert between odds and probability and judge a probability claim.
Official code: 12A.P.1
Combined Events
Mutually exclusive and non-mutually exclusive events
I can find the probability of mutually exclusive and overlapping events.
Official code: 12A.P.2
Independent and dependent events
I can find the probability of independent and dependent events.
Official code: 12A.P.3
Counting, Permutations, and Combinations
The fundamental counting principle
I can count outcomes using the fundamental counting principle.
Official code: 12A.P.4
Permutations with factorial notation
I can count arrangements using factorials and the permutation formula.
Official code: 12A.P.5
Permutations with identical elements
I can count arrangements when some elements are identical.
Official code: 12A.P.5
Combinations
I can count selections where order does not matter.
Official code: 12A.P.6
The official wording · 7 outcomes
- 12A.P.1
- Interpret and assess the validity of odds and probability statements.
- 12A.P.2
- Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events.
- 12A.P.3
- Solve problems that involve the probability of independent and dependent events.
- 12A.P.4
- Solve problems that involve the fundamental counting principle.
- 12A.P.5
- Solve problems that involve permutations.
- 12A.P.5
- Solve problems that involve permutations.
- 12A.P.6
- Solve problems that involve combinations.
Key ideas
Probability compares favourable outcomes to the whole (part-whole).
Mutually exclusive events cannot both happen, so we add their probabilities.
If one choice has m ways and another has n ways, together they have m x n ways.
Odds compare favourable to unfavourable outcomes (part-part).
For non-mutually exclusive events we subtract the overlap to avoid double-counting.
Watch out for
- Treating odds and probability as the same ratio.
- Adding probabilities of overlapping events without subtracting the overlap.
- Adding the number of choices instead of multiplying.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 4 skills
Relations and Functions
Polynomial Models
Modelling data with polynomial functions
I can fit a polynomial function to data and use it to solve a problem.
Official code: 12A.R.1
Exponential, Logarithmic, and Sinusoidal Models
Modelling data with exponential functions
I can fit an exponential function to growth or decay data.
Official code: 12A.R.2
Modelling data with logarithmic functions
I can fit a logarithmic function to data that levels off.
Official code: 12A.R.2
Modelling data with sinusoidal functions
I can fit a sinusoidal function to repeating data.
Official code: 12A.R.3
The official wording · 4 outcomes
- 12A.R.1
- Represent data, using polynomial functions (of degree ≤ 3), to solve problems.
- 12A.R.2
- Represent data, using exponential and logarithmic functions, to solve problems.
- 12A.R.2
- Represent data, using exponential and logarithmic functions, to solve problems.
- 12A.R.3
- Represent data, using sinusoidal functions, to solve problems.
Key ideas
A polynomial regression finds the curve of best fit for data that bends.
An exponential model fits data that grows or decays by a constant factor.
The graph's shape (turning points, intercepts) reveals features of the situation.
The base determines whether the model grows or decays.
A logarithmic model fits data that rises quickly then flattens.
Watch out for
- Forcing a straight line onto data that clearly curves.
- Using an exponential model for data that grows at a constant rate.
- Extrapolating a polynomial model far beyond the data.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 3 skills
Mathematics Research Project
The Research Project
Designing the project and collecting data
I can choose a math-related topic and collect data on it.
Official code: 12A.RP.1
Assessing and analyzing the data
I can judge whether my data is trustworthy and analyze it.
Official code: 12A.RP.1
Organizing and presenting the project
I can present my research project clearly and fairly.
Official code: 12A.RP.1
The official wording · 3 outcomes
- 12A.RP.1
- Research and give a presentation on a current event or an area of interest that involves mathematics.
- 12A.RP.1
- Research and give a presentation on a current event or an area of interest that involves mathematics.
- 12A.RP.1
- Research and give a presentation on a current event or an area of interest that involves mathematics.
Key ideas
A good topic is a real current event with mathematics behind it.
Data can be primary (collected yourself) or secondary (from a source).
Data can carry bias from how it was collected or reported.
Cross-checking sources shows whether data is consistent and relevant.
A fair presentation shows more than one side of a controversial issue.
Watch out for
- Picking a topic with no real mathematical content.
- Collecting data before framing a clear question.
- Treating all sources as equally reliable.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 6 · 2 skills
Design and Measurement
Design and Costing
Costing with measurement and unit prices
I can cost a design from its measurements and unit prices.
Official code: 12A.D.1
Designing within a budget
I can design something that meets requirements within a budget.
Official code: 12A.D.1
The official wording · 2 outcomes
- 12A.D.1
- Analyze objects, shapes, and processes to solve cost and design problems.
- 12A.D.1
- Analyze objects, shapes, and processes to solve cost and design problems.
Key ideas
Cost is found by multiplying a measured quantity (area, volume) by a unit price.
A simplified model gives a good estimate for a complex measurement problem.
A design must satisfy requirements while staying within the budget.
Trade-offs between size, material, and cost shape the final design.
Watch out for
- Using the wrong measurement (perimeter instead of area) for a cost.
- Mismatching the unit price with the measured unit.
- Designing first and checking the budget only at the end.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Plan the term
Pick your term and the days you study. Each unit gets its share of the weeks and comes back a week later for a review. The last two weeks go over the whole course.
The mark you need
Your class mark counts for 80% of the final mark, the exam for 20%.
You need
50% on the exam
With 75% in class, your final mark lands between 60% (0 on the exam) and 80% (100% on it).
Which course?
Manitoba has 4 math courses for Grade 12. Here they are side by side.
- Applied Mathematics, Grade 12 (40S)This course6 units · 27 skillsGrade 12 Applied Mathematics Achievement TestWhat it coversFinancial Mathematics · Logical Reasoning · Probability · Relations and Functions · Mathematics Research Project · Design and Measurement
- Essential Mathematics, Grade 12 (40S)9 units · 24 skillsGrade 12 Essential Mathematics Achievement TestWhat it coversAnalysis of Games and Numbers · Vehicle Finance · Statistics · Precision Measurement · Career Life · Home Finance · Geometry and Trigonometry · Business Finance · Probability
- Introduction to Calculus, Grade 12 (40S)45S4 units · 19 skillsNo provincial examWhat it coversLimits · Derivatives · Applications of Derivatives · Integration (Integrals)
- Pre-Calculus Mathematics, Grade 12 (40S)3 units · 34 skillsGrade 12 Pre-Calculus Mathematics Achievement TestWhat it coversTrigonometry · Relations and Functions · Permutations, Combinations and Binomial Theorem
What a university, college or program asks for is theirs to say: check its admission page, and your school’s course guide.
The official curriculum
This page follows Manitoba’s own curriculum for Applied Mathematics, Grade 12 (40S).
Study it in MapleMind
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Course Companion
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Questions about Applied Mathematics, Grade 12 (40S)
What is Applied Mathematics, Grade 12 (40S)?
Manitoba’s Grade 12 math course: 6 units and 27 skills, from Financial Mathematics to Design and Measurement.
What units are in Applied Mathematics, Grade 12 (40S)?
1. Financial Mathematics, 2. Logical Reasoning, 3. Probability, 4. Relations and Functions, 5. Mathematics Research Project and 6. Design and Measurement.
Is there a provincial exam for Applied Mathematics, Grade 12 (40S)?
Yes. The Grade 12 Applied Mathematics Achievement Test counts for 20% of the final mark. Next sitting: January 26, 2027.
Can MapleMind help with Applied Mathematics, Grade 12 (40S)?
Yes. MapleMind teaches every skill of Applied Mathematics, Grade 12 (40S), step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.
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