Get help with Applied Mathematics, Grade 12 (40S)
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The official Manitoba Applied Mathematics, Grade 12 (40S) curriculum
Manitoba defines Applied Mathematics, Grade 12 (40S) by strands and outcomes. MapleMind teaches the same curriculum reorganized for one-skill-at-a-time tutoring — the table shows exactly where every official strand lands, and the ministry's own wording is quoted under each unit below.
Official source Manitoba's official curriculumRead it on the government site — edu.gov.mb.ca ↗| Official strand | Outcomes | Where MapleMind teaches it |
|---|---|---|
| Strand FM | 3 | Financial Mathematics |
| Strand L | 3 | Logical Reasoning |
| Strand P | 6 | Probability |
| Strand R | 3 | Relations and Functions |
| Strand RP | 1 | Mathematics Research Project |
| Strand D | 1 | Design and Measurement |
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How MapleMind teaches Applied Mathematics, Grade 12 (40S) — every unit, lesson, and skill
Every skill below runs as a short session: a plain-words lesson, a worked example, solving it together, then a five-question skill check that earns up to three stars. Guided Mode keeps it teaching instead of answer-handing — turning it off needs a parent's password.
Unit 1Financial MathematicsOfficial strand · Strand FM
Compound interest in financial decisions, the costs and benefits of renting, leasing, and buying, and analyzing an investment portfolio.
Compound Interest
- Compound versus simple interest12A.FM.1 — Compare the advantages and disadvantages of compound and simple interest, and graph and describe how the compounding period and other variables affect the total interest earned or paid.
- Loan costs and credit options12A.FM.1 — Determine, using technology, the total cost of a loan under different amortization periods, interest rates, and compounding terms, and compare credit options such as bank or store credit cards and special promotions.
Renting, Leasing, and Buying
- Appreciation, depreciation, and comparing options12A.FM.2 — Identify and describe assets that appreciate or depreciate, and compare renting, leasing, and buying using examples.
- Justifying a rent, lease, or buy decision12A.FM.2 — Justify, for a specific set of circumstances, whether renting, leasing, or buying is advantageous, and solve a cost-and-benefit problem using technology.
Investment Portfolios
- Investment value and the Rule of 7212A.FM.3 — Determine and graph the total value of an investment with and without regular contributions, and apply the Rule of 72 to estimate doubling time, explaining its limitations.
- Strategies and comparing portfolios12A.FM.3 — Determine investment strategies to achieve a financial goal, explain the advantages of long-term versus short-term options, and compare the strengths and weaknesses of two or more portfolios.
The official wording — 3 outcomes in this unit
- 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.3
Analyze an investment portfolio in terms of Q Q interest rate Q Q rate of return Q Q total return
Unit 2Logical ReasoningOfficial strand · Strand L
Puzzles and games with numerical and logical reasoning, set theory, and conditional statements.
Puzzles and Games
- Strategies for puzzles and games12A.L.1 — Determine, explain, and verify a strategy to solve a puzzle or win a game using problem-solving strategies, correct errors in a strategy, and create a variation on a puzzle or game.
Set Theory
- Sets and Venn diagram operations12A.L.2 — Explain how set theory is used, provide examples of empty, disjoint, subset, and universal sets, describe regions of a Venn diagram, and determine the complement, intersection, or union of two sets.
- Solving problems with sets12A.L.2 — Organize information using graphic organizers, identify and correct errors in a set solution, and solve and record a contextual problem that involves sets.
Conditional Statements
- If-then statements and their forms12A.L.3 — Analyze an if-then statement to make and justify a conclusion, determine its converse, inverse, and contrapositive, judge each one's truth, and provide a counter-example when false.
- Biconditionals and truth tables12A.L.3 — Identify contexts where a biconditional statement is justified, make and justify decisions using 'what if?' questions, and summarize logical arguments using a truth table or Venn diagram.
The official wording — 3 outcomes in this unit
- 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.3
Solve problems that involve conditional statements.
Unit 3ProbabilityOfficial strand · Strand P
Odds and probability statements, mutually exclusive and non-mutually exclusive events, independent and dependent events, the fundamental counting principle, permutations, and combinations.
Odds and Probability
- Interpreting odds and probability12A.P.1 — Interpret and assess probability and odds statements, explain the relationship between odds (part-part) and probability (part-whole), and express odds as a probability and vice versa.
Combined Events
- Mutually exclusive and non-mutually exclusive events12A.P.2 — Classify events as mutually exclusive or non-mutually exclusive, identify complementary events, and solve contextual problems involving their probabilities.
- Independent and dependent events12A.P.3 — Compare dependent and independent events, and determine the probability of two dependent or two independent events, including the probability of an event given a previous event.
Counting, Permutations, and Combinations
- The fundamental counting principle12A.P.4 — Represent counting problems with a graphic organizer, generalize the fundamental counting principle, and solve a counting problem using it.
- Permutations with factorial notation12A.P.5 — Represent arrangements using factorial notation, evaluate factorials, simplify fractions containing factorials, and determine the number of permutations of n elements taken r at a time.
- Permutations with identical elements12A.P.5 — Determine the number of permutations of n elements where some elements are identical, explain the effect of identical elements, and solve a contextual problem involving probability and permutations.
- Combinations12A.P.6 — Explain why order matters for permutations but not combinations, determine the number of combinations of n elements taken r at a time, and solve a contextual problem involving probability and combinations.
The official wording — 6 outcomes in this unit
- 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.6
Solve problems that involve combinations.
Unit 4Relations and FunctionsOfficial strand · Strand R
Modelling data with polynomial, exponential and logarithmic, and sinusoidal functions using technology.
Polynomial Models
- Modelling data with polynomial functions12A.R.1 — Graph data and determine the polynomial function (degree three or less) that best approximates it, describe its characteristics, and interpret the graph to solve a contextual problem using technology.
Exponential, Logarithmic, and Sinusoidal Models
- Modelling data with exponential functions12A.R.2 — Graph data and determine the exponential function that best approximates growth or decay data, describe its characteristics, and interpret the graph to solve a problem using technology.
- Modelling data with logarithmic functions12A.R.2 — Graph data and determine the logarithmic function that best approximates data that rises then levels off, describe its characteristics, and interpret the graph to solve a problem using technology.
- Modelling data with sinusoidal functions12A.R.3 — Graph periodic data and determine the sinusoidal function that best approximates it, describe its characteristics, and interpret the graph to solve a contextual problem using technology.
The official wording — 3 outcomes in this unit
- 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.3
Represent data, using sinusoidal functions, to solve problems.
Unit 5Mathematics Research ProjectOfficial strand · Strand RP
Researching and presenting on a current event or area of interest that involves mathematics.
The Research Project
- Designing the project and collecting data12A.RP.1 — Choose a current event or area of interest that involves mathematics, and collect primary or secondary data related to the topic.
- Assessing and analyzing the data12A.RP.1 — Assess the accuracy, reliability, and relevance of the collected data, identifying bias and collection methods, and interpret the data using statistical methods where applicable.
- Organizing and presenting the project12A.RP.1 — Identify any controversial issues and present multiple sides with supporting data, then organize and present the research project with or without technology.
The official wording — 1 outcome in this unit
- 12A.RP.1
Research and give a presentation on a current event or an area of interest that involves mathematics.
Unit 6Design and MeasurementOfficial strand · Strand D
Analyzing objects, shapes, and processes to solve cost and design problems.
Design and Costing
- Costing with measurement and unit prices12A.D.1 — Solve problems involving perimeter, area, and volume using dimensions and unit prices, estimate costs for a given design, and identify and correct errors in a costing solution.
- Designing within a budget12A.D.1 — Design an object, shape, layout, or process within a specified budget, balancing measurement, cost, and design requirements.
The official wording — 1 outcome in this unit
- 12A.D.1
Analyze objects, shapes, and processes to solve cost and design problems.
Printable workbook · A keepsake of the year
A Applied Mathematics, Grade 12 (40S) workbook worth keeping
Built from the same official curriculum as this page. Before and after each skill above, your student colours in how sure they feel — so the two of you can see, on one page, what's clicking and what needs another look. It's a quiet way to follow how the year is really going.
By June it's full of their own handwriting: units worked through, confidence grown, a mid-year check-in, notes from parent-teacher night, and a certificate at the end. Less a worksheet, more a record of the year worth keeping on the shelf.
Instant download · see every page, reviews and the full description · five or more workbooks are $2.99 each
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Common questions
Can MapleMind help me with Applied Mathematics, Grade 12 (40S)?
Yes. MapleMind's AI tutor covers all 27 skills in Manitoba's Applied Mathematics, Grade 12 (40S) — you pick the exact skill, and the tutor teaches it step by step: a short lesson, a worked example, solving together, then a skill check to show it stuck.
Is MapleMind aligned to Manitoba's official curriculum?
Yes. Every skill in this course maps to an official outcome code from Manitoba's Grade 12 Mathematics curriculum, and the ministry's own wording is quoted under each unit on this page — with the official government source linked so you can check it yourself.
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That's the point of skill-level tutoring: open Applied Mathematics, Grade 12 (40S) in the app, tap the exact skill from the list on this page, and the tutor teaches just that — no wading through lessons you don't need.
Does MapleMind work in French or other languages?
Yes — 14 languages, including French. Both the app and the tutor's explanations switch to the language you choose.
Where can I see the official Manitoba curriculum for Applied Mathematics, Grade 12 (40S)?
The official source is linked on this page — Manitoba's official curriculum. The outline here follows it: every MapleMind skill carries its official outcome code, and the ministry's own wording is quoted under each unit.
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