British Columbia · Grade 12
Foundations of Mathematics 12
- FOM 12
British Columbia’s Grade 12 math course, from Geometric Explorations: Constructions, Conics & Fractals to Financial Planning.
- Units
- 4
- Lessons
- 5
- Skills
- 10
- Provincial exam
- None
- Official curriculum
- BC Mathematics 12
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 3 skills
Geometric Explorations: Constructions, Conics & Fractals
Geometric Constructions
Constructions: bisectors, tangents, polygons, tessellations
I can perform classical constructions and explain the circle-geometry facts that make them work.
Skill 1.1
Conic sections as loci
I can define the circle, ellipse, parabola, and hyperbola as loci and name their applications.
Skill 1.2
Fractals as iteration
I can build classic fractals by iteration and quantify how their lengths and areas change per step.
Skill 1.3
The official wording · 3 outcomes
- 1.1
- geometric explorations
- 1.2
- geometric explorations
- 1.3
- geometric explorations
Key ideas
A perpendicular bisector construction works because every point equidistant from two endpoints lies on that bisector — the two arcs FIND those points.
A tangent to a circle is perpendicular to the radius at the contact point — the construction builds that right angle.
Regular polygons come from equal arc steps around a circle; shapes that tile the plane without gaps make tessellations.
A locus is the set of points obeying a rule: constant distance from a centre (circle), constant SUM of distances to two foci (ellipse), equal distance to focus and directrix (parabola), constant DIFFERENCE (hyperbola).
Slicing a cone at different angles yields all four curves — hence 'conic sections'.
Watch out for
- Measuring with a ruler mid-construction — classical construction allows only compass and unmarked straightedge.
- Assuming every polygon tessellates — regular pentagons famously leave gaps.
- Calling an ellipse 'a squashed circle with two centres' — the foci are not centres; the string-sum rule is the definition.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 2 skills
Function Graphs & Regression (Technology)
Recognizing Function Families
Identifying function families from graphs
I can name a graph's function family from its signature features.
Skill 2.1
Regression analysis: choosing and applying the model
I can choose an appropriate regression model for a data set, fit it with technology, and use it to predict.
Skill 2.2
The official wording · 2 outcomes
- 2.1
- graphical representations of polynomial, logarithmic, exponential, and sinusoidal functions
- 2.2
- regression analysis
Key ideas
Signatures: polynomials turn (finitely many hills); exponentials hug a horizontal asymptote then explode; logs hug a vertical asymptote then crawl; sinusoids repeat forever between two bounds.
Symmetry and end behaviour narrow the polynomial's degree; period and midline describe the sinusoid.
Technology lets you test a guess instantly: overlay a candidate function and compare.
The scatter plot chooses the model: look at its shape FIRST, then fit — a high r² on the wrong family still lies.
Interpolation (inside the data) is trustworthy; extrapolation (beyond it) is a bet that the pattern continues.
Watch out for
- Confusing log and radical graphs — the log's vertical asymptote at x = 0 is the tell.
- Calling any wavy graph sinusoidal — true sinusoids have constant period and amplitude.
- Chasing the highest r² across families without looking at the scatter — an overfit polynomial wiggles through noise.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 3 skills
Combinatorics, Odds & Probability
Permutations, Combinations & Pascal's Triangle
Permutations, combinations, and pathways
I can decide between permutations and combinations, compute both, and count pathways with Pascal's triangle.
Skill 3.1
Odds, Probability & Expected Value
Odds and compound, conditional probability
I can work with odds, compound events, Venn diagrams, and conditional probability.
Skill 3.2
Expected value
I can compute expected value and use it to judge games and decisions.
Skill 3.3
The official wording · 3 outcomes
- 3.1
- combinatorics
- 3.2
- odds, probability, and expected value
- 3.3
- odds, probability, and expected value
Key ideas
Order matters → permutation (nPr); order doesn't → combination (nCr). 'President and VP' permutes; 'a committee of two' combines.
Odds compare favourable TO unfavourable (3:1); probability compares favourable to TOTAL (3/4) — convertible both ways.
The fundamental counting principle multiplies stage choices: 4 shirts × 3 pants = 12 outfits.
Addition rule: P(A or B) = P(A) + P(B) − P(A and B); the overlap subtraction vanishes only for mutually exclusive events.
Grid pathways and nCr meet in Pascal's triangle — each entry counts the routes to reach it.
Watch out for
- Using permutations for committees — handshakes and committees don't care about order; dividing by r! fixes the overcount.
- Reading 3:1 odds as probability 1/3 — odds ratios exclude the total; the probability is 3/4 (for) or 1/4 (against).
- Adding stage choices instead of multiplying — AND-choices multiply; OR-choices add.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 2 skills
Financial Planning
Building a Financial Plan
Developing a personal financial portfolio
I can assemble a personal financial portfolio: accounts, credit strategy, savings, and investment options.
Skill 4.1
Mortgages, risk, and changing rates
I can analyze a mortgage and stress-test a financial plan against rate changes and risk.
Skill 4.2
The official wording · 2 outcomes
- 4.1
- financial planning
- 4.2
- financial planning
Key ideas
A portfolio is the whole picture: income, accounts, credit, insurance, savings, and investments working as one plan.
Credit is a tool with a price — used and cleared monthly it builds a score; carried at 21% it compounds against you.
Market options ladder by risk: savings accounts and GICs guard money; index funds and stocks grow it with swings; diversification spreads the risk.
A mortgage renews: today's rate is rented, not owned — a renewal at +2% can raise payments by hundreds.
Fixed rates buy certainty; variable rates buy (usual) savings with exposure — the choice IS a risk decision.
Watch out for
- Treating investing as gambling and avoiding it entirely — long horizons and diversification tame volatility that single stocks don't.
- Chasing credit-card points while carrying a balance — interest devours rewards many times over.
- Assuming today's mortgage payment is fixed for 25 years — the TERM (3-5 yrs) renews at market rates.
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.
Which course?
British Columbia has 3 math courses for Grade 12. Here they are side by side.
- Calculus 12CALC 124 units · 11 skillsNo provincial examWhat it coversFunctions for Calculus · Limits & Continuity · Differentiation · Integration
- Foundations of Mathematics 12This courseFOM 124 units · 10 skillsNo provincial examWhat it coversGeometric Explorations: Constructions, Conics & Fractals · Function Graphs & Regression (Technology) · Combinatorics, Odds & Probability · Financial Planning
- Pre-calculus 12PREC 124 units · 13 skillsNo provincial examWhat it coversTransformations of Functions & Relations · Exponential & Logarithmic Functions · Polynomial & Rational Functions · Trigonometric Functions, Equations & Identities
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 British Columbia’s own curriculum for Foundations of Mathematics 12.
Textbooks
In British Columbia, each school district chooses its own textbooks: the ministry no longer recommends them. The ministry’s page
Study it in MapleMind
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Course Companion
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Questions about Foundations of Mathematics 12
What is Foundations of Mathematics 12?
British Columbia’s Grade 12 math course: 4 units and 10 skills, from Geometric Explorations: Constructions, Conics & Fractals to Financial Planning.
What units are in Foundations of Mathematics 12?
1. Geometric Explorations: Constructions, Conics & Fractals, 2. Function Graphs & Regression (Technology), 3. Combinatorics, Odds & Probability and 4. Financial Planning.
Is there a provincial exam for Foundations of Mathematics 12?
No. British Columbia gives no provincial exam for Foundations of Mathematics 12.
What textbook does Foundations of Mathematics 12 use?
Each school district in British Columbia chooses its own textbooks, so ask your teacher which one your class uses.
Can MapleMind help with Foundations of Mathematics 12?
Yes. MapleMind teaches every skill of Foundations of Mathematics 12, 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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