British Columbia · Grade 12
Pre-calculus 12
- PREC 12
British Columbia’s Grade 12 math course, from Transformations of Functions & Relations to Trigonometric Functions, Equations & Identities.
- Units
- 4
- Lessons
- 5
- Skills
- 13
- Provincial exam
- None
- Official curriculum
- BC Mathematics 12
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 2 skills
Transformations of Functions & Relations
Translations, Stretches, Reflections & Inverses
Transforming parent functions
I can graph y = a·f(b(x - h)) + k from any parent function and write the equation from a transformed graph.
Skill 1.1
Inverses: graphs and equations
I can find an inverse graphically (reflection in y = x) and algebraically (swap and solve).
Skill 1.2
The official wording · 2 outcomes
- 1.1
- transformations of functions and relations
- 1.2
- transformations of functions and relations
Key ideas
Outside acts on y (visible as written): a stretches vertically, k slides vertically. Inside acts on x — backwards: (x - h) slides RIGHT h, and b compresses horizontally by 1/b.
Negative a reflects over the x-axis; negative b reflects over the y-axis.
The same grammar drives every parent — absolute value, radical, reciprocal, exponential, log, trig — learn it once, apply it everywhere.
The inverse undoes the function: inputs and outputs trade places, so the graph reflects across y = x.
Algebraically: swap x and y, then solve for y. Domain and range swap along with the variables.
Watch out for
- Moving left for (x - 4) — inside-the-bracket moves oppose their sign; that's a RIGHT shift.
- Reading y = f(2x) as a horizontal stretch by 2 — b = 2 COMPRESSES by half; the inside works in reciprocal.
- Reading f⁻¹(x) as 1/f(x) — the inverse function is not the reciprocal.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 5 skills
Exponential & Logarithmic Functions
Exponential Functions & Equations
Graphing exponential functions
I can graph transformed exponential functions and identify asymptote, intercepts, and behaviour.
Skill 2.1
Solving exponential equations
I can solve exponential equations by matching bases or by taking logarithms, including base e.
Skill 2.2
Geometric sequences and series
I can find general terms and sums of geometric sequences and series, including convergent infinite series.
Skill 2.3
Logarithms: Operations, Functions & Equations
Logarithms and the laws of logarithms
I can evaluate logarithms, convert between log and exponential form, and apply the log laws.
Skill 2.4
Logarithmic functions and equations
I can graph log functions, solve log equations, and reject extraneous roots from domain violations.
Skill 2.5
The official wording · 5 outcomes
- 2.1
- exponential functions and equations
- 2.2
- exponential functions and equations
- 2.3
- geometric sequences and series
- 2.4
- logarithms: operations, functions, and equations
- 2.5
- logarithms: operations, functions, and equations
Key ideas
y = c^x with c > 1 grows; 0 < c < 1 decays — both hug a horizontal asymptote (y = 0 for the parent).
log_c(a) = x means c^x = a — a logarithm IS an exponent; the two forms are the same sentence twice.
Transformations move the asymptote with k: y = 2^x + 3 floors at y = 3, never touching it.
The laws mirror exponent laws: log(MN) = log M + log N; log(M/N) = log M − log N; log(M^p) = p·log M.
The y-intercept of the parent is (0, 1) — every c^0 = 1; transformations relocate it predictably.
Watch out for
- Believing the curve eventually touches its asymptote — it approaches forever without arriving.
- Splitting log(M + N) into log M + log N — the sum law applies to PRODUCTS only.
- Confusing y = (1/2)^x (exponential decay) with y = x^(1/2) (a root function) — the variable's position is everything.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 3 skills
Polynomial & Rational Functions
Polynomial Functions & Equations
The factor and remainder theorems
I can use the remainder theorem to evaluate divisions and the factor theorem to factor cubics and quartics.
Skill 3.1
Graphing polynomial functions and solving equations
I can sketch a polynomial from its factored form and read degree, zeros, multiplicity, and end behaviour.
Skill 3.2
Rational functions: asymptotes, holes, and end behaviour
I can find a rational function's asymptotes, holes, intercepts, and domain from its factored form.
Skill 3.3
The official wording · 3 outcomes
- 3.1
- polynomial functions and equations
- 3.2
- polynomial functions and equations
- 3.3
- rational functions
Key ideas
Remainder theorem: dividing P(x) by (x - a) leaves remainder P(a) — evaluate instead of dividing.
Factor theorem: P(a) = 0 exactly when (x - a) is a factor — test candidates from the constant term's factors.
After one factor is found, synthetic or long division drops the degree, and the quotient factors by Grade-11 methods.
End behaviour follows degree and leading sign: even degrees match both ends; odd degrees split them.
Zeros come from factors; MULTIPLICITY shapes the crossing — odd multiplicity cuts through, even multiplicity bounces.
Watch out for
- Testing (x - a) by computing P(-a) — the factor (x - 3) pairs with P(3), sign matters.
- Stopping after one factor — a cubic hides a quadratic quotient that usually factors further.
- Drawing a crossing at every zero — even-multiplicity zeros touch and turn back.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 3 skills
Trigonometric Functions, Equations & Identities
Radians & the Unit Circle
Radians, degrees, and the unit circle
I can convert radians and degrees, and give exact trig values for special angles using the unit circle.
Skill 4.1
Graphing trigonometric functions
I can graph transformed sine and cosine functions, reading amplitude, period, phase shift, and midline.
Skill 4.2
Trigonometric equations and identities
I can solve trig equations (with general solutions) and verify or apply the standard identities.
Skill 4.3
The official wording · 3 outcomes
- 4.1
- trigonometry: functions, equations, and identities
- 4.2
- trigonometry: functions, equations, and identities
- 4.3
- trigonometry: functions, equations, and identities
Key ideas
π radians = 180° — the whole conversion table in one fact; multiply by π/180 or 180/π.
On the unit circle, cos θ and sin θ ARE the x and y coordinates of the terminal point.
Special angles (π/6, π/4, π/3 and their reflections) tile the circle with exact values; reference angles carry them to every quadrant with CAST signs.
y = a sin(b(x - c)) + d: |a| = amplitude, period = 2π/b, c = phase shift, d = midline.
b and period are inverses — a bigger b squeezes more cycles into the same window.
Watch out for
- Treating π as 3.14 units of angle rather than 180° — losing exactness the whole course depends on.
- Assigning quadrant signs from the reference angle alone — the QUADRANT of the original angle sets the signs.
- Reading b as the period — the period is 2π/b; b = 2 halves the period rather than doubling it.
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 12FOM 124 units · 10 skillsNo provincial examWhat it coversGeometric Explorations: Constructions, Conics & Fractals · Function Graphs & Regression (Technology) · Combinatorics, Odds & Probability · Financial Planning
- Pre-calculus 12This coursePREC 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 Pre-calculus 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
MapleMind teaches Pre-calculus 12 one skill at a time. Each skill gets a short lesson, practice as you go and a check worth up to three stars. It remembers where you stopped.
Course Companion
Your year in one workbook
A fun way to keep Pre-calculus 12 organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
- Pages
- 27
- Fillable fields
- 1,148
- Price
- $4.99
Questions about Pre-calculus 12
What is Pre-calculus 12?
British Columbia’s Grade 12 math course: 4 units and 13 skills, from Transformations of Functions & Relations to Trigonometric Functions, Equations & Identities.
What units are in Pre-calculus 12?
1. Transformations of Functions & Relations, 2. Exponential & Logarithmic Functions, 3. Polynomial & Rational Functions and 4. Trigonometric Functions, Equations & Identities.
Is there a provincial exam for Pre-calculus 12?
No. British Columbia gives no provincial exam for Pre-calculus 12.
What textbook does Pre-calculus 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 Pre-calculus 12?
Yes. MapleMind teaches every skill of Pre-calculus 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.
Get ready for Pre-calculus 12
Practise every skill of Pre-calculus 12 in MapleMind, free with daily limits.
