BC Pre-Calculus 12 (formerly called Principles of Mathematics 12) is the highest-level Grade 12 mathematics course in the British Columbia curriculum. It is the standard prerequisite for first-year calculus at BC universities (UBC, SFU, UVIC, UVic, etc.) and is required for admission to engineering, mathematics, science, and economics programmes.
The course builds on Pre-Calculus 11 and covers topics that directly prepare students for university calculus. It is assessed through school-based exams and formerly through a BC provincial exam (the provincial exam requirement was modified in 2020 — check with your school for the current assessment structure).
Pre-Calculus 12 covers six major topic areas:
| Unit | Topics | Exam Weight |
|---|---|---|
| Transformations & Function Operations | Horizontal/vertical shifts, stretches, reflections; composite and inverse functions | ~15% |
| Radical & Rational Functions | Domain, asymptotes, sketching radical and rational graphs | ~12% |
| Polynomial Functions | Factor theorem, remainder theorem, graphing degree 3+ polynomials, end behaviour | ~15% |
| Trigonometry | Unit circle, radians, trig graphs and transformations, trig identities, solving trig equations | ~22% |
| Exponential & Logarithmic Functions | Laws of exponents/logs, graphing, solving exponential/log equations, applications (growth/decay) | ~18% |
| Permutations, Combinations & Binomial Theorem | Counting principles, Pascal's triangle, binomial expansion | ~18% |
Trigonometry and Exponentials/Logarithms together account for roughly 40% of assessments and are also the most heavily tested topics in university Calculus 1. Students who are weak in these areas tend to struggle significantly in first-year calculus.
| University | Minimum Grade | Notes |
|---|---|---|
| UBC (Science/Engineering) | 70% | Higher grades competitive for Engineering admission |
| SFU (Science) | 65–70% | Calculus 12 also accepted |
| UVIC (Engineering) | 70% | Calculus 12 preferred for Engineering |
| Kwantlen / Langara CEGEP transfer | 60% | Minimum for Calculus 1 prerequisite |
| Province | Equivalent Course | Key Similarities |
|---|---|---|
| BC | Pre-Calculus 12 | Trig, logs, polynomials, combinatorics |
| Ontario | Advanced Functions 4U + Calculus & Vectors 4U | Ontario adds differentiation intro; BC adds more trig depth |
| Alberta | Math 30-1 (Pure Math) | Very similar content — logs, trig identities, functions |
| Quebec | Sec 5 SN + CEGEP Calculus 1 | CEGEP goes further (full Calculus 1) — better university preparation |
Our BC tutors cover the full Pre-Calculus 12 curriculum, from trig identities to combinatorics. We also offer university transition support for students starting MATH 100/110.
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