MCV4U Practice Questions
Grade 12 Calculus and Vectors — free, with full solutions
Limits, derivatives, curve sketching and vectors — the calculus course Ontario engineering, physics and computer science programs expect, and where first-year university calculus picks up. 39 questions, every one with a complete step-by-step worked solution. Free to use, no sign-up needed.
Average versus instantaneous rate of change, the difference quotient, and evaluating limits algebraically — the ideas every derivative rule is built on.
Power, product, quotient and chain rules, tangent lines and implicit differentiation — the toolkit the rest of the course runs on.
Critical points, increasing and decreasing intervals, concavity, optimization and related rates — turning derivatives into information about shape and motion.
Differentiating exponential, logarithmic and trigonometric functions, and combining them with the product and chain rules.
Magnitude and direction, resultants, the cosine law for vector sums, and resolving vectors into components — vectors before coordinates.
Vectors in component form: dot products and angles, cross products, areas, and projections in three dimensions.
Vector, parametric, symmetric and scalar equations, intersections, distances and angles — where vectors turn back into geometry.
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💡 How to actually get better with these
- Try the question first — properly. Solutions are hidden behind a click for a reason. Reading a solution you didn't attempt teaches almost nothing.
- Write out your steps. Most lost marks come from skipped lines, not wrong ideas.
- If you get it wrong, find the exact step where it went wrong — not just the right answer. That step is the thing to fix.
- Come back in a week. Redo the ones you missed. If you can do them cold, you've actually learned them.
Free practice is step one. The classes are where it clicks.
Interactive pre-recorded online math classes where the student solves as they learn — math online, at their own pace and in their own time — plus a self-assessment test every 2 weeks and a practice assignment every 3 classes, each with full solutions. Start with 3 complete classes free.
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