NCEA Level 3 Differentiation Exam Survival Kit (91578)

The NCEA Level 3 Calculus exam is on Monday 16 November 2026, 9:30am. Differentiation (91578) is worth 6 credits, and this kit covers every method it tests, step by step and in plain language.

WHAT'S INSIDE (36 pages)

• 12 topic study guides: the algebra you need, standard derivatives (including sec, cosec and cot), the chain, product and quotient rules, tangents and normals, rates of change, stationary points, inflection and concavity, parametric differentiation (first and second derivatives), related rates, optimisation, and limits, continuity and differentiability

• 24 practice questions graded Achieved to Excellence, with step-by-step worked answers

• A full mock exam in the real three-question format, parts (a) to (e), with a marking guide that shows what earns Achieved, Merit and Excellence, and worked solutions

• How 91578 is marked, what NZQA's 2025 report says, a topic checklist, a two-week plan and a night-before summary

WHY IT WORKS

• Built around NZQA's 2026 specification and 2025 report, including the mistakes that cost marks: missing brackets, the missing ÷ dx/dt in parametric second derivatives, and dropping the denominator before setting dy/dx = 0

• Shows every derivative and every line of algebra. A calculator answer alone gets no credit in 91578

FORMAT

Instant PDF download (A4). Use it on screen, or print the mock exam.

Please note: covers 91578 only, not 91577 (complex numbers) or 91579 (integration). Original material written by Kola at MathTutor. Not affiliated with NZQA. For the buyer's own study: please don't share or resell.

Want 1:1 help before the exam? Email mathtutor@outlook.co.nz or message 021 0828 5560.