✕ NCEA Level 3

Calculus

Complex numbers, differentiation and integration: three externals, 17 credits.

6 Standards 27 Total credits 3 Externals · 17 cr 0/6 Reviewed

Achievement standards

External · 17 credits

AS 91577 Complex numbers Argand diagrams, polar form, De Moivre’s theorem & roots. External 5 credits AS 91578 Differentiation methods Chain/product/quotient rules, implicit, related rates & optimisation. External 6 credits AS 91579 Integration methods Techniques, areas, volumes of revolution & differential equations. External 6 credits

Internal · 10 credits

AS 91575 Apply trigonometric methods in solving problems Trig equations, identities and fitting a sinusoidal model to a real cycle. Internal 4 credits AS 91587 Apply systems of simultaneous equations in solving problems 3×3 systems, and what unique / no / infinite solutions mean geometrically. Internal 3 credits AS 91574 Apply linear programming methods in solving problems Constraints, the feasible region, and optimising at the vertices. Internal 3 credits

Where this leads in business & finance

Calculus is finance once you get past year one. Optimisation (your max/min problems) is how firms set prices and allocate capital; rates of change are how interest compounds and how bonds respond to yield moves; integration is how you value a cash flow stream. The Black–Scholes model that underpins global options markets is a differential equation. Every finance, economics, actuarial and data-science degree opens with exactly this content — arriving already fluent puts you a year ahead.

Watch: Calculus in the real world Opens a YouTube search: a good one to watch when motivation dips