NCEA Level(s)

Course aims / learning outcomes

Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired.

This is normally a full year course for students who have completed level two mathematics and wish to pursue the sciences further or just love a challenge.

It will prepare students for first year university courses in mathematics, computer science, physics and engineering as well as providing a foundation for a future studies in subjects such as bio-mathematics and economics.


Course content

  • Term 1: Trigonometry, then Algebra and Complex Numbers.
  • Term 2: Algebra and Complex Numbers then Differentiation.
  • Term 3: Differentiation then Integration.
  • Term 4: Study for exams.

Much of the content in this course will be learned by doing - solving lots and lots of math problems on paper. We will use technology where appropriate (often Desmos graphing) and graphic calculators. 



Assessment statement

  • 21 credits at Level 3 NCEA.
  • Students sometimes decide to sit only two external exams out of the three.



  • In the internal all work must be completed in class, in a google doc shared with the Learning Advisor.


Appeal Procedures

  • Students have the right to appeal the mark they have been awarded. If a student wishes to appeal a grade, they should initially talk to the subject learning advisor about the marking process immediately after the marked assessment task is shown to them. If still dissatisfied the student should make an appointment and discuss grades with the Principal’s Nominee who will check that the correct procedures have been followed as outlined in the school and subject policies taking into account any special circumstances.


Table of Assessments

NumberNameCredit valueInternal or ExternalLiteracy Numeracy UE Reading/WritingWhenReassessment opportunityType of assessment
AS91575Pākoki | Trigonometry4InternalNumeracyTerm 1PossiblyIn class Report
AS91578Pārōnaki | Differentiation6ExternalNumeracyTerm 4NoExam
AS91579Pāwhaitua | Integration6ExternalNumeracyTerm 4NoExam
AS91577Pāngarau | Algebra5ExternalNumeracyTerm 4NoExam