Year 13 calculus

This course is designed for you if you are interested in pursuing Mathematics to a higher level or interested in studying an Applied Science, Engineering, Computer Science, Medicine, Architecture or Technology at university. The course is also useful for you if you are interested in careers in Commerce, or in any field where analysis is important.

Calculus involves sophisticated ideas about how the world changes, how we measure that change, and how we use those measurements to guide our existence. Calculus is about the infinite and the infinitesimal, and how they come together in mind-boggling ways. 

Mathematicians and scientists and engineers use concepts of Calculus in all sorts of contexts and use jargon and notations that, without your learning about Calculus, would be completely inscrutable to you. 

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 has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves), these two branches are related to each other by the fundamental theorem of calculus. In this course you will learn both of these areas along with complex numbers and advanced trigonometry. 

In this course, you will

• explore the complex number world

• investigate the instantaneous change (called the "derivative") of various functions. (The process of doing so is called "differentiation".)

• use derivatives to solve various kinds of problems.

• go back from the derivative of a function to the function itself. (This process is called "integration".)

• explore detailed methods for integrating functions of certain kinds.

We recommend this course if you gain 14 credits at Level 2, with the minimum of an achieved grade in standards 91261 (2.6) Algebra, 91262 (2.7) Calculus, and 91269 (2.14) Systems of equations.

Entry into the course is subject to HOD approval.

Assessment

This course offers four NCEA Level 3 achievement standards. One standard is internally assessed and three standards are assessed externally. Able students have the opportunity to sit for NZ Scholarship. 

The following standards may be offered and assessed:

• 91575 v2 (3.3) Apply trigonometric methods in solving problems

• 91577 v2 (3.5) Apply the algebra of complex numbers in solving problems

• 91578 v2 (3.6) Apply differentiation methods in solving problems

• 91579 v2 (3.7) Apply integration methods in solving problems

Note: A casio fx–9750GII graphics calculator is compulsory for this course.

Qualifications: Credits towards NCEA Level 3

Scholarship Calculus

You will be invited into the scholarship calculus programme in the middle of term 1. Regular morning classes will start in term 1, every Thursday at 7:30am in LC5. Information regarding scholarship calculus and resources can be found via: http://www.nzqa.govt.nz/qualifications-standards/awards/scholarship/scholarship-subjects/scholarship-mathematics-with-calculus

NZQA Mathematics Subject Resources

http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/subjects/mathematics/levels

School Policy for NCEA Assessment

You should be aware of the school procedures for NCEA assessment.  They can be found on the school website at this link. There you will find answers to frequently asked questions about how NCEA works as well as guidance about how to apply for extensions, reconsiderations or the process for withdrawing from a standard.