ASHS Coursebook: 3MAC (Level 3 Mathematics with Calculus)

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Information icon.svg 3MAC
NCEA Level:
Primary Qualification:
Primary Learning Area:

What is this course about?

This course is intended for those students who have successfully completed an NCEA level 2 course including Algebra and Calculus, or equivalent and are wanting to focus on Calculus. It will prepare students for first year university courses in mathematics, physics and engineering as well as providing a foundation for future studies in subjects such as biomechanics, architecture and economics.

By studying calculus, students develop the ability to think creatively, critically, strategically, and logically. They carry out procedures flexibly and accurately, and learn to enjoy intellectual challenge.

It is recommended that students should have at least gained Achieved (preferably Merits or above) in NCEA achievement standards 91257 (Graphs), 91269 (Simultaneous Equations), 91261 (Algebra) and 91262 (Calculus) before entering this course. Those who have not will need to show considerable commitment and seek additional support if they wish to achieve in this course. A period of review may apply early in the year for students who are yet to demonstrate their understanding of these topics.

What will I learn?

You will:

  • deepen your knowledge and understanding of calculus and its applications to include nested functions, product and quotient functions, trigonometric, exponential and logarithmic functions and their applications in the fields of Differential Equations and Rates of Change, Volume and Area problems and Kinematics;
  • learn how trigonometric functions can be used to model wave and oscillating motion;
  • investigate new methods for solving simultaneous equations beyond 2 variables to include graphical methods and matrices;
  • be introduced to the work of number theorists and the powerful concept of imaginary numbers and use these concept to solve algebraic problems in the complex plane.

What sorts of things will I do?

You will use your creativity alongside your graphical calculator or software such as Geogebra or Desmos to model real world situations and find general solutions. You will work with your peers in class to conceptualise and generalise ideas

What standards can I enter?

The main part of this table summarises the standard course provided. At the end are listed alternatives which students can select in consultation with their parents, maths teachers and tutor teachers.

The code letters under Assessment have the following meanings:

N - NCEA and UE numeracy                     L - NCEA literacy                    R - UE reading literacy                     W - UE writing literacy

Summary of standards:
NCEA Level: Standard Number: Name of standard: Version Number: Credits: Assessment: Assessment Date:
Apply systems of simultaneous equations in solving problems
2 3



Term 1 Week 4
91577 Apply the algebra of complex numbers in solving problems



Apply trigonometric methods in solving problems 2



Term 2 Week 4
Apply differentiation methods in solving problems



Apply integration methods in solving problems 2




Total credits:

Additional standard offered as a self study opportunity
Apply linear programming methods in solving problems



Term 4 Week 2

Please check the actual date of the assessment on the ASHS Assessment Calendar

Vocational Pathways provide a framework for students to show how their learning and achievement is valued in the workplace by aligning learning to the skills needed for industry.  Follow this link to see the profile for this course.

Scholarship opportunities

Students who excel at algebra and calculus will be encouraged and supported in their study of the Scholarship subject material. It is preferable that students will already have considerable experience with Level 3 Calculus content. They will be provided with resources, direction and support but, to have a chance of achieving well, will need to commit to:

  • extensive self directed study and practice;
  • participation in a student work group on a regular basis throughout the year;
  • attend workshops given by teachers to support Scholarship exam preparation.

Frequently asked questions:

What calculator will I need?

The Casio FX9750GII Graphical Calculator is recommended. Students using only a basic scientific calculator will be significantly disadvantaged since NZQA assumes that all students have access to graphics calculators. Graphical calculators are normally available for about $95 at the beginning of the year.

Are there any reassessments for internal standards?

Reassessments are usually offered in term 4. The possibility of a further opportunity for 91575 will be considered at the end of the year. There will be no further opportunities for 91574 or 91587.

What happens if I miss an internal assessment?

  • You must submit a "Missed Assessment" form and get it approved by the specialist subject leader.
  • Approval will only be given if the requirements of the missed assessment policy are met, it is practical for the assessment to be done at another time and that other time is before the final grades are returned to students.
  • If you do not sit an assessment you will automatically receive a "Not Achieved" grade as per NZQA rules.

Do I have to do all the standards in the course?

  • YES. You will be entered for all standards in the core course and are expected to give your best effort in all of them. The only exceptions will where an individual learning plan is approved by the specialist subject leader after consultation with your parents, tutor and student services.
  • This will only be approved where students have attempted the external topics.
  • Students and parents must ensure that the individualised learning plan will still meet the entry requirements for tertiary study. Some courses specify 14 or 17 credits from Calculus or Mathematics as a prerequisite for entry. This may not be achieved in a reduced individualised plan.