NCEA Level 3 Differentiation (91578)

📘 Course Overview

AS91577 : Apply Differentiation Methods in Solving Problems.

Master the essential concepts of the Differentiation Techniques.

This course is designed to help students apply differentiation methods in solving problems, with a strong focus on achieving Merit and Excellence in the NCEA Level 3 external examination. Students are guided step by step through key topics, including differentiation of polynomial, algebraic, exponential, logarithmic, and trigonometric functions, as well as the chain, product, and quotient rules. Where required, trigonometric equation solving is explicitly taught and applied, ensuring students can progress confidently through higher-level differentiation problems.

The course also develops strong problem-solving skills through coordinate geometry–based differentiation questions, including equations of tangents and normals to curves. Differentiation is then applied to advanced topics such as stationary points, increasing and decreasing functions, points of inflection, rates of change, parametric and implicit differentiation. 

A major emphasis is placed on optimisation problems, including maximising and minimising area, volume, cost, efficiency, and profit - a key requirement for Merit and Excellence. 

Throughout the course, students learn how to structure solutions clearly, justify results mathematically, and interpret answers in context, exactly as expected by NZQA examiners.

Who This Course is For?

• Students sitting Level 3 Calculus
• Students preparing for external exams or scholarship-level problems
• Students seeking strong conceptual understanding of differentiation

Student Outcomes

Students who complete this course typically:

• Gain confidence in differentiation techniques
• Apply derivatives effectively in problem-solving
• Structure answers clearly to meet Merit/Excellence criteria
• Score higher in Level 3 external exams