Level 2 Calculus Walkthrough
2025 NCEA Level 2 Calculus Question 3(b)
2025 Paper — Rate of change of triangle area with respect to height
Question
The base is always \(4\) times the perpendicular height.
Find the rate of change of the area of the triangle with respect to its vertical height when the area of the triangle is \(98\text{ cm}^2\).
Start by writing the area in terms of height, use the area \(98\) to find the height, then differentiate and evaluate the rate when the height is \(7\).
First walkthrough idea
Tip to try first
Use the relationship between base and height first so the area can be written using only one variable.
Step 1
Write the base in terms of height
Reveal the explanation and working for this step.
Show the first step’s working
Express the base in terms of the height \(h\).
Worked result
The base is always four times the height, so \(b=4h\).
Walkthrough overview
What this question practises
This 2025 walkthrough is part of AS91262 — Apply calculus methods in solving problems.
Method: Forming an area expression, finding the height from the given area, and evaluating the rate of change.
This is Question 3(b) from the 2025 NCEA Level 2 Calculus paper for AS91262 — Apply calculus methods in solving problems. Use the guided hints to practise the method before revealing the full working.
Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91262.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise forming an area expression, finding the height from the given area, and evaluating the rate of change. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check intersections, signs, and whether the question asks for signed area or total geometric area.