Level 3 Integration Walkthrough
2025 NCEA Level 3 Integration Question 3(a)
2025 Paper
Question
The diagram below shows the cross-section of a hole dug in the ground.
The depth of the hole is measured every \(5\) metres across the top of the hole.
Using the trapezium rule, find an estimate for the area of the cross-section of the hole.
The diagram is shown in its initial state. JavaScript adds any interactive controls and later walkthrough visuals.
First walkthrough idea
Hint to try first
The spacing is every \(5\) metres, so that is the trapezium width \(h\).
Step 1
Identify the trapezium width
Each trapezium is \(5\) metres wide.
Show the first step’s working
Each trapezium is \(5\) metres wide.
Key result
\[ 5 \]Walkthrough overview
What this question practises
This 2025 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Estimating cross-sectional area with the trapezium rule.
This is Question 3(a) from the 2025 NCEA Level 3 Integration paper for AS91579 — Apply integration 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 AS91579.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise estimating cross-sectional area with the trapezium rule. 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.
Continue practising
- All 2025 Integration walkthroughs
- All AS91579 Integration years
- Practise more questions using this skill: Integration techniques