Level 3 Integration Walkthrough

2023 NCEA Level 3 Integration Question 3(a)

2023 Paper

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Question

A garden designer wants an approximation of the area of the shaded garden section below.

10 metres 13 metres 16 metres 15 metres 14 metres 3 metres3 metres3 metres3 metres path Diagram is not to scale

Using these measurements, and Simpson’s Rule, find an approximation of the area of the garden section.

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First walkthrough idea

Focus to try first

Read the equally spaced ordinates carefully, identify \(h\), then slot the values into Simpson’s Rule in the correct odd-even pattern.

Step 1

Find h

The measurements are taken every \(3\) metres.

Show the first step’s working

The measurements are taken every \(3\) metres.

Key result

\[ 3 \]

Walkthrough overview

What this question practises

This 2023 walkthrough is part of AS91579 — Apply integration methods in solving problems.

Method: Using Simpson’s Rule with measured garden ordinates.

This is Question 3(a) from the 2023 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 using Simpson’s Rule with measured garden ordinates. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.

Continue practising

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