Level 2 Algebra Walkthrough
2025 NCEA Level 2 Algebra Question 1(d)
2025 Paper
Question
A rectangle is inscribed in a circle of radius \(r\), as shown below. The length of the rectangle is twice its width.
Find a fully simplified expression for the area of the rectangle in terms of \(r\).
First walkthrough idea
Hint to try first
Let the width be \(x\), so the length is \(2x\) and the area is \(2x^2\).
Step 1
Write the area in terms of x
Width times length gives \(A=x(2x)=2x^2\).
Show the first step’s working
Width times length gives \(A=x(2x)=2x^2\).
Key result
Walkthrough overview
What this question practises
This 2025 walkthrough is part of AS91261 — Apply algebraic methods in solving problems.
Method: Using Pythagoras to write area in terms of the radius.
This is Question 1(d) from the 2025 NCEA Level 2 Algebra paper for AS91261 — Apply algebraic 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 AS91261.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise using Pythagoras to write area in terms of the radius. 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.