Level 2 Algebra Walkthrough

2025 NCEA Level 2 Algebra Question 3(e)

2025 Paper

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Question

Shiloh's golf ball starts \(2\) m above ground level.

The ball reaches a maximum height of \(20\) m when it is \(110\) m from the start.

The tree is \(7.5\) m high and is \(200\) m from the start.

Assume the flight of the ball can be modelled by a quadratic equation. Will the ball be high enough to clear the tree?

First walkthrough idea

Hint to try first

Use vertex form, because the maximum point is given directly.

Step 1

Write the quadratic in vertex form

The turning point is \((110,20)\), so vertex form is the best start.

Show the first step’s working

The turning point is \((110,20)\), so vertex form is the best start.

Key result

\[ y = a \left(x - 110\right)^{2} + 20 \]

Walkthrough overview

What this question practises

This 2025 walkthrough is part of AS91261 — Apply algebraic methods in solving problems.

Method: Modelling a golf shot with a quadratic and interpreting the result.

This is Question 3(e) 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 modelling a golf shot with a quadratic and interpreting the result. 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