Level 2 Algebra Walkthrough
2025 NCEA Level 2 Algebra Question 3(e)
2025 Paper
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
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.