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91261 – Worked Solutions - 2025

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QUESTION THREE

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2.6 (AS 91261) – 2025 Answers

Quite often, there are different ways to solve a Mathematics problem.

These solutions/strategies show one possible way to solve them.

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Question 3(a)

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Question 3(c)

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Question 3(e)

Shiloh is about to play a golf hole. She starts (tee) at point A, as shown in the diagram. Normally golfers take the route ABC to get to the end of the hole (flag). She decides to take a risk and go direct from the start (tee) to the end (flag). However, there is a tree in the way that she will need to clear.

The start (tee) is 2 m above ground level (i.e the flag). The ball reaches its maximum height of 20 m when it is 110 m from the start. The tree is 7.5 m high, and is 200 m away from the start.

Assume the flight of the ball can be modelled by a quadratic equation.

Will the golf ball be high enough to clear the tree?

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Question 3(e)

Shiloh is about to play a golf hole. She starts (tee) at point A, as shown in the diagram. Normally golfers take the route ABC to get to the end of the hole (flag). She decides to take a risk and go direct from the start (tee) to the end (flag). However, there is a tree in the way that she will need to clear.

The start (tee) is 2 m above ground level (i.e the flag). The ball reaches its maximum height of 20 m when it is 110 m from the start. The tree is 7.5 m high, and is 200 m away from the start.

Assume the flight of the ball can be modelled by a quadratic equation.

Will the golf ball be high enough to clear the tree?

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We use the vertex form when we do not know the two roots, but we do know the position of the vertex, V.

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