Numeracy Higher November 2023 Unit 2 Q10
10. The diagram below shows the dimensions of a goal in football.
Players take a penalty kick from the penalty spot.
The penalty spot is 10·97 m from the goal line and central to the goal.
Diagram not drawn to scale
Mark takes a penalty kick.
He misses, and the ball hits the top left-hand corner of the goal.
Calculate the straight-line distance from the penalty spot to the top left-hand corner of the goal. [4]
| Scheme | Marks | Comments |
|---|---|---|
| 10.97\(^2\) + (7.32÷2)\(^2\) OR (7.32÷2)\(^2\) + 2.44\(^2\) OR 2.44\(^2\) + 10.97\(^2\) or \(\sqrt{10.97^2 + (7.32 \div 2)^2}\) OR \(\sqrt{(7.32 \div 2)^2 + 2.44^2}\) OR \(\sqrt{2.44^2 + 10.97^2}\) | M1 | May be embedded within incorrect work and possibly in stages |
| (Distance from penalty spot to A =) \(\sqrt{10.97^2 + (7.32 \div 2)^2 + 2.44^2}\) | M2 | May be seen in stages Implies previous M1 M1 for 10.97\(^2\) + (7.32÷2)\(^2\) + 2.44\(^2\) |
| (Distance from penalty spot to A =) 11.82 (m) or an answer in the range 11.814 to 11.821 (m) | A1 | Allow 11.8 or 11.81 (m) Needs to come from use of √139.5872 to √139.7332 if method done in stages with premature rounding |