Foundation November 2017 Paper 2 Q22
22. Sid has built the two walls, as shown in the diagram below.
Diagram not drawn to scale.
Sid measures the distance shown by the dotted line.
He finds that it measures exactly 14 m.
Sid thinks that his two walls meet at right angles.
Is he correct?
Show all your working and explain your answer. [3]
| Scheme | Marks | Comments |
|---|---|---|
| Use of Pythagoras Theorem \(7^2 + 12^2 = (\text{hypotenuse})^2\) | M1 | |
| (Hypotenuse =) 13.89 (m) | A1 | |
| Conclusion stated or implied that he is not correct, e.g. ‘Sid’s walls do not meet at right angles’ or equivalent. | E1 | Only award E1 provided M1 previously awarded. |
| (3) |
Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| \(7^2 + 12^2\) | B1 | |
| 193 AND \(14^2 = 196\) | B1 | |
| No because they are not the same. | E1 |
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| \(14^2 - 12^2 = 196 - 144\) (= 52) | B1 | |
| 52 AND \(7^2 = 49\) | B1 | |
| \(52 \neq 49\), so no. | E1 |