Foundation November 2023 Paper 3 Q29
29 \(A\), \(B\), \(C\) and \(D\) are points on a circle such that \(ABCD\) is a square.
The square \(ABCD\) has sides of length 3.5 cm.
Calculate the circumference of the circle.
Give your answer correct to 1 decimal place.
You must show all your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 15.6 | P1 | for beginning process to use Pythagoras to find diameter or radius, eg \(3.5^2 + 3.5^2\ (= 24.5)\) or \(1.75^2 + 1.75^2\ (= 6.125)\) |
| P1 | for complete process to find diameter or radius, eg \(\sqrt{3.5^2 + 3.5^2}\) or \(\sqrt{24.5}\ (= 4.94..)\) or \(\sqrt{1.75^2 + 1.75^2}\) or \(\sqrt{6.125}\ (= 2.47\ldots)\) | |
| P1 | for process to find circumference of circle, eg \(\pi \times \text{``}4.94\ldots\text{''}\ (= 15.55\ldots)\) or \(2 \times \pi \times \text{``}2.47\ldots\text{''}\ (= 15.55\ldots)\) | |
| A1 | for answer in range 15 to 16 |
Additional guidance
Award P1 for a correct Pythagorean statement eg
\(3.5^2 + 3.5^2 = \text{diameter}^2\)
4.94.. or 2.47.. truncated or rounded can imply P2
Accept use of 3.14 or better for \(\pi\)
Accept use of truncated values for 4.94.. or 2.47..
If an answer is shown in the range in working and then incorrectly rounded award full marks. Award 0 marks for a correct answer without correct supportive working.