Higher November 2023 Paper 1 Q10
10 Shape A is a circle with radius \(\dfrac{\sqrt{17}}{2}\) cm
Shape B is a sector of a circle with radius 5 cm
Not drawn accurately
Which shape has the greater area, A or B?
You must show your working. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((\pi \times) \left(\dfrac{\sqrt{17}}{2}\right)^2\) | M1 | oe condone missing brackets |
| \(\dfrac{17}{4}(\pi)\) or \(4\dfrac{1}{4}(\pi)\) or \(4.25(\pi)\) | A1 | oe fraction, mixed number or decimal |
| \((\pi \times)\ 5^2\) or \((\pi \times)\ 25\) or \(\dfrac{60}{360}\) used | M1 | oe |
| \(\dfrac{25}{6}(\pi)\) or \(4\dfrac{1}{6}(\pi)\) or \(4.1(6…)(\pi)\) or \(4.17(\pi)\) | A1 | oe fraction, mixed number or decimal |
| A with values in comparable form or A by \(\dfrac{1}{12}(\pi)\) or A by \(0.08(3…)(\pi)\) | A1 | eg values \(\dfrac{51}{12}(\pi)\) and \(\dfrac{50}{12}(\pi)\) \(4\dfrac{1}{4}(\pi)\) and \(4\dfrac{1}{6}(\pi)\) \(4.2(5)(\pi)\) and \(4.1(6…)(\pi)\) \(4.2(5)(\pi)\) and \(4.17(\pi)\) accept ‘circle’ for A allow comparison of fraction or decimal parts only if integer parts shown as equal |
Additional guidance
For the final mark, presence or absence of \(\pi\) must be the same for both values
Accept consistent use of a numerical value of \(\pi\) throughout.
The value can be 3 or 3.1 or 3.14 or 3.142 or better