Higher June 2019 Paper 3 Q16
16 Here are two sectors from different circles.
Not drawn accurately
Which sector has the bigger area?
Tick a box.
- Sector A
- Sector B
Show working to support your answer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{x}{360} \times \pi \times (1.5r)^2\) or \(\dfrac{1}{160}\pi x r^2\) or \(0.019…xr^2\) or \(\dfrac{2x}{360} \times \pi \times r^2\) or \(\dfrac{1}{180}\pi x r^2\) or \(0.017…xr^2\) | M1 | oe eg (working in radians) \(\dfrac{1}{2} \times (1.5r)^2 \times x\) or \(\dfrac{1}{2} \times r^2 \times 2x\) |
| \(\dfrac{1}{160}\pi x r^2\) and \(\dfrac{1}{180}\pi x r^2\) and A or \(0.019…xr^2\) and \(0.017…xr^2\) and A | A1 | oe eg (working in radians) \(\dfrac{9}{8}r^2 x\) and \(r^2 x\) and A |
Additional guidance
Methods must be algebraic, containing \(x\), \(\pi\) and \(r\)
If a box is not ticked, must say ‘A’ without contradiction in working to award M1A1
To award A1 their areas must be in a comparable form eg
\(\dfrac{2.25}{360}\pi x r^2\) and \(\dfrac{2}{360}\pi x r^2\) and A ticked
Ignore further incorrect working after A1 scored