O-LevelMathematicsMensuration4024/12 · Oct/Nov 2023 · Q215 Marks
[Figure 21] Diagram A shows a sector of a circle, centre D and radius (3/4)y cm. The obtuse angle EDF = 6x°. Diagram B shows a sector of a circle, centre P and radius y cm. The sector angle is x°.
- (a)The length of the major arc EF is 9 times the length of the arc QR. Show that x = 20.[3]
- (b)Find the value of y when the area of sector QPR is equal to 2πcm².[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [3] (360-6x)/360 × 2π(3y/4) = 9×(x/360)×2πy or (3y/4) × (360-6x)/360 × 2π = 9×(y)×(x/360)×2π
- M2
- M1 for (x/360) × 2πy oe or (3y/4) × (360-6x)/360 × 2π oe or for (360 - 6x) seen
- A1 At least one extra step of rearrangement leading to x = 20
- A0 if any errors or omissions
- [2] 6
- M1 for (20/360) × π× y² = 2π oe or better
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →