O-LevelMathematicsMensuration4024/22 · Oct/Nov 2025 · Q235 Marks
The diagram shows a shaded area in a large circle, centre O. The radius of the large circle is 10 cm. OAB is a sector of a small circle, centre O. The radius of the small circle is 7 cm and the sector angle is 130°. C is on the circumference of the large circle and AC = BC. Calculate the percentage of the area of the large circle that is shaded. [Figure 23]
- The diagram shows a shaded area in a large circle, centre O. The radius of the large circle is 10 cm. OAB is a sector of a small circle, centre O. The radius of the small circle is 7 cm and the sector angle is 130°. C is on the circumference of the large circle and AC = BC. Calculate the percentage of the area of the large circle that is shaded.[5]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [5] 37.9 or 37.87 to 37.89... B4 for answer 62.1[%] or 62.10... [%]to 62.13[%] OR M3 for a complete correct method to find the shaded area or unshaded area
- [1] M1 for (their shaded or their unshaded area / π×10²) [x100] oe OR M1 for (130/360) × π × 7² oe
- [2] M2 for [2x]1/2×7×10×sin((360-130)/2) or B1 for ∠COA or ∠COB = 115
- [1] M1 for (their shaded area / π×10²) [x100] oe
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