A-LevelMathematicsIntegration9709/12 · Feb/Mar 2022 · Q88 Marks
The diagram shows the circle with equation (x – 2)² + y² = 8. The chord AB of the circle intersects the positive y-axis at A and is parallel to the x-axis. [Figure 8.1]
- (a)Find, by calculation, the coordinates of A and B.[3]
- (b)Find the volume of revolution when the shaded segment, bounded by the circle and the chord AB, is rotated through 360° about the x-axis.[5]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.
- [B1] (-2)² + y² = 8 leading to y = 2 leading to A = (0,2)
- [M1] Substitute y = their 2 into circle leading to (x - 2)² + 4 = 8
- [A1] B = (4, 2)
- [*M1] Attempt to find [π]∫(8-(x-2)²)dx
- [A1] [π][8x-(x-2)³/3] or [π][8x-(x³/3-2x²+4x)]
- [DM1] [π][(32-16/3)] or [π][(32-(64/3-32+16))]
- [B1 FT] Volume of cylinder = π×2²×4=16π
- [A1] [Volume of revolution = 26⅔π - 16π =]10⅔π
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