A-LevelMathematicsDifferentiation9709/12 · Feb/Mar 2025 · Q25 Marks
The diagram shows the curve with equation y = 2x² - 5/x + 3. The curve crosses the x-axis at the point P(1,0) and M is a minimum point. [Figure X.X]
- (a)Find the gradient of the curve at P.[2]
- (b)Find the coordinates of M. Give each coordinate correct to 3 significant figures.[3]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.
- [B1] 4x + 5/x² OE
- [B1] [dy/dx =] 9 FT Correct use of x=1 in their two-term differentiated expression, defined as an expression with one correct power.
- [M1] Their (4x + 5/x²) = 0 and valid method as far as 'x=...' Equate their derivative of the form Ax ± B/x² to zero, where A, B ≠ 0, and solve. If no working is seen, this can be implied by a correct answer for x.
- [A1] x=-1.08 AWRT
- [A1] y = 9.96 AWRT
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