A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2024 · Q35 Marks
The equation of a curve is y = 2x² - 3. Two points A and B with x-coordinates 2 and (2 + h) respectively lie on the curve.
- (a)Find and simplify an expression for the gradient of the chord AB in terms of h.[3]
- (b)Explain how the gradient of the curve at the point A can be deduced from the answer to part (a), and state the value of this gradient.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [B1] [f(2+h)=] 2(2+h)²-3 SOI
- [M1] {their (2(2+h)²-3)}-their 5 / (2+h)-2 can be implied by the simplified expression or the correct answer. Their 5 must come from 2(2)² -3.
- [A1] 2h+8 or 2(h+4)
- [B1] h→0, or chord [AB] → tangent [at A]
- [B1FT] 8 Could come from anywhere except wrong working. Either correct or FT their linear expression from (a).
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