A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2023 · Q107 Marks

The equation of a curve is y = f(x), where f(x) = (4x – 3)³/² - 20x.

(a)Find the x-coordinates of the stationary points of the curve and determine their nature.[6]
(b)State the set of values for which the function f is increasing.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[B2,1,0] B2 Three correct unsimplified { } and no others. B1 Two correct { }or three correct { } and an additional term e.g. + c. B0 More than one error.
[M1] Equating their dy/dx to 0 and using a valid method to arrive at 2 answers.
[A1]
[B1] OE
[B1] If d²y/dx² evaluated the answers for both must be correct OR Clear use of change in sign of dy/dx correctly for both B1's.
[B1] Allow < and/or ≥. FT only from special case x<-1/4, x>11/4. Condone: 1<x<1/2.

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Topic: Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, Oct/Nov 2023 Paper 1 Variant 2, question 10.

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