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May 2025 Section II

0/54 marks

2025 · 6 questions · 24 parts · 54 marks

0Correct0Partial0Wrong24Unattempted
1(A)1(B)1(C)1(D)2(A)2(B)2(C)2(D)3(A)3(B)3(C)3(D)4(A)4(B)4(C)4(D)5(A)5(B)5(C)5(D)6(A)6(B)6(C)6(D)
Context for question 4
The continuous function f is defined on the closed interval −6≤x≤12. The graph of f, consisting of two semicircles and one line segment, is shown in the figure.
The graph of f, consisting of two semicircles and one line segment, is shown in the figure
Let g be the function defined by g(x)=∫6x​f(t)dt.
4(A)Definite Integrals and the Fundamental TheoremEasy2 marks
Find g′(8). Give a reason for your answer.
4(B)Stationary Points, Concavity and Curve SketchingEasy2 marks
Find all values of x in the open interval −6<x<12 at which the graph of g has a point of inflection. Give a reason for your answer.
4(C)Definite Integrals and the Fundamental TheoremEasy2 marks
Find g(12) and g(0). Label your answers.
4(D)Stationary Points, Concavity and Curve SketchingHard3 marks
Find the value of x at which g attains an absolute minimum on the closed interval −6≤x≤12. Justify your answer.
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