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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.
Graph of f on a grid for x from -6 to 12 (x-axis marked at every integer, y-axis from -4 to 4): a lower semicircle from (-6, 0) through (-3, -3) to (0, 0), an upper semicircle from (0, 0) through (3, 3) to (6, 0), and a straight line segment from (6, 0) to (12, 3). The points (-6, 0), (0, 0), (6, 0) and (12, 3) are marked with dots.
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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