A-LevelMathematicsMechanics9709/41 · May/June 2019 · Q510 Marks

A particle P moves in a straight line from a fixed point O. The velocity v m s⁻¹ of P at time t s is given by v = t² – 8t + 12 for 0 ≤ t ≤ 8.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[M1] Differentiate to find a
[M1] Set a = 0 and solve for t
[A1] Minimum v = −4 ms⁻¹
Alternative method for question 5(i)
[M1] Attempt to complete the square for v
[M1] Choose the t value which gives minimum v
[A1] Minimum v = −4 ms⁻¹
[M1] Find values of t when v = 0, factorise or formula
[A1] t = 2 or t = 6
[M1] Integrate v to find s
[A1] Correct integration
[M1] Attempt to find s1, s2 and s3 Look for consideration of the need for 3 intervals Allow use of symmetry when finding s1, and s3
[A1] 2 correct values of displacement
[A1] All correct

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source: A-Level Mathematics, May/June 2019 Paper 4 Variant 1, question 5.

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