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A-LevelMathematicsMechanics9709/42 · May/June 2024 · Q25 Marks

A particle P moves in a straight line. At time ts after leaving a point O on the line, P has velocity vms⁻¹, where v = 44t-6t² - 36.

  1. (a)Find the set of values of t for which the acceleration of the particle is positive.[2]
  2. (b)Find the two values of t at which P returns to O.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [M1] Decrease power by 1 and a change in coefficient in at least one term (which must be the same term); allow unsimplified.
  2. [A1] OE, e.g. 44/12, 11/3, 3.67 or better.
  3. [M1] Increase power by 1 and a change in coefficient in at least one term (which must be the same term). Use of s = vt is M0.
  4. [A1] Allow unsimplified.
  5. [A1] CWO Ignore t = 0 if not rejected.

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About this question

Topic
Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2024 Paper 4 Variant 2, question 2.

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