A particle moves in a straight line such that its displacement, x m, from a fixed point O after t s, is given by x = 10ln(t² + 4) – 4t.

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

1. [1] (i) B1 10ln4 or 13.9 or better
2. [4] (ii) M1 attempt to differentiate and equate to zero
3. [4] (ii) B1 20t / (t² + 4) or equivalent seen
4. [4] (ii) DM1 attempt to solve their dx/dt = 0, must be a 2 or 3 term quadratic equation with real roots
5. [4] (ii) A1 for both t=1, t=4
6. [5] (iii) M1 attempt to differentiate their dx/dt
7. [5] (iii) A1 20(t²+4)
8. [5] (iii) A1 20t(2t)
9. [5] (iii) A1 20(4-t²) or 80-20t² or 4-t² or equivalent expression involving – t²
10. [5] (iii) B1 t = 2, dependent on obtaining first and second A marks