O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2021 · Q88 Marks
A particle moves in a straight line so that, t seconds after passing through a fixed point O, its velocity, v ms⁻¹, is given by v = 3t² - 30t+72.
- (a)Find the distance between the particle's two positions of instantaneous rest.[6]
- (b)Find the acceleration of the particle when t = 2.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- (a) M1 Factorises or solves 3t²-30t+72=0 or t² -10t + 24 = 0
- (a) A1 t = 4, t = 6
- (a) M2 M1 for any two terms correct Integrates v to find F(t): 3t³/3 - 30t²/2 + 72t
- (a) M1 dep on at least M1 for integration Correct substitution for F(6) – F(4) or F(4) – F(6) FT their 4 and their 6 provided they are both positive
- (a) A1 dep on all previous marks being awarded 4 (m)
- (b) B1 [a=]6t-30
- (b) B1 [When t = 2: a = 6(2) – 30 =] -18 (ms⁻²) cao
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →