The derivative as a rate of change, velocity and acceleration as derivatives of displacement, velocity–time graphs, and related rates of change for areas and volumes.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Velocity is the rate of change of displacement. Acceleration is the rate of change of velocity. Differentiate once, then again — and you describe all motion.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Move through time and watch displacement, velocity and acceleration.
Copy these into your notebook in your own words — that is how they stick.
v = ds/dt.
a = dv/dt = d²s/dt².
v = 0.
Split at the times when v = 0 and add the absolute displacements.
Acceleration; area gives distance.
dy/dt = dy/dx × dx/dt.
Sphere V = (4/3)πr³, S = 4πr²; circle A = πr²; cube V = x³.
m/s, m/s², cm³/s — state them.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (26 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [14 marks]
A particle moves in a straight line so that its displacement s metres from a fixed point O at time t seconds is s = 2t³ − 9t² + 12t.
(a) Find expressions for the velocity and acceleration of the particle. [2]
(b) Find the values of t at which the particle is at rest. [3]
(c) Find the displacement of the particle at each of these times. [2]
(d) Find the acceleration at each of these times and state what it shows. [3]
(e) Find the total distance travelled in the first 3 seconds. [4]
Question 2 [12 marks]
A spherical balloon is inflated so that its radius increases at a constant rate of 0.5 cm/s.
(a) Find the rate of increase of the volume when the radius is 4 cm, leaving your answer in terms of π. [4]
(b) Find the rate of increase of the surface area S = 4πr² at that instant. [3]
(c) The edge x of a cube is increasing so that the volume increases at 12 cm³/s. Find dx/dt when x = 2. [3]
(d) Explain why dV/dt = dV/dr × dr/dt. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.