Graphs of y = a/x, y = a/x² and y = ax³, distance–time and speed–time graphs, and solving problems that combine linear and non-linear graphs.
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.
A car speeds up, cruises, then brakes. A graph of its speed tells you the acceleration (the slope) and the distance travelled (the area).
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Change the journey and read acceleration and distance.
Copy these into your notebook in your own words — that is how they stick.
Hyperbola with two branches; asymptotes the axes; x ≠ 0.
Both branches on the same side of the x-axis (sign of a); symmetric about the y-axis.
Smooth S-curve through the origin; rotational symmetry about the origin.
Gradient = speed; flat = stationary; negative gradient = returning.
Total distance ÷ total time.
Gradient = acceleration; area = distance; flat = constant speed.
Split into triangles, rectangles or trapeziums: trapezium ½(a + b)h.
The x-values where two graphs meet solve the equation f(x) = g(x).
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 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 (19 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
A car starts from rest and accelerates uniformly to 20 m/s in 10 seconds. It then travels at 20 m/s for 20 seconds and finally slows uniformly to rest in 10 seconds.
(a) Sketch the speed–time graph (axes labelled, points (0, 0), (10, 20), (30, 20), (40, 0)). [3]
(b) Calculate the acceleration during the first 10 seconds and the deceleration in the last 10 seconds. [3]
(c) Calculate the total distance travelled. [3]
Question 2 [10 marks]
A table of values is needed for y = 8/x for x = ±1, ±2, ±4, ±8.
(a) Complete the table for y = 8/x. [2]
(b) On the same axes, draw the graphs of y = 8/x and y = x + 2. (Check: two smooth branches; line through (0, 2) and (−2, 0).) [4]
(c) Use the graph to solve 8/x = x + 2 and show algebraically that your answers are correct. [4]
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.