Writing and using the relationships y ∝ x, y ∝ x², y ∝ 1/x and y ∝ 1/x², finding the constant k, and solving real-world problems.
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.
More workers, less time. More fuel, more distance. Variation is the algebra of “as one goes up, the other goes …” — and it takes four steps every time.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Compare direct and inverse variation.
Copy these into your notebook in your own words — that is how they stick.
y ∝ x → y = kx. Straight line through the origin; ratio y/x is constant.
y ∝ 1/x → y = k/x. Product xy is constant. Hyperbola.
y ∝ x² → y = kx²; y ∝ 1/x² → y = k/x²; y ∝ √x → y = k√x.
Substitute the given pair of values and solve for k.
Write with k → find k → rewrite formula → solve.
“varies directly as”, “is proportional to” → y = kx; “varies inversely as” → y = k/x.
If x is multiplied by n, y ∝ x² is multiplied by n²; y ∝ 1/x is divided by n.
Give the answer with units and check it is sensible (more workers → fewer days).
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 (17 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
y varies directly as x, and y = 18 when x = 6.
(a) Write down an equation connecting x and y. [3]
(b) Find y when x = 10, and x when y = 45. [2]
(c) Given instead that y varies inversely as x and y = 5 when x = 8, find (i) the relationship, (ii) y when x = 20, (iii) x when y = 16. [4]
Question 2 [8 marks]
The time, T hours, taken to travel a fixed distance varies inversely as the average speed, v km/h. A journey takes 3 hours at 80 km/h.
(a) Write T in terms of v. [3]
(b) Find the time taken at an average speed of 60 km/h. [2]
(c) The cost of a bag of rice varies directly as its mass. 3 kg cost $12. Find the cost of 5 kg, and the mass that can be bought for $30. [3]
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.