Turning y = abˣ and y = axⁿ into straight lines by taking logarithms, reading a, b and n from the gradient and intercept, and using data to find the constants.
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.
Experimental data rarely sits on a straight line — until you take logs. Then the curve straightens and the gradient tells you the law.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
lg y = lg a + x lg b → plot lg y vs x; gradient lg b; intercept lg a.
lg y = lg a + n lg x → plot lg y vs lg x; gradient n; intercept lg a.
a = 10^{intercept}; b = 10^{gradient}.
(Y₂ − Y₁)/(X₂ − X₁) using two well-separated points on the line.
y = ax² + b → y vs x²; y = a + b/x → y vs 1/x.
x in the index → lg y vs x; x as the base → lg y vs lg x.
Substitute one data point into the final law.
Interpret a and b in the situation.
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 (24 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [14 marks]
The relationship between two variables x and y is y = a·bˣ, where a and b are constants. Experimental values are: x = 1, 2, 3, 4 and y = 6, 12, 24, 48.
(a) Express the relationship in the form lg y = lg a + x lg b and state what you would plot to obtain a straight line. [3]
(b) Complete the table of lg y and find the gradient. [4]
(c) Hence find the values of a and b. [3]
(d) Calculate the value of x when y = 1 000, correct to 2 decimal places. [4]
Question 2 [10 marks]
The relationship y = axⁿ is such that lg y plotted against lg x gives a straight line through (0, 0.699) and (2, 1.301).
(a) Find the gradient of the line. [2]
(b) State the values of n and a, giving a to 1 decimal place. [3]
(c) Write down the relationship and find y when x = 1 000. [3]
(d) State one reason why a graph of y against x would not be a straight line. [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.