O-LevelAdditional MathematicsStraight line graphs4037/22 · Oct/Nov 2013 · Q88 Marks

The table shows experimental values of two variables x and y. | x | 2 | 4 | 6 | 8 | |---|---|---|---|---| | y | 9.6 | 38.4 | 105 | 232 | It is known that x and y are related by the equation y = ax³ + bx, where a and b are constants.

(i)A straight line graph is to be drawn for this information with y/x on the vertical axis. State the variable which must be plotted on the horizontal axis.[1]
(ii)Draw this straight line graph on the grid below.[2]
(iii)Use your graph to estimate the value of a and of b.[3]
(iv)Estimate the value of x for which 2y = 25x.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

[B1] x² Implied by axes or values in a table. May be seen in (ii)
[B1] Plot y/x against x² with linear scales Must be linear scales
[B1] At least 3 correct points plotted and no incorrect points
[B1] Line must be ruled and through at least 2 correct points
[M1] Finds gradient (0.4) Condone use of correct values from table/graph to find gradient and/or equation. Values read from graph must be correct.
[A1] a = 0.4±0.02
[B1] b = 3.2±0.4
[M1] Read y/x = 12.5 Obtaining (x²)= 22 to 24 from graph. As far as x2 = +ve constant
[A1] 4.8 4.7 to 4.9 ignore -4.8 or 0

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.