O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2015 · Q97 Marks

You are not allowed to use a calculator in this question. The diagram shows the graph of y = √4+x, which meets the y-axis at the point A and the line x = 5 at the point B. Using your answer to part (i), find the area of the region enclosed by the curve and the straight line AB. [Figure 9.1]

(i)Find ∫√4+x dx.[2]
(ii)The diagram shows the graph of y = √4+x, which meets the y-axis at the point A and the line x = 5 at the point B. Using your answer to part (i), find the area of the region enclosed by the curve and the straight line AB.[5]

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 2015). The mark or mark type is shown in brackets.

[B1, B1] B1 for k(4+x)^(3/2) only, B1 for (2/3)(4+x)^(3/2) only. Condone omission of c
[M1] for attempt to find the area of the trapezium
[A1] = 12.5
[M1] for correct use of limits using k(4+x)^(3/2) only (must be using 5 and 0)
[A1] for 18 - 16/3 or equivalent
[A1] for 1/6 or awrt 0.17

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.