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Date May Example question Marks available 3 Reference code EXM.2.AHL.TZ0.12
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number 12 Adapted from N/A

Question

The curve  y = f ( x )  is shown in the graph, for  0 x 10 .

The curve  y = f ( x )  passes through the following points.

It is required to find the area bounded by the curve, the x -axis, the y -axis and the line x = 10 .

One possible model for the curve  y = f ( x )  is a cubic function.

Use the trapezoidal rule to find an estimate for the area.

[3]
a.

Use all the coordinates in the table to find the equation of the least squares cubic regression curve.

[3]
b.i.

Write down the coefficient of determination.

[1]
b.ii.

Write down an expression for the area enclosed by the cubic regression curve, the x -axis, the y -axis and the line x = 10 .

[1]
c.i.

Find the value of this area.

[2]
c.ii.

Markscheme

Area =  2 2 ( 2 + 2 ( 4.5 + 4.2 + 3.3 + 4.5 ) + 8 )         M1A1

Area = 43        A1

[3 marks]

a.

y = 0.0389 x 3 0.534 x 2 + 2.06 x + 2.06       M1A2

[3 marks]

b.i.

R 2 = 0.991      A1

[1 mark]

b.ii.

Area =  0 10 y d x      A1

[1 mark]

c.i.

42.5     A2

[2 marks]

c.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.i.
[N/A]
c.ii.

Syllabus sections

Topic 5—Calculus » SL 5.8—Trapezoid rule
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Topic 4—Statistics and probability » AHL 4.13—Non-linear regression
Topic 4—Statistics and probability
Topic 5—Calculus

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