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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)y=f(x) is shown in the graph, for 0x10.

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 = 22(2+2(4.5+4.2+3.3+4.5)+8)        M1A1

Area = 43        A1

[3 marks]

a.

y=0.0389x30.534x2+2.06x+2.06      M1A2

[3 marks]

b.i.

R2=0.991     A1

[1 mark]

b.ii.

Area = 100ydx     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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