Mathematical Methods — Question 15

QCAA 2020, Paper 2 · 3 marks

Q15 · 2020 · Technology-activeSimple familiar3 marks

QUESTION 15 (3 marks)

A field is divided into five sections as shown. The width of each section is 1 metre. The perpendicular height, in metres, of each section is given in the diagram. The area of the field was approximated using the trapezoidal rule and found to be

11.12\;\mathrm{m^2}

Field divided into five one-metre sections with perpendicular heights 1, 3, 2.6, 2.2, x and 1.76 metres.

Determine the height marked

x

on the diagram.

[2 marks]

Determine the area of the field, given the shape of the field is modelled by the function

f(x)=\frac{4x}{x^2+1}+1,\qquad0\le x\le5.

[1 mark]

Question linkOriginal paper

WORKED SOLUTION

QCAA guide · typeset solution

3 marks

ANSWER

x=1.94\;\mathrm m

; b)

11.5162\;\mathrm{m^2}

Worked solution

a) Using the trapezoidal rule,

11.12=\frac{1+3}{2}+\frac{3+2.6}{2}+\frac{2.6+2.2}{2}+\frac{2.2+x}{2}+\frac{x+1.76}{2}.

This gives

x=1.94\;\mathrm m

\int_0^5\left(\frac{4x}{x^2+1}+1\right)dx=11.5162\;\mathrm{m^2}.

correctly establishes equation in

x

[1 mark]

determines

x

[1 mark]

correctly determines the area

[1 mark]

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Mathematical Methods — Question 15

QUESTION 15 (3 marks)

QCAA guide · typeset solution

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