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Date November 2017 Marks available 2 Reference code 17N.2.SL.TZ0.T_3
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number T_3 Adapted from N/A

Question

Abdallah owns a plot of land, near the river Nile, in the form of a quadrilateral ABCD.

The lengths of the sides are AB = 40 m, BC = 115 m, CD = 60 m, AD = 84 m and angle B A ^ D = 90 .

This information is shown on the diagram.

N17/5/MATSD/SP2/ENG/TZ0/03

The formula that the ancient Egyptians used to estimate the area of a quadrilateral ABCD is

area = ( AB + CD ) ( AD + BC ) 4 .

Abdallah uses this formula to estimate the area of his plot of land.

Show that BD = 93  m correct to the nearest metre.

[2]
a.

Calculate angle B C ^ D .

[3]
b.

Find the area of ABCD.

[4]
c.

Calculate Abdallah’s estimate for the area.

[2]
d.i.

Find the percentage error in Abdallah’s estimate.

[2]
d.ii.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

B D 2 = 40 2 + 84 2     (M1)

 

Note:     Award (M1) for correct substitution into Pythagoras.

Accept correct substitution into cosine rule.

BD = 93.0376     (A1)

= 93     (AG)

 

Note:     Both the rounded and unrounded value must be seen for the (A1) to be awarded.

 

[2 marks]

a.

cos C = 115 2 + 60 2 93 2 2 × 115 × 60   ( 93 2 = 115 2 + 60 2 2 × 115 × 60 × cos C )     (M1)(A1)

 

Note:     Award (M1) for substitution into cosine formula, (A1) for correct substitutions.

 

= 53.7   ( 53.6679 )     (A1)(G2)

[3 marks]

b.

1 2 ( 40 ) ( 84 ) + 1 2 ( 115 ) ( 60 ) sin ( 53.6679 )     (M1)(M1)(A1)(ft)

 

Note:     Award (M1) for correct substitution into right-angle triangle area. Award (M1) for substitution into area of triangle formula and (A1)(ft) for correct substitution.

 

= 4460   m 2   ( 4459.30   m 2 )     (A1)(ft)(G3)

 

Notes:     Follow through from part (b).

 

[4 marks]

c.

( 40 + 60 ) ( 84 + 115 ) 4     (M1)

 

Note:     Award (M1) for correct substitution in the area formula used by ‘Ancient Egyptians’.

 

= 4980   m 2   ( 4975   m 2 )     (A1)(G2)

 

 

[2 marks]

d.i.

| 4975 4459.30 4459.30 | × 100     (M1)

 

Notes:     Award (M1) for correct substitution into percentage error formula.

 

= 11.6   ( % )   ( 11.5645 )     (A1)(ft)(G2)

 

Notes:    Follow through from parts (c) and (d)(i).

 

[2 marks]

d.ii.

Examiners report

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

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.2—2d and 3d trig, sine rule, cosine rule, area
Show 133 related questions
Topic 3— Geometry and trigonometry
Prior learning

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