O-LevelMathematicsGeometry4024/22 · May/June 2014 · Q18 Marks

The scale drawing shows three airfields, A, B and C, with B due north of A. The scale is 1 cm to 20 km. [Figure of A, B, C and North arrow]

(a)Find the actual distance between A and B.[1]
(b)A beacon, D, is to the west of the line AB. It is 100 km from A and 120km from B. Construct the position of D on the scale drawing.[2]
(c)Measure the bearing of C from B.[1]
(d)(i)An aircraft is • equidistant from A and C, • 90km from B. By constructing suitable loci, mark on the diagram the two possible positions, P and Q, of the aircraft.[3]
(d)(ii)Given that the aircraft is east of the line AB, find, by measuring, its bearing from C.[1]

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 (May/June 2014). The mark or mark type is shown in brackets.

[1] (a) 138 to 140
[2] (b) D marked at intersection of correct arcs
[2] (b) B1 for a correctly positioned D with one correct construction arc or no correct arcs Or, provided D to the west of AB B1 for D on one correct arc or radii 5 cm and 6 cm reversed with arcs Or, provided D to the east of AB B1 for D on intersection of two correct construction arcs
[1] (c) 103°
[1] (c) Tolerance ± 2°
[3] (d)(i) P and Q marked at intersection of perpendicular bisector and circle
[3] (d)(i) B1 for perpendicular bisector of AC minimum 3 cm long B1 for arcs radius 4.5 cm centre B, minimum 3 cm long cumulatively B1 for P and Q at correct positions
[1] (d)(ii) 249°
[1] (d)(ii) Tolerance ± 2°

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