Question
The diagram shows a field ABCDE.
(a) Calculate the perimeter of the field ABCDE.
m [4]
(b) Calculate angle ABD.
Angle ABD = [4]
(c) (i) Calculate angle CBD.
Angle CBD = [2]
(ii) The point C is due north of the point B.
Find the bearing of D from B.[2]
(d) Calculate the area of the field ABCDE.
Give your answer in hectares.
[1 hectare = 10 000m2]
hectares [4]
Answer/Explanation
Ans:
3(a) 530
3(b) 52.9 or 52.89…
3(c)(i) 28.1 or 28.07…
3(c)(ii) 331.9 or 331.9…
3(d) 1.5[0] or 1.498… nfww
Question
Brad travelled from his home in New York to Chamonix.
- He left his home at 1630 and travelled by taxi to the airport in New York.
This journey took 55 minutes and had an average speed of 18km/h. - He then travelled by plane to Geneva, departing from New York at 2215.
The flight path can be taken as an arc of a circle of radius 6400km with a sector angle of 55.5°.
The local time in Geneva is 6 hours ahead of the local time in New York.
Brad arrived in Geneva at 1125 the next day. - To complete his journey, Brad travelled by bus from Geneva to Chamonix.
This journey started at 1300 and took 1 hour 36 minutes.
The average speed was 65km/h.
The local time in Chamonix is the same as the local time in Geneva.
Find the overall average speed of Brad’s journey from his home in New York to Chamonix.
Show all your working and give your answer in km/h.
km/h [11]
Answer/Explanation
Ans:
11 [Total time =]16 h 6 min or 16.1 h
[Distance to airport in New York =] 16.5
[Arc length =] 6200 or 6199 to 6200. …
[Distance Geneva to Chamonix = ] 104
392 to 393
Question
The diagram is a scale drawing of three straight roads, AB, BC and CD.
The scale is 1 :5000.
(a) Find the actual length of the road BC.
Give your answer in metres.
Answer/Explanation
Ans: 475 or 465 to 485
(b) Another straight road starts at M, the midpoint of AB.
This road is perpendicular to AB and it meets the road CD at X.
Using a straight edge and compasses only, construct MX.
Answer/Explanation
Ans: Correct perpendicular bisector with
two pairs of intersecting arcs
(c) There is a park in the area enclosed by the four roads.
The park is
• less than 290m from B
and
• nearer to CD than to CB.
Using a ruler and compasses only, construct the boundaries of the park.
Leave in all your construction arcs and label the park P.
Answer/Explanation
Ans: Compass drawn arc centre B radius 5.8
Accurate angle bisector at C with
correct intersecting arcs
