CIE Mathematics Paper-1: Specimen Questions 151 - 153 of 175

Question number: 151

Short Answer Question▾

Write in Short

The scale on a map is 2: 300000. A road is 5.8 centimeters long on the map. Solve for the actual length of the road (in kilometers).

Explanation

Here, meaning of 2: 300000 is 2 cm long road is magnified by 300000 times on the map.

  • So, here 5.8 cm long road on the map can be 5.8×300000=1740000cmlong
  • Now, 100 cm = 1 m, so 174000 cm =?

1740000100=17400m

  • Now, 1000 m = 1 km, so 17400 m =?

174001000=17.4km

  • So, length of road is 17.4 kilometers.

Question number: 152

Essay Question▾

Describe in Detail

(a) Solve for volume of a cylinder of radius 50 cm and height 138 cm.

(b) Answer in cubic meters.

Explanation

Here,

(a) Formula of Volume of Cylinder V=πr2h , where r = radius, h = height

So, here r = 50 cm and h = 138 cm.

So, Volume V=π×(50)2×138=3.14×2500×138=1083300cm3

(b) For answer in cubic meters: 1meter=100cm1m3=1003cm31m3=1000000cm3

So, 1000000cm3=1m3

1083300cm3=?m3

1083300×11000000=1.0833m3

Question number: 153

Short Answer Question▾

Write in Short

On a journey a bus takes 35 minutes to travel the first 10 kilometers. It then travels a further 20 kilometers in the next 40 minutes.

  1. The bus started the journey at 18: 50. At what time did it complete the journey?
  2. Calculate the average speed of the whole journey in

    (i) kilometers/minute,

    (ii) kilometers/hour.

Explanation

Here, bus takes 35 minutes to travel the first 10 kilometers then travels a further 20 kilometers in the next 40 minutes.

(a) Bus started the journey at 18: 50.

It takes total 35+40=75minutes=1hourand15minutes.

So, it had completed the journey at 18: 50 + 1 hour + 15 minutes = 19: 50 + 15 minutes = 19: 50 + 10 minutes + 5 minutes = 20: 05.

(b) Here total distance = 10+20=30kilometers

Total time = 35+40=75minutes

(i) Average speed = totaldistancetotaltime=3075=0.4kmm

(ii) 60 minutes = 1 hour

75 minutes =? hours

75×160=1.25 hours

So, average speed = totaldistancetotaltime=301.25=24kmh.

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