Home / iGCSE Mathematics (0580) :C1.12 Calculate a given percentage of a quantity. . iGCSE Style Questions Paper 3

iGCSE Mathematics (0580) :C1.12 Calculate a given percentage of a quantity. . iGCSE Style Questions Paper 3

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IGCSE Mathematics(0580) Practice Questions Paper 3 - All Chapters
Question

Two friends, Diego and Javier, meet at a swimming pool. The travel graph shows Diego’s journey by bicycle from his home to the swimming pool.

(a) Calculate Diego’s speed for his journey from his home to the swimming pool. Give your answer in kilometers per hour.

(b) Diego stays at the swimming pool until 1220.

(i) On the grid, draw the line representing the time he stays at the swimming pool.

(ii) Work out how long, in hours and minutes, he is at the swimming pool.

(c) Javier leaves his home 15 minutes later than Diego. He walks to the swimming pool at a constant speed of 6km/h. On the grid, show Javier’s journey from his home to the swimming pool.

(d) They both leave the swimming pool at 1220 and return to their own homes, each at a constant speed. Diego arrives home at 1245. Javier arrives home 5 minutes later than Diego. Complete the travel graph.

▶️ Answer/Explanation
Solution

(a) Ans: 9 km/h

Diego’s journey:
• Distance: 6 km (from 10 km to 4 km on y-axis)
• Time: 40 minutes (from 10:00 to 10:40)
• Speed = Distance/Time = 6 km ÷ (40/60) hours = 9 km/h

(b)

(i) Graph line: Horizontal line from (10:40, 6 km) to (12:20, 6 km)

(ii) Ans: 1 hour 40 minutes
Duration: 12:20 – 10:40 = 1 hour 40 minutes

(c) Ans: Line from (10:15, 10 km) to (10:55, 6 km)

Javier’s journey:
• Starts at 10:15 (15 minutes after Diego)
• Distance: 4 km (from 10 km to 6 km)
• Time = Distance/Speed = 4 km ÷ 6 km/h = 40 minutes
• Arrives at 10:55

(d)

Return journeys:
• Diego: Line from (12:20, 6 km) to (12:45, 0 km)
• Javier: Line from (12:20, 6 km) to (12:50, 10 km)

Calculations:
• Diego’s return speed: 6 km ÷ (25/60) hours = 14.4 km/h
• Javier’s return speed: 4 km ÷ (30/60) hours = 8 km/h

Question

(a) Sara rides her bicycle at a speed of 420 metres per minute.
Work out her speed in kilometres per hour.

(b) Jan cycles a distance of 51km.
She starts at 11:55.
She has a rest stop for 25 minutes.
She finishes at 14:41.
Calculate her average speed, in km/h, for the time she is cycling.

▶️ Answer/Explanation
Solution

(a) Ans: 25.2 km/h

Conversion steps:

1. Convert metres to kilometres:
420 m/min = 0.42 km/min

2. Convert minutes to hours:
0.42 km/min × 60 min/h = 25.2 km/h

This is because there are 1000 metres in 1 km and 60 minutes in 1 hour.

(b) Ans: 21.7 km/h

Calculation steps:

1. Calculate total time:
From 11:55 to 14:41 = 2 hours 46 minutes = 166 minutes

2. Subtract rest time:
166 minutes – 25 minutes = 141 minutes cycling

3. Convert to hours:
141 minutes ÷ 60 = 2.35 hours

4. Calculate average speed:
Speed = Distance ÷ Time = 51 km ÷ 2.35 h ≈ 21.7 km/h

Note: The exact value is 21.702… km/h, which rounds to 21.7 km/h (1 d.p.)

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