Graphs in Practical Situations (Copy)

IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Practical Graphs (Travel Graphs, Conversion Graphs, Gradient)
Includes Full Worked Solutions
No graph drawing required—questions are designed for written interpretation as per Paper 1 & 2 style.

Paper 1 – Non-Calculator Section

Q1.

A car travels 60 km in 2 hours at constant speed.
a) What is the speed of the car?
b) How far will it travel in 5 hours at the same speed?

Solution:
a) Speed = Distance ÷ Time = 60 ÷ 2 = 30 km/h
b) Distance = Speed × Time = 30 × 5 = 150 km

Answer:
a) 30 km/h
b) 150 km

Q2.

A travel graph shows a person walking 3 km in 1 hour, resting for 30 minutes, then walking another 2 km in 1 hour.
a) Describe each part of the graph.
b) What is the total time of the journey?

Solution:
a)

• First part: straight line rising – walking at constant speed
• Flat line for 30 min – resting
• Rising again – walking at slower speed (since 2 km in 1 hour)

b) Total time = 1 hour + 30 mins + 1 hour = 2 hours 30 minutes

Answer:
a) Walk, rest, walk again at slower speed
b) 2 hours 30 minutes

Q3.

A conversion graph shows 1 kg = 2.5 pounds.
How many pounds is 6 kg?

Solution:
6 × 2.5 = 15 pounds

Answer: 15 pounds

Q4.

A distance-time graph shows a person walking 2 km in 30 minutes, then resting for 15 minutes.
a) What is the walking speed in km/h?
b) How long was the total journey?

Solution:
a) Speed = Distance ÷ Time = 2 ÷ 0.5 = 4 km/h
b) 30 min + 15 min = 45 minutes

Answer:
a) 4 km/h
b) 45 minutes

Paper 2 – Calculator Allowed Section

Q5.

Use the conversion: 1 USD = 280 PKR
a) Convert $50 to Pakistani Rupees
b) How many USD is ₨70,000?

Solution:
a) 50 × 280 = ₨14,000
b) 70,000 ÷ 280 = $250

Answer:
a) ₨14,000
b) $250

Q6.

A person runs 4 km in 30 minutes.
a) What is their average speed in km/h?
b) If they continued at this speed, how far would they run in 1 hour 15 minutes?

Solution:
a) Time = 0.5 h → Speed = 4 ÷ 0.5 = 8 km/h
b) Time = 1.25 hours
Distance = 8 × 1.25 = 10 km

Answer:
a) 8 km/h
b) 10 km

Q7.

A graph shows a straight line passing through (0, 0) and (4, 16).
a) What is the gradient of the line?
b) What does this gradient represent if the graph is time (h) vs. distance (km)?

Solution:
a) Gradient = change in y ÷ change in x = (16 – 0) ÷ (4 – 0) = 4
b) Gradient = Speed, so 4 km/h

Answer:
a) 4
b) 4 km/h

Q8.

A conversion graph shows litres on x-axis and gallons on y-axis.
It passes through (0, 0) and (5, 1.1).
a) What is the conversion rate from litres to gallons?
b) How many gallons is 12 litres?

Solution:
a) Rate = gallons ÷ litres = 1.1 ÷ 5 = 0.22 gallons per litre
b) 12 × 0.22 = 2.64 gallons

Answer:
a) 0.22 gallons per litre
b) 2.64 gallons

Q9.

A person travels 40 km in 2 hours, then 60 km in 3 hours.
a) What is their average speed for the full journey?
b) Draw the overall shape of the distance–time graph (describe in words).

Solution:
a) Total distance = 40 + 60 = 100 km
Total time = 2 + 3 = 5 hours
Speed = 100 ÷ 5 = 20 km/h

b) Graph shape:

• First line rises steadily (40 km in 2 h)
• Second line is less steep (slower speed – 60 km in 3 h)

Answer:
a) 20 km/h
b) Two rising lines, second less steep

Q10.

A currency conversion graph shows 1 Euro = $1.2
a) How much is €75 in dollars?
b) A product costs $96. How many euros is that?

Solution:
a) 75 × 1.2 = $90
b) 96 ÷ 1.2 = €80

Answer:
a) $90
b) €80

This paper covers all CORE-level graph applications, including distance–time graphs, conversion rates, and gradient interpretation.