Plot the temperatures on the line graph
Mon: 15°C, Tue: 10°C, Wed: 10°C
Mon: 15°C, Tue: 10°C, Wed: 10°C
Worked Solution & Answer
Mon=15°C, Tue=10°C, Wed=10°C B1
Answer: Points plotted at 15°C, 10°C, 10°C
Real life graphs — Notes & Worked Examples Show / Hide
Explanation:
On a distance–time graph, a sloping straight line represents constant speed, a horizontal flat line means the object is stationary (stopped), and the gradient equals the speed (DistanceTime). Always check the time scale on the horizontal axis (e.g. 15 mins = 0.25 hours).
On a cost or conversion graph (such as taxi fares or utility bills), the y-intercept is the fixed standing charge, and the gradient (Change in yChange in x) is the rate per unit (e.g. cost per mile).
Example 1: A cyclist leaves at 09:00, travels 18 km by 09:45, rests 15 mins, then cycles 18 km home by 10:30. Find Stage 1 speed in km/h.
Dist = 18 km
45 min = 0.75 h
Speed = 180.75 = 24 km/h
Example 2: A plumber's graph goes from (0, 45) through (3, 135) for hours x and cost y (£). Find the call-out fee and hourly rate.
Fee (0 hrs) = £45
Rate = 135 − 453 = £30/h
Find the increase in temperature from Mon to Tue
Worked Solution & Answer
20°C - 5°C = 15°C B1
Answer: 15°C
A train travels from Derby to Sheffield.
The travel graph shows information about the train’s journey.
The travel graph shows information about the train’s journey.
(a) Work out the speed of the train.
Give your answer in miles per hour. [2 marks]
Give your answer in miles per hour. [2 marks]
miles per hour
(b) Show this information on the travel graph. [1 mark]
Worked Solution & Answer
(a)
(Average speed = distance ÷ time)
Distance = 35 miles, Time = 30 minutes = 0.5 hours M1
Speed = 35 ÷ 0.5 = 70 mph A1
Distance = 35 miles, Time = 30 minutes = 0.5 hours M1
Speed = 35 ÷ 0.5 = 70 mph A1
Answer (a): 70 miles per hour
(b)
(Average speed = distance ÷ time)
Draw horizontal line at distance 35 from t = 30 to t = 45 B1
Draw horizontal line at distance 35 from t = 30 to t = 45 B1
Answer (b): Horizontal line from (30, 35) to (45, 35)
Jenny leaves home at 06.00
She runs for 3 hours.
Here is a distance-time graph of her run.
She runs for 3 hours.
Here is a distance-time graph of her run.
(a) How far from home is she after 3 hours? [1 mark]
Answer
km
(b) For the next hour she rests.
She then gets a bus home.
She arrives home at 11.30
Complete the distance-time graph.
Assume the bus travels at a constant speed. [2 marks]
She then gets a bus home.
She arrives home at 11.30
Complete the distance-time graph.
Assume the bus travels at a constant speed. [2 marks]
Worked Solution & Answer
(a)
At 09.00 (3 hours after 06.00), read the distance from the vertical axis: 20 km. B1
Answer (a): Answer 20 km
(b)
(Average speed = distance ÷ time)
Resting for 1 hour: draw a horizontal line at 20 km from 09.00 to 10.00 M1
Bus travels home: draw a straight line from (10.00, 20) to (11.30, 0). A1
Resting for 1 hour: draw a horizontal line at 20 km from 09.00 to 10.00 M1
Bus travels home: draw a straight line from (10.00, 20) to (11.30, 0). A1
Answer (b): Horizontal line from (09.00, 20) to (10.00, 20), then a straight line from (10.00, 20) to (11.30, 0).
You can use this graph to change between ounces and grams.
(a) Change 850 grams to ounces. [1 mark]
ounces
(b) Change 80 ounces to grams. [2 marks]
grams
Worked Solution & Answer
(a)
850 g = 30 oz B1
Answer (a): 30 ounces
(b)
20 oz ≈ 568 g M1
⇒ 80 oz = 4 × 568 ≈ 2270 g A1
⇒ 80 oz = 4 × 568 ≈ 2270 g A1
Answer (b): 2270 grams
You can use this graph to change between stones and kilograms.
(a) Change 3 stones to kilograms. [1 mark]
kilograms
(b) Change 80 kilograms to stones. [2 marks]
stones
Worked Solution & Answer
(a)
At 3 stones, read 19 kg B1
Answer (a): 19 kilograms
(b)
At 40 kg, read 6.25 stones M1
2 × 6.25 = 12.5 stones A1
2 × 6.25 = 12.5 stones A1
Answer (b): 12.5 (accept 12.4 to 12.8) stones
Amy walked from her home to the skate park.
The travel graph of Amy’s walk to the skate park is shown below.
The travel graph of Amy’s walk to the skate park is shown below.
(a) How far is it from her friend’s house to the skate park? [1 mark]
km
(b) Complete the travel graph. [2 marks]
Worked Solution & Answer
(a)
5 – 3 = 2 km B1
Answer (a): 2 km
(b)
(Average speed = distance ÷ time) M1 A1
Answer (b): Horizontal line from (3pm, 5) to (5pm, 5), then straight line to (6:30pm, 0)
Steve drove from his home to his friend's house.
He stayed at his friend's house and then drove home.
Here is Steve's travel graph.
He stayed at his friend's house and then drove home.
Here is Steve's travel graph.
(a) For how many minutes did Steve stay at his friend's house? [1 mark]
minutes
(b) What was Steve's average speed on his journey home? [2 marks]
km/h
Worked Solution & Answer
(a)
Horizontal from 12 45 to 13 30 = 45 minutes B1
Answer (a): 45 minutes
(b)
Distance = 25 km in 30 minutes (0.5 hours) → Speed = 25 ÷ 0.5 = 50 km/h M1 A1
Answer (b): 50 km/h
Here is the distance-time graph for a car between 1 pm and 3 pm
(a) Work out the total time that the car is not moving between 1 pm and 3 pm
State the units of your answer. [2 marks]
State the units of your answer. [2 marks]
Answer
minutes
(b) Work out the total distance the car travels between 1 pm and 3 pm [2 marks]
Answer
miles
Worked Solution & Answer
(a)
The car is not moving during the horizontal sections: M1
From 1.30 pm to 2.00 pm: 30 minutes
From 2.15 pm to 2.30 pm: 15 minutes
Total time = 30 + 15 = 45 minutes (or 34 hour) A1
From 1.30 pm to 2.00 pm: 30 minutes
From 2.15 pm to 2.30 pm: 15 minutes
Total time = 30 + 15 = 45 minutes (or 34 hour) A1
Answer (a): Answer 45 minutes minutes
(b)
From 1.00 pm to 1.30 pm: 29 miles M1
From 2.00 pm to 2.15 pm: travels 29 - 25 = 4 miles
From 2.30 pm to 3.00 pm: travels 25 miles
Total distance = 29 + 4 + 25 = 58 miles A1
From 2.00 pm to 2.15 pm: travels 29 - 25 = 4 miles
From 2.30 pm to 3.00 pm: travels 25 miles
Total distance = 29 + 4 + 25 = 58 miles A1
Answer (b): Answer 58 miles
Scarlett leaves home at 10.00 to cycle to the supermarket.
Here is part of a distance-time graph of her trip to the supermarket.
Here is part of a distance-time graph of her trip to the supermarket.
(a) She arrives at the supermarket at 10.20
How far is the supermarket from her home? [1 mark]
How far is the supermarket from her home? [1 mark]
Answer
km
(b) She leaves the supermarket at 10.35
How long does she stay at the supermarket? [1 mark]
How long does she stay at the supermarket? [1 mark]
Answer
minutes
(c) Scarlett cycles home at a constant speed using the same route.
It takes her 3 minutes longer than her journey to the supermarket.
Complete the distance-time graph. [2 marks]
It takes her 3 minutes longer than her journey to the supermarket.
Complete the distance-time graph. [2 marks]
Answer
Worked Solution & Answer
(a)
Reading the vertical axis at 10.20: distance is 7 km. B1
Answer (a): Answer 7 km
(b)
Time stayed = 10.35 - 10.20 = 15 minutes. B1
Answer (b): Answer 15 minutes
(c)
(Average speed = distance ÷ time)
Outbound journey took 20 minutes (10.00 to 10.20) M1
Return journey takes 20 + 3 = 23 minutes
Leaves at 10.35, arrives home at 10.35 + 23 minutes = 10.58
Draw a straight line from (10.35, 7) down to (10.58, 0). A1
Outbound journey took 20 minutes (10.00 to 10.20) M1
Return journey takes 20 + 3 = 23 minutes
Leaves at 10.35, arrives home at 10.35 + 23 minutes = 10.58
Draw a straight line from (10.35, 7) down to (10.58, 0). A1
Answer (c): Answer Line from (10.35, 7) to (10.58, 0)