KS3 Maths · Year 7 · Chapter 7: Graphs · Lesson 4

Real-life graphs

Year 7About 75 minutesNo calculator45 marks

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Date

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Quick questions to start.

A1
Needed today
Write $20$ minutes as a fraction of an hour.
[1 mark]
Answer
A2
Needed today
A train goes $60$ km in one hour. How far does it go in $15$ minutes?
[1 mark]
Answer
A3
Last lesson
Work out $y = x^{2} - 8$ when $x = - 3$ .
[1 mark]
Answer
A4
From chapter 6
A cube has edges of $3$ cm. Work out its surface area.
[1 mark]
Answer

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

The graph shows Ella's bike ride from home. Describe her ride. Give the speed of each part in km/h.

Hint Up means moving away from home, flat means stopped, down means coming back. Change the minutes to hours before you divide.

B1
The graph shows Sam's walk from home. For how many minutes did Sam stop? Work out his speed on the way out, in km/h.
[3 marks]
Answer

Example 2

The graph shows what a plumber charges. Write down the call-out charge (the cost for $0$ hours) and the charge for each hour.

Hint The call-out charge is where the line meets the cost axis. The charge for each hour is how much the cost goes up for one hour across.

B3
The graph shows the cost of a taxi. Write down (i) the fixed charge, (ii) the cost for each mile, (iii) the cost of an $8$ mile journey.
[3 marks]
Answer

Example 3

Cars $A$ and $B$ leave the same place along the same road. When and how far from the start does $B$ pass $A$ ?

Hint They are at the same place at the same time where the two lines cross.

B4
$P$ and $Q$ walk towards each other along one path. The graph shows each one's distance from $P$ 's home. When do they meet, and how far from $P$ 's home?
[2 marks]
Answer

Year 7

C1
The graph changes pounds into euros. Change (a) £ $25$ into euros, (b) € $150$ into pounds.
[3 marks]
Answer
C2
The graph shows a journey in three stages, $A$ , $B$ and $C$ . Which stage was the fastest? Work out its speed in km/h.
[3 marks]
Answer

C3
A train travels at $80$ km/h. How many minutes does it take to travel $20$ km?
[2 marks]
Answer
C4
A bus travels $12$ km in $20$ minutes. Work out its speed in km/h.
[2 marks]
Answer

GCSE Foundation

D1
Ana says, "Leo ran faster in part $P$ , because part $P$ lasted longer."
The graph shows Leo's run. Ana is wrong. Work out Leo's speed in km/h in part $P$ and in part $Q$ .
[4 marks]
Answer

D2
A van leaves the depot at $8 : 00$ and makes two deliveries. The graph shows its journey until $11 : 00$ .
(a)
How far from the depot was the van at $10 : 00$ ?
[1 mark]
Answer
(b)
For how many minutes was the van stopped altogether?
[1 mark]
Answer
(c)
At $11 : 00$ the van drives back to the depot at $80$ km/h. Complete the graph.
[2 marks]
(d)
Work out the average speed of the van from $8 : 00$ until it is back at the depot, stops included.
[2 marks]
Answer
Total for D2: 6 marks
D3
Firm $A$ and firm $B$ hire out a cement mixer. The graph shows what each firm charges.
(a)
Write down the fixed charge for firm $A$ .
[1 mark]
Answer
(b)
For how many hours do the two firms charge the same?
[1 mark]
Answer
(c)
Which firm is cheaper for $6$ hours, and by how much?
[2 marks]
Answer
Total for D3: 4 marks
D4
Raj says, "My average speed was $16$ km/h, because $12$ and $20$ have a mean of $16$ ."
Raj cycles $18$ km at $12$ km/h, then $10$ km at $20$ km/h. Work out his average speed for the whole ride.
[4 marks]
Answer

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can describe a journey from a distance-time graph and work out a speed from it.
I can read a conversion graph both ways.
I can read a fixed charge and a cost per unit from a graph.
I can work out an average speed for a whole journey.

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