GCSE Maths · Higher · Chapter 5: Ratio and proportion · Lesson 1

Ratio and direct proportion

Grades 4–7About 45 minutesCalculator allowed35 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Write $25 : 45$ in its simplest form.
[1 mark]
Answer
A2
From chapter 3
Write down the midpoint of the class $10 < t \leq 30$ .
[1 mark]
Answer
A3
Last lesson
Find the second difference of $8, 15, 24, 35, 48$ .
[1 mark]
Answer
A4
Key Stage 3
Write $\frac{7}{8}$ as a decimal.
[1 mark]
Answer

Grades 4–6

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

Example 1

Share £264 in the ratio $5 : 7$ .

Hint Add the parts of the ratio to find how many parts there are altogether.

B1
Share £203 in the ratio $3 : 4$ .
[2 marks]
Answer£ $\dots\dots$ and £ $\dots\dots$

Example 2

A 300 g bag of nuts costs £2.55. A 500 g bag costs £4.10. Which bag is better value?

Hint Work out the cost of one gram from each bag, in pence.

B2
A pack of 6 yoghurts costs £2.94. A pack of 10 of the same yoghurts costs £4.80. Which is better value? Show your working.
[3 marks]
Answer

Grades 5–6

C1
Write 48 minutes : 2 hours in the form $1 : n$ .
[2 marks]
Answer
C2
8 identical books weigh 5.6 kg. Work out the weight of 13 of the books.
[2 marks]
Answer

C3
Juice and water are mixed in the ratio $3 : 8$ . How much juice goes with 440 ml of water?
[2 marks]
Answer
C4
Sam and Tia share sweets in the ratio $3 : 5$ . Tia gets 18 more than Sam. How many sweets are there?
[2 marks]
Answer
C5
$a : b = 3 : 4$ and $b : c = 6 : 5$ . Write $a : b : c$ in its simplest form.
[2 marks]
Answer
C6
The graph shows that the cost of petrol is directly proportional to the number of litres bought. Work out the cost of 70 litres.
[2 marks]
Answer

Grades 6–7

D1
Ellie says, "When £160 is shared in the ratio $3 : 5$ , the smaller share is £96, because $160 \div 5 = 32$ and $3 \times 32 = 96$ ."
Explain why Ellie is wrong, and give the correct smaller share.
[2 marks]

D2
Concrete is made by mixing cement, sand and gravel in the ratio $1 : 2 : 4$ by mass. A builder makes 280 kg of concrete.
(a)
Work out the mass of gravel he uses.
[2 marks]
Answer
(b)
Cement is sold in 25 kg bags. How many bags of cement must he buy?
[2 marks]
Answer
(c)
For his next job he has only 75 kg of sand, and plenty of cement and gravel. Work out the greatest mass of concrete he can make.
[2 marks]
Answer
Total for D2: 6 marks
D3
Ali and Ben have money in the ratio $5 : 3$ . Ali gives Ben £20. Now they have the same amount. How much did Ali have at the start?
[3 marks]
Answer

Grade 8 and beyond

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 write a ratio in its simplest form and in the form $1 : n$ .
I can share an amount in a ratio and use the unitary method.
I can decide which of two packs is better value.

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