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Either paper 4 marks
Here is a list of the ingredients needed to make 6 pancakes.
plain flour 156 g milk 48 ml sugar 36 g (a)Callum wants to make 16 pancakes.
Calculate how much milk he needs.
(b)On another day Callum has 624 g of plain flour and plenty of the other ingredients.
Find the greatest number of pancakes he can make.
Show answer
(a) \(128\ \text{ml}\)
(b) \(24\)Find the amount needed for one pancake first:
\(48 \div 6 = 8\) ml
Then multiply by 16:
\(16 \times 8 = 128\) ml
\(624 \div 156 = 4\), so Callum has enough plain flour for 4 times the recipe.
\(4 \times 6 = 24\) pancakes
- (a) M1amount for one pancake \(8\) ml
- (a) A1amount of milk for 16 pancakes \(128\) ml
- (b) M1enough plain flour for \(4\) times the recipe
- (b) A1\(24\) pancakes
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Either paper 4 marks
Priya buys 6 bottles of water. She pays £3.30 altogether.
All the bottles of water cost the same.
(a)Find the cost of 4 bottles of water.
(b)Work out how many bottles of water can be bought for £4.95.
Show answer
(a) \(\text{£}2.20\)
(b) \(9\)Find the cost of one bottle of water first:
\(£3.30 \div 6 = £0.55\)
Then multiply by 4:
\(4 \times £0.55 = £2.20\)
Each bottle of water costs £0.55, so divide the money by the cost of one:
\(£4.95 \div £0.55 = 9\)
- (a) M1cost of one bottle of water \(£0.55\)
- (a) A1cost of 4 bottles of water \(£2.20\)
- (b) M1\(£4.95 \div £0.55\)
- (b) A19 bottles of water
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Either paper 3 marks
A recipe for 12 flapjacks uses 220 g of oats, 130 g of butter and 60 g of golden syrup.
Owen wants to make 60 flapjacks. Owen has 700 g of butter.
Does Owen have enough butter to make 60 flapjacks?
You must show how you get your answer.
Show answer
Yes. 60 flapjacks need \(650\) g of butter, and Owen has \(700\) g.The recipe is for 12 flapjacks and Owen wants 60, so the amounts are multiplied by
\(60 \div 12 = 5\)
The recipe uses 130 g of butter, so 60 flapjacks need
\(5 \times 130 = 650\) g
Owen has 700 g of butter, which is more than the 650 g needed.
The answer is Yes.
- M1scale factor \(60 \div 12 = 5\)
- M1amount of butter needed \(650\) g
- A1Yes, comparing \(650\) g with \(700\) g
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Either paper 3 marks
1.2 metres of ribbon cost £2.64.
Find the cost of 3.5 metres of ribbon.
Show answer
\(\text{£}7.70\)The target is the cost of 3.5 metres, so first find the cost of one metre:
\(£2.64 \div 1.2 = £2.20\)
Now find the cost of 3.5 metres:
\(£2.20 \times 3.5 = £7.70\)
- M1cost of one metre \(£2.64 \div 1.2 = £2.20\)
- M1multiplying by 3.5
- A1£7.70
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Either paper 3 marksA machine prints labels at a steady rate. The table should show how many labels it prints.
One of the four values in the second column is wrong.Time (min) Labels 2 12 7 42 10 60 16 97 (a)Which row of the table is wrong?
You must show your working.
(b)Calculate the value that should be there.
Show answer
(a) The row for \(16\), which gives \(97\)
(b) \(96\ \text{labels}\)Directly proportional means every value in the second column is the same number of times its value in the first.
Divide down each row and look for the odd one out. Three of them give
\(12 \div 2 = 6\)
and the row for \(16\) gives \(97 \div 16\), which is not \(6\).
Every row multiplies the first column by \(6\).
\(16 \times 6 = 96\) labels
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Either paper 3 marks
A school disco must have at least one staff member for every 19 pupils.
(a)99 pupils want to take part.
Find the smallest number of staff members needed.
(b)On a different day only 3 staff members are available.
Find the greatest number of pupils who can take part.
Show answer
(a) \(6\ \text{staff members}\)
(b) \(57\ \text{pupils}\)Each staff member can take 19 pupils.
\(99 \div 19 = 5\) remainder 4
5 staff members can take \(5 \times 19 = 95\) pupils, and 99 is more than 95, so one more staff member is needed.
\(5 + 1 = 6\) staff members
Each of the 3 staff members can take 19 pupils:
\(3 \times 19 = 57\) pupils
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Either paper 5 marks
Last week, Ben worked for 13 hours.
Ben paid no tax and received £169.00.
(a)This week, Ben works for 21 hours.
Ben assumes he will be paid at the same rate per hour and pay no tax.
Work out how much Ben expects to receive this week.
(b)In fact, this week Ben is paid an extra 50p per hour and pays £10.50 tax.
What does this tell you about the amount Ben receives?
Tick one box.
☐ It is less than he expected
☐ It is the same as he expected
☐ It is more than he expected
Show working to support your answer.
Show answer
(a) \(\text{£}273\)
(b) It is the same as he expected: \(£273.00\) received against \(£273.00\) expectedRate per hour: \(£169.00 \div 13 = £13.00\)
Expected pay: \(£13.00 \times 21 = £273.00\)
Extra pay from the rise: \(50\text{p} \times 21 = 1050\text{p} = £10.50\)
Actual pay: \(£273.00 + £10.50 - £10.50 = £273.00\)
Compare with the expected pay of \(£273.00\): the actual pay is the same as he expected.
- (a) M1rate per hour \(£13.00\), from \(£169.00 \div 13\)
- (a) A1expected pay \(£273.00\)
- (b) M1extra pay from the rise \(£10.50\), from \(21\) hours at \(50\)p
- (b) M1actual pay \(£273.00\), after adding \(£10.50\) and taking off \(£10.50\) tax
- (b) A1ticks the same as, comparing the actual pay with \(£273.00\)
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Either paper 6 marks
Marcus buys 2 metres of linen at £9.50 per metre.
He also buys 2 metres of cotton.
The total cost is £31.90.
(a)Find the cost of one metre of cotton.
(b)Buttons cost 87p each.
The greatest number of buttons Marcus can buy with £11 is 12.
Marcus says, "The greatest number of buttons I can buy with £22 is 24 because £22 is double £11."
Is Marcus correct?
You must show your working.
Show answer
(a) \(£6.45\)
(b) No: with £22 Marcus can buy 25 buttons, and \(2 \times 12 = 24\), which is not equal to 25The linen costs \(2 \times 9.50 = £19.00\).
Take the linen from the total:
\(31.90 - 19.00 = 12.90\), so the cotton costs £12.90.
Divide by the 2 metres of cotton:
\(12.90 \div 2 = 6.45\)
One metre of cotton costs £6.45.
Double the money is £22, which is 2200p.
Divide by the price of a button:
\(2200 \div 87 \approx 25.29\)
Only whole buttons can be bought, so the greatest number is 25.
Check: \(25 \times 87 = 2175\), which is no more than 2200.
Twice the first number of buttons is \(2 \times 12 = 24\), which is not equal to 25, so the answer is No.
- (a) M1cost of the linen \(2 \times 9.50 = £19.00\)
- (a) M1cost of the cotton \(31.90 - 19.00 = £12.90\)
- (a) A1dividing by 2 to get £6.45 per metre
- (b) M1£22 is 2200p, and \(2200 \div 87 \approx 25.29\)
- (b) B1the greatest number of whole buttons is 25
- (b) A1No, comparing 25 with \(2 \times 12 = 24\)
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Either paper 3 marks
A machine folds a constant number of leaflets per minute.
The machine takes 6 minutes to fold a batch of 384 leaflets.
How long does it take the machine to fold a larger batch of 2320 leaflets?
Give your answer in minutes and seconds.
Show answer
\(36\) minutes \(15\) secondsFind how many leaflets per minute:
\(384 \div 6 = 64\)
Divide the new number of leaflets by the rate:
\(2320 \div 64 = 36.25\) minutes
The decimal part of a minute is not a number of seconds, so change it to seconds by multiplying by 60:
\(0.25 \times 60 = 15\) seconds
So the time is \(36\) minutes \(15\) seconds.
- M1rate \(384 \div 6 = 64\) leaflets per minute
- M1time \(2320 \div 64 = 36.25\) minutes
- A1\(36\) minutes \(15\) seconds, from \(0.25 \times 60 = 15\)
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Either paper 3 marks
It takes 8 gardeners 21 hours to clear a field.
Calculate how long it would take 7 gardeners to clear the same field.
Assume that all the gardeners work at the same rate.
Show answer
\(24\ \text{hours}\)The number of gardeners and the time taken are in inverse proportion: more gardeners take less time, fewer gardeners take longer. The two numbers always multiply to the same total.
One gardener working alone would take \(8 \times 21 = 168\) hours.
Sharing that between 7 gardeners:
\(168 \div 7 = 24\) hours
- M1total work \(8 \times 21 = 168\) hours
- M1sharing between 7 gardeners: \(168 \div 7\)
- A124 hours