-
Non-calculator 3 marks
Work these out without using a calculator.
(a)Work out 10% of £500.
(b)Work out 55% of £500.
Show answer
(a) \(\text{£}50\)
(b) \(\text{£}275\)To find 10%, divide by 10.
\(500 \div 10 = 50\)
10% of £500 is £50.
Split the percentage into pieces you can already find: 55% = 50% + 5%.
10% of £500 is £50, and 50% is 5 lots of 10%:
\(5 \times 50 = 250\)
5% is half of 10%:
\(50 \div 2 = 25\)
Add the two pieces:
\(250 + 25 = 275\)
55% of £500 is £275.
- (b) M150% of the amount, \(5 \times 50 = 250\), and 5% of the amount, \(25\)
- (b) A1adds the pieces to get \(£275\)
-
Either paper 1 markThe table shows the number of emails a company received each month.
Write down the percentage decrease from October to November.October November 350 259 Show answer
\(26\ \%\)The change is \(350 - 259 = 91\).
As a fraction of the first figure, \(\frac{ 91 }{ 350 } \times 100 = 26\%\).
The decrease is 26%.
-
Either paper 3 marks
There are 1000 spaces in a car park.
(a)80% of the spaces are being used.
Work out how many spaces are being used.
(b)Work out how many spaces are not being used.
Show answer
(a) \(800\)
(b) \(200\)80% means 80 out of every 100, so multiply by \(\frac{ 80 }{100}\).
\(1000 \times \frac{ 80 }{100} = 800\)
800 spaces are being used.
Take the answer to part (a) away from the total:
\(1000 - 800 = 200\)
- (a) M1multiplies the total by \(\frac{ 80 }{100}\), \(1000 \times \frac{ 80 }{100}\)
- (a) A1\(800\)
-
Either paper 3 marks
Owen is paid £2900 a month.
He is given a pay rise of 8%.
Work out his new monthly pay.
Show answer
\(\text{£}3132\)One way is to find the rise and add it on.
\(2900 \times \frac{ 8 }{100} = 232\), so the rise is £232.
\(£2900 + £232 = £3132\)
A quicker way is to use a multiplier. Increasing by 8% keeps the original 100% and adds 8% on top, so it multiplies by
\(1 + \frac{ 8 }{100} = 1.08\)
\(2900 \times 1.08 = 3132\)
His new monthly pay is £3132.
- M18% of the pay, \(\frac{ 8 }{100} \times 2900 = 232\)
- M1adds the rise to the pay, \(2900 + 232\), or multiplies by \(1.08\)
- A1new monthly pay \(£3132\)
-
Either paper 3 marks
The normal price of a sofa is £420.
In a sale the price is reduced by 20%.
Find the sale price of the sofa.
Show answer
\(\text{£}336\)One way is to find the reduction and take it off.
\(420 \times \frac{ 20 }{100} = 84\), so the price comes down by £84.
\(£420 - £84 = £336\)
A quicker way is to use a multiplier. Taking 20% off leaves 80% of the price, so it multiplies by
\(1 - \frac{ 20 }{100} = 0.8\)
\(420 \times 0.8 = 336\)
The sale price is £336.
- M1reduction \(84\), or multiplier \(0.8\)
- M1subtracting from \(420\), or multiplying \(420\) by \(0.8\)
- A1sale price £\(336\)
-
Either paper 4 marks(a)
Joel scored 38 out of 50 in a French test.
Work out his French score as a percentage.
(b)In a History test Joel scored 18 out of 40.
In which test did Joel do better?
You must show your working.
Show answer
(a) \(76\%\)
(b) FrenchWrite the score as a fraction of the total, then multiply by 100.
\(\frac{ 38 }{ 50 } \times 100 = 76\)
Joel scored 76% in French.
The two tests are out of different totals, so the raw marks cannot be compared directly. Turn the second one into a percentage as well.
\(\frac{ 18 }{ 40 } \times 100 = 45\)
French: 76%. History: 45%.
Joel did better in French.
- (a) M1score as a fraction of the total, multiplied by 100, \(\frac{ 38 }{ 50 } \times 100\)
- (a) A1\(76\%\)
- (b) M1writes both scores as percentages, or as fractions over a common denominator
- (b) A1French
-
Either paper 2 marks
In a test, Omar needs to score at least 60% of the 60 marks to pass.
He scores 33 marks.
Show that Omar does not pass the test.
Show answer
Pass mark = 36 marks. 33 is less than 36, so Omar does not pass the test.Work out the pass mark first:
\(60 \times \frac{ 60 }{100} = 36\) marks
Omar scored 33 marks, which is less than 36 marks.
So Omar does not pass the test.
- M1pass mark \(60 \times \frac{ 60 }{100} = 36\) marks, or \(33 \div 60 \times 100 = 55.0\%\)
- A1does not pass, comparing 33 with 36 marks (or 55.0\% with 60\%)
-
Either paper 3 marks
Here is a large rectangle with a smaller rectangle cut out of it. The shaded part is what is left.
Work out the percentage of the large rectangle that is shaded.
Show answer
\(62.5\%\)The areas are not given, so work them out from the lengths on the diagram.
Large rectangle: \(16 \times 12 = 192\) cm²
Cut-out: \(9 \times 8 = 72\) cm²
Shaded area: \(192 - 72 = 120\) cm²
Write the shaded area as a fraction of the whole rectangle and multiply by 100.
\(\frac{ 120 }{ 192 } \times 100 = 62.5\)
62.5% of the large rectangle is shaded.
Check: the cut-out is \(37.5\%\) of the rectangle and \(37.5 + 62.5 = 100\).
- M1large rectangle \(192\) cm² and cut-out \(72\) cm²
- M1shaded area \(120\) cm²
- A1\(62.5\%\)
-
Either paper 2 marksOmar and Grace each bought a tent and a sleeping bag. The table shows how much they paid.
Grace says, “In total, I paid more than Omar.” Is Grace correct? Tick a box. Yes / No You must show calculations to support your answer.Tent Sleeping bag Omar £145 £53 Grace 15% less than Omar 35% more than Omar Show answer
No: Grace paid \(£194.80\) in total, compared with \(£198.00\) for OmarGrace pays 15% less than \(£145\) for the tent, so Grace pays \(85\%\) of it:
\(£145 \times \frac{ 85 }{100} = £123.25\)
Grace pays 35% more than \(£53\) for the sleeping bag, so Grace pays \(135\%\) of it:
\(£53 \times \frac{ 135 }{100} = £71.55\)
Grace's total is \(£123.25 + £71.55 = £194.80\).
Omar's total is \(£145 + £53 = £198.00\).
Comparing \(£194.80\) with \(£198.00\): No, since Grace paid \(£194.80\), which is less than Omar's \(£198.00\).
- M1Grace's total, \(£123.25 + £71.55 = £194.80\)
- A1No, comparing \(£194.80\) with Omar's \(£198.00\)
-
Either paper 1 mark
The number of people subscribed to a channel increases from 40,000 to 80,000.
The channel's owner says, "My subscribers have increased by 100%, because 80,000 is 40,000 times 2."
Are they correct? Tick a box.
☐ Yes ☐ No
Give a reason for your answer.
Show answer
Yes — the increase is 40,000, which is 100% of 40,000, so the claim of 100% is correct80,000 is 40,000 times 2, so the number has been multiplied by 2.
The increase is the new figure take away the old figure:
\(80000 - 40000 = 40000\)
As a percentage of the old figure:
\(\frac{ 40000 }{ 40000 } \times 100 = 100\%\)
"2 times as many" keeps the whole of the old figure (100%) and adds 100% on top, so the increase is 100%. The 200% is the new figure as a percentage of the old figure, which is not the same as the increase.
The claim of 100% is correct.