Complete the following conversions between fractions, decimals and percentages.
(a)Write 7/10 as a percentage.(1)
(b)Write 0.35 as a percentage.(1)
(c)Write 45% as a decimal.(1)
(Total for Question 1 is 3 marks)
2
Find the following percentages of amounts without using a calculator.
(a)Find 10% of 250 g.(1)
(b)Find 25% of 96 ml.(1)
(c)Find 50% of L48.(1)
(Total for Question 2 is 3 marks)
3
Use known percentages (such as 10% and 5%) to build up other percentages. Show your method for each part.
(a)Calculate 15% of 60 kg.(2)
(b)Calculate 35% of 80 minutes.(2)
(Total for Question 3 is 4 marks)
4
Which of the following is equivalent to 3/8?
A) 37.5%
B) 35%
C) 38%
D) 40%
(Total for Question 4 is 1 mark)
5
Answer the following questions about one quantity as a percentage of another.
(a)Express 18 out of 40 as a percentage.(2)
(b)In a class of 32 pupils, 20 are girls. What percentage of the class are boys?(3)
(Total for Question 5 is 5 marks)
6
Write these four values in order of size, starting with the smallest: 7/25, 0.37, 36%, 7/20.
(Total for Question 6 is 2 marks)
7
Priya buys a coat priced at L80. The shop increases the price of the coat by 15%. Work out the new price of the coat.
(Total for Question 7 is 3 marks)
8
A jacket costs L64. In a sale it is reduced by 30%. Find the sale price of the jacket.
(Total for Question 8 is 3 marks)
9
A recipe for 8 people requires 320 g of flour. Grace wants to make the recipe for 10 people.
(a)What percentage of the original recipe does Grace need to make?(2)
(b)Calculate how much flour Grace needs to make the recipe for 10 people.(2)
(Total for Question 9 is 4 marks)
10
Two shops sell the same jumper. Shop A prices the jumper at L45 and offers 20% off. Shop B prices the same jumper at L50 and offers 30% off.
(a)Calculate the sale price at Shop A.(2)
(b)Calculate the sale price at Shop B.(2)
(c)State which shop offers the better deal, and by how much.(1)
(Total for Question 10 is 5 marks)
11
The population of a village was 2,400 in 2020. By 2024 the population had increased by 12%. Calculate the population of the village in 2024.
(Total for Question 11 is 3 marks)
12
Tomasz invests L500 in a savings account that pays 4% simple interest per year.
(a)Calculate the interest earned after 3 years.(3)
(b)Work out the total amount in the account after 3 years.(1)
(Total for Question 12 is 4 marks)
13
After a pay rise of 20%, Aisha's annual salary is L30,000. Calculate her annual salary before the pay rise.
(Total for Question 13 is 3 marks)
14
A shop reduces all its prices by 15% in a sale. A jacket now costs L51 in the sale. Calculate the original price of the jacket before the sale.
(Total for Question 14 is 3 marks)
15
In January, 40% of the pupils at a school walked to school. In February, this rose to 44%.
(a)Calculate the increase in percentage points from January to February.(1)
(b)Calculate the percentage increase in the proportion of pupils walking to school (as a percentage of the original 40%).(3)
(Total for Question 15 is 4 marks)
16
A school has 300 pupils. 60% of the pupils are girls.
(a)Calculate the number of girls at the school.(2)
(b)20% of the girls and 25% of the boys walk to school. Calculate the total number of pupils who walk to school.(4)
(Total for Question 16 is 6 marks)
17
A price of L200 is increased by 10%. The new price is then decreased by 10%.
(a)Work out the final price.(3)
(b)Explain why the final price is not equal to the original price of L200.(2)
(Total for Question 17 is 5 marks)
18
A laptop priced at L600 is first reduced by 20%. A student discount of a further 10% is then applied to the reduced price.
(a)Calculate the final price of the laptop.(3)
(b)A sales assistant claims that a 20% discount followed by a 10% discount is the same as a single 30% discount. Show that the assistant is wrong, and find the single percentage discount that is equivalent to the two discounts combined.(4)
(Total for Question 18 is 7 marks)
19
Farida buys and sells vintage bicycles.
(a)She buys a bicycle for L150 and sells it for L180. Calculate her percentage profit.(3)
(b)She buys another bicycle for L220 and sells it for L187. Calculate her percentage loss.(3)
(Total for Question 19 is 6 marks)
20
A cafe's electricity bill before tax was L120. A tax of 5% is added to the bill.
(a)Calculate the total bill, including tax.(2)
(b)The following year, the pre-tax bill rises to L150 and the tax rate rises to 8%. Calculate the increase in the total bill (including tax) from the previous year to this year.(4)
(Total for Question 20 is 6 marks)
21
A price is increased by 25%. The new price is then decreased by 20%. Show that the final price is equal to the original price, whatever the starting price was.
(Total for Question 21 is 3 marks)
Mark scheme · EP.M5 Percentages
Question 1
(a) B1 70% cao
(a) Answer: 70%
(b) B1 35% cao
(b) Answer: 35%
(c) B1 0.45 cao
(c) Answer: 0.45
Question 2
(a) B1 25 g cao
(a) Answer: 25 g
(b) B1 24 ml cao
(b) Answer: 24 ml
(c) B1 L24 cao
(c) Answer: L24
Question 3
(a) M1 finds 10% of 60 (= 6) and 5% of 60 (= 3), or equivalent method
(a) A1 9 kg cao
(a) Answer: 9 kg
(b) M1 finds 10% of 80 (= 8) and uses it to build 35%, or equivalent method
(b) A1 28 minutes cao
(b) Answer: 28 minutes
Question 4
B1 A (37.5%) cao
Answer: A) 37.5%
Question 5
(a) M1 18/40 oe seen (e.g. 9/20 or 0.45)
(a) A1 45% cao
(a) Answer: 45%
(b) M1 number of boys = 32 - 20 (= 12)
(b) M1 dep on first M1: 12/32 oe seen
(b) A1 37.5% cao
(b) Answer: 37.5%
Question 6
M1 converts all four values to the same form (e.g. decimals: 0.28, 0.37, 0.36, 0.35)
A1 7/25, 7/20, 36%, 0.37 cao (correct order, allow ft from correct conversions)
Answer: 7/25, 7/20, 36%, 0.37
Question 7
M1 15% of 80 found (= 12), e.g. via 10% = 8 and 5% = 4
M1 dep: 80 + their 15% increase
A1 L92 cao
Answer: L92
Question 8
M1 30% of 64 found (= 19.20), e.g. via 10% = 6.40
M1 dep: 64 - their 30% reduction
A1 L44.80 cao
Answer: L44.80
Question 9
(a) M1 10/8 oe seen
(a) A1 125% cao
(a) Answer: 125%
(b) M1 320 x 1.25 oe (ft from part a as a decimal multiplier)
(b) A1 400 g cao
(b) Answer: 400 g
Question 10
(a) M1 20% of 45 found (= 9)
(a) A1 L36 cao
(a) Answer: L36
(b) M1 30% of 50 found (= 15)
(b) A1 L35 cao
(b) Answer: L35
(c) B1 Shop B, L1 cheaper (ft from parts a and b)
(c) Answer: Shop B, by L1
Question 11
M1 12% of 2400 found (= 288), e.g. via 10% = 240 and 2% = 48
M1 dep: 2400 + their 12% increase
A1 2688 cao
Answer: 2688
Question 12
(a) M1 4% of 500 found (= 20)
(a) M1 dep: 20 x 3
(a) A1 L60 cao
(a) Answer: L60
(b) B1 L560 (ft from part a: 500 + their interest)
(b) B1 states the final price (L198, ft) is less than the original price of L200
(b) B1 correct reason: the 10% decrease is applied to L220 (a larger amount than L200), so it removes more (L22) than the 10% increase added (L20)
(b) Answer: The final price is L2 less than the original because the second 10% is taken from a larger amount (L220) than the first 10% added to (L200).
Question 18
(a) M1 600 x 0.8 oe (= 480)
(a) M1 dep: their 480 x 0.9 oe
(a) A1 L432 cao
(a) Answer: L432
(b) M1 tests the claim: 600 x 0.7 (= 420)
(b) A1 420 does not equal 432 (ft from part a), so the assistant is wrong (cso)
(b) M1 combined multiplier found: 0.8 x 0.9 (= 0.72), or (600 - 432)/600
(b) A1 28% cao
(b) Answer: 28% (not 30%); the assistant is incorrect since a single 30% discount would give L420, not L432
Question 19
(a) M1 profit found (= 180 - 150 = 30)
(a) M1 dep: their 30/150 oe seen
(a) A1 20% cao
(a) Answer: 20%
(b) M1 loss found (= 220 - 187 = 33)
(b) M1 dep: their 33/220 oe seen
(b) A1 15% cao
(b) Answer: 15%
Question 20
(a) M1 5% of 120 found (= 6)
(a) A1 L126 cao
(a) Answer: L126
(b) M1 8% of 150 found (= 12)
(b) M1 dep: total this year found (= 150 + 12 = 162)
(b) M1 dep: their 162 - their 126 (ft from part a)
(b) A1 L36 cao
(b) Answer: L36
Question 21
M1 multiplier for the increase found (x1.25)
M1 dep: multiplier for the decrease found and combined (1.25 x 0.8)
A1 1.25 x 0.8 = 1, so the final price equals the original price (cso, answer printed)
Answer: Final price = original price, since the combined multiplier is 1