Revision mat · Percentages

14 marks

Question mix weighted by 439 real exam questions from 215 GCSE papers (2017–24), so the most common question types get the most space. Show your working.

Percentage of an amount $p\%\text{ of }N=\dfrac{p}{100}\times N$Increase / decrease $\times\left(1\pm\dfrac{p}{100}\right)$Percentage change $\dfrac{\text{change}}{\text{original}}\times100$Reverse percentage $\text{original}=\dfrac{\text{new value}}{\text{multiplier}}$
Increase, decrease & % change≈49% of real exam Qs
1A house was worth £250 thousand.
It is now worth £310 thousand.
Work out the percentage increase in the value of the house.
Answer: (3 marks)
2The area of rectangle B is 30% less than the area of rectangle A.
The area of rectangle C is 30% greater than the area of rectangle B.
Work out the percentage decrease from rectangle A to rectangle C.
Answer: (3 marks)
Reverse percentages≈11% of real exam Qs
3A garage gives a 8% discount for paying cash.
Joe pays £368 cash for a car.
Work out the normal price of the car.
Answer: (3 marks)
Calculate a percentage≈10% of real exam Qs
4Tom is a ski jumper.
The longest skis he may use are 110% of his height.
Tom’s height is 4 m.
Work out the longest skis Tom may use.
Answer: (2 marks)
★ Exam capstonemixed & other forms ≈30% of real exam Qs
5In a sale, normal prices are reduced by 25%.
The normal price of a washing machine is reduced by £50.
Work out the sale price of the washing machine.
Answer: (3 marks)

Mark scheme · Percentages

Total: 14 marks

Award the marks shown for each correct step, then add up the total out of 14. A method mark counts even if the final answer is wrong.

1A house was worth £250 thousand.
It is now worth £310 thousand.
Work out the percentage increase in the value of the house.[3 marks]
Method
Change $= 310 - 250 = 60$.
Percentage change $= \dfrac{60}{250} \times 100 = 24\%$.
Answer: $24$
Marks
✔1 markchange = 60
✔1 markdivide by the ORIGINAL 250
✔1 mark24%
2The area of rectangle B is 30% less than the area of rectangle A.
The area of rectangle C is 30% greater than the area of rectangle B.
Work out the percentage decrease from rectangle A to rectangle C.[3 marks]
Method
Multiplier A→B $= 0.7$; multiplier B→C $= 1.3$.
Overall multiplier $= 0.7 \times 1.3 = 0.91$.
That is a 9% decrease (since $0.91 = 91\%$).
Answer: $9$
Marks
✔1 marktwo multipliers 0.7 and 1.3
✔1 markoverall multiplier 0.91
✔1 mark9% decrease
3A garage gives a 8% discount for paying cash.
Joe pays £368 cash for a car.
Work out the normal price of the car.[3 marks]
Method
The £368 represents $92\%$ of the original.
Original $= 368 \div 0.92 = 400$.
Answer: $400$
Marks
✔1 mark368 is 92% of the original
✔1 markdivide by 0.92
✔1 mark£400
4Tom is a ski jumper.
The longest skis he may use are 110% of his height.
Tom’s height is 4 m.
Work out the longest skis Tom may use.[2 marks]
Method
$110\% = 1.1$ as a decimal multiplier.
$1.1 \times 4 = 4.4$ m.
Answer: $4.4$
Marks
✔1 mark110% = 1.1
✔1 mark4.4 m
5In a sale, normal prices are reduced by 25%.
The normal price of a washing machine is reduced by £50.
Work out the sale price of the washing machine.[3 marks]
Method
The £50 reduction is 25% of the normal price.
Normal price $= 50 \div 0.25 = 200.00$.
Sale price $= 200.00 - 50 = 150$.
Answer: $150$
Marks
✔1 mark50 = 25% of normal price
✔1 marknormal price = 200.00
✔1 marksale price £150
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