Calculate — 3 marks
A student measures the resistance of a wire at room temperature (20°C) and finds it to be 8.5 Ω. When the wire is heated to 80°C, the resistance increases to 10.2 Ω due to increased atomic vibrations.
-
Calculate the increase in resistance of the wire.
[1 mark]
-
Calculate the percentage change in resistance when the wire is heated from 20°C to 80°C.
[1 mark]
-
If the resistance increases by the same percentage when heated from 80°C to 140°C, calculate the resistance at 140°C.
[1 mark]
Show mark scheme
Explain — 4 marks
A school is upgrading its lighting system. The old system uses 500 W of electrical power. The new LED system uses 150 W of electrical power.
-
Calculate the reduction in power consumption in watts.
[1 mark]
-
Calculate the percentage reduction in power consumption.
[2 marks]
-
Explain why reducing power consumption by this percentage is beneficial to the school.
[1 mark]
Show mark scheme
Calculate — 2 marks
A shop is having a sale on all items. The original price of a jacket is £45.
-
(01.1) In the sale, the price of the jacket is reduced by 20%. Calculate the sale price of the jacket.
[1 mark]
-
(01.2) After one week, the shop increases the sale price by 15%. Calculate the new price of the jacket.
[1 mark]
Show mark scheme
Show — 3 marks
A shop sells a tablet for £240. In a sale, the price of the tablet is reduced by 20%. After the sale, the price is increased from the sale price back to £240.
-
(01.1) Show that the sale price of the tablet is £192.
[2 marks]
-
(01.2) Calculate the percentage increase from the sale price back to £240.
[1 mark]
Show mark scheme
- (01.1) 20% of £240 = £48 or £240 × 0.20 seen
- (01.1) £240 − £48 = £192 or £240 × 0.80 = £192
- (01.2) 25% or complete method: (£240 − £192) ÷ £192 × 100
Describe — 3 marks
A clothing shop sells jackets. In January, the shop increases the price of a jacket by 20%. In February, the shop reduces the price of the same jacket by 20% of the new price.
-
(01.1) Describe how to calculate the price of the jacket in February as a percentage of the original price before January.
[1 mark]
-
(01.2) The shop owner claims the jacket returns to its original price after the two changes. Describe why this claim is incorrect, using calculations to support your answer.
[2 marks]
Show mark scheme
- (01.1) Multiply by 1.20 then by 0.80 (or equivalent method)
- (01.2) States that 1.20 × 0.80 = 0.96 (or 96%)
- (01.2) Concludes the final price is 96% of original / 4% less than original (not the same)
GCSE Perfect