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.
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(a) Calculate the increase in resistance of the wire.
[1 mark]
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(b) Calculate the percentage change in resistance when the wire is heated from 20°C to 80°C.
[1 mark]
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(c) 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
- (a) 10.2 − 8.5 = 1.7 Ω (1 mark for correct calculation and unit)
- (b) (1.7 ÷ 8.5) × 100 = 20% (1 mark for correct percentage change calculation with or without showing working)
- (c) 10.2 × 1.20 = 12.24 Ω OR 10.2 + (10.2 × 0.20) = 12.24 Ω (1 mark for correct final answer with unit; accept 12.2 Ω or 12.24 Ω)
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.
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(a) Calculate the reduction in power consumption in watts.
[1 mark]
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(b) Calculate the percentage reduction in power consumption.
[2 marks]
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(c) Explain why reducing power consumption by this percentage is beneficial to the school.
[1 mark]
Show mark scheme
- (a) 500 - 150 = 350 W (or equivalent correct calculation)
- (b) Correct method: (350 ÷ 500) × 100 or equivalent fraction calculation
- (b) Correct answer: 70% (accept 70.0%)
- (c) Lower power consumption reduces electricity costs / energy bills / running costs for the school (or equivalent statement about financial saving)
Calculate — 2 marks
A shop is having a sale on all items. The original price of a jacket is £45.
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(a) In the sale, the price of the jacket is reduced by 20%. Calculate the sale price of the jacket.
[1 mark]
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(b) 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.
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(a) Show that the sale price of the tablet is £192.
[2 marks]
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(b) Calculate the percentage increase from the sale price back to £240.
[1 mark]
Show mark scheme
- (a) 20% of £240 = £48 or £240 × 0.20 seen
- (a) £240 − £48 = £192 or £240 × 0.80 = £192
- (b) 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.
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(a) Describe how to calculate the price of the jacket in February as a percentage of the original price before January.
[1 mark]
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(b) 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
- (a) Multiply by 1.20 then by 0.80 (or equivalent method)
- (b) States that 1.20 × 0.80 = 0.96 (or 96%)
- (b) Concludes the final price is 96% of original / 4% less than original (not the same)
GCSE Perfect