Operations with integers, decimals, fractions

Show — 4 marks

A student is investigating the energy efficiency of different household appliances. They measure the power consumption of three devices: a kettle uses 2.4 kW, a microwave uses 0.8 kW, and a toaster uses 1.6 kW. The student needs to calculate total energy usage and compare efficiencies using fractional and decimal operations.

[1 mark]
[2 marks]
[1 mark]

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Mark 1: Correct calculation for kettle: 2.4 × 1/3 = 0.8 kWh
Mark 2: Correct calculation for microwave: 0.8 × 1/4 = 0.2 kWh, and addition 0.8 + 0.2 = 1.0 kWh (or equivalent working shown)
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Describe — 2 marks

A student is conducting an experiment to measure the density of different materials. They measure the mass of a copper block as 178.5 g and its volume as 20 cm³. To find the density, they need to divide the mass by the volume.

Describe the steps you would follow to calculate the density of the copper block using the values 178.5 g and 20 cm³. [2 marks]

Show mark scheme

{'mark': 1, 'description': 'Divide 178.5 by 20 (or equivalent statement showing correct operation)'}
{'mark': 1, 'description': 'Obtain the answer of 8.925 g/cm³ (or 8.9 g/cm³ to 1 d.p.) with correct units'}

Explain — 3 marks

A student is investigating the efficiency of different renewable energy systems. A solar panel array produces 2.5 kW of power on a sunny day. However, due to system losses, only 3/4 of this power is actually delivered to the home. On a cloudy day, the output is reduced by 0.4 of the sunny day's delivered power.

Calculate the power actually delivered to the home on a sunny day. Show your working. [1 mark]
Calculate the power delivered on a cloudy day. Show your working. [1 mark]
Explain why the difference between sunny and cloudy day outputs (as a fraction of the sunny day delivered power) is important when designing a battery storage system for the home. [1 mark]

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Describe — 4 marks

A physics student is investigating the density of different materials. They measure the mass of a copper block as 178.5 g and calculate its volume using water displacement. The volume reading changes from 15.2 cm³ to 35.7 cm³ when the block is submerged.

Calculate the volume of the copper block in cm³. Show your working. [1 mark]
The student needs to convert the mass to kilograms. Describe the process of converting 178.5 g to kilograms as a decimal. [1 mark]
Using your answers from parts (a) and (b), describe the steps you would use to calculate the density of copper in kg/cm³. You do not need to give a final numerical answer. [2 marks]

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Calculate — 2 marks

A bakery uses standard recipes for its cakes. One recipe requires \frac{3}{4} kg of flour and 1.25 kg of sugar. The baker needs to prepare multiple batches for upcoming orders.

(01.1) Calculate the total amount of flour needed for 2 batches. [1 mark]
(01.2) Calculate the total amount of sugar needed for 3 batches. [1 mark]

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(01.1) 1.5 kg or equivalent (e.g., \frac{3}{2} kg, 1\frac{1}{2} kg)
(01.2) 3.75 kg or equivalent (e.g., \frac{15}{4} kg, 3\frac{3}{4} kg)

Show — 4 marks

Describe — 2 marks

Explain — 3 marks

Describe — 4 marks

Calculate — 2 marks

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