Edexcel GCSE Maths (1MA1), Higher tier · Ratio, proportion and rates of change
Practise Converting units. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy2 marks
Hal says, '2.5 m2 is equal to 250 cm2, because there are 100 cm in 1 m.'
(a) Explain Hal's mistake.[1]
(b) Convert 2.5 m2 to cm2.[1]
Show the answer and mark scheme
(a)Answer: \(1 \text{ m}^2 = 100 \times 100 = 10\,000 \text{ cm}^2\), so he should multiply by 10 000, not 100.
C1 for explaining that 1 m2 = 10 000 cm2 (100 × 100), so the conversion factor is 10 000
Worked solution: A square of side 1 m is 100 cm by 100 cm, so its area is 10 000 cm2.
(b)Answer: 25 000 cm²
B1 for 25 000
Worked solution: \(2.5 \times 10\,000 = 25\,000\) cm2.
Question 2Medium2 marks
A tank holds 0.15 m3 of water. A barrel holds 580 litres of water. Which holds more water, the tank or the barrel? You must show your working.[2]
Show the answer and mark scheme
Answer: The barrel (0.15 m³ = 150 litres)
M1 for \(0.15 \times 1000 = 150\) litres or \(580 \div 1000 = 0.58\) m³
C1 for the barrel, supported by correct figures
Worked solution: \(1\text{ m}^{3} = 1000\text{ litres}\), so the tank holds 150 litres. The barrel holds more.
Question 3Hard4 marks
Ruby is going to paint one wall of a room. The wall is a rectangle 5 m long and 300 cm high. The wall needs two coats of paint. One litre of paint covers 12 m2 for one coat. The paint is sold in 1 litre tins. How many tins of paint does Ruby need to buy?[4]
Show the answer and mark scheme
Answer: 3 tins
P1 for the area of the wall in m², \(5 \times 3 = 15\)
P1 for doubling for two coats, \(2 \times 15 = 30\) m²
P1 for \(30 \div 12 = 2.5\) litres
A1 for 3 cao
Worked solution: Area of the wall \(= 5 \times 3 = 15\) m². Two coats: \(2 \times 15 = 30\) m², which needs \(30 \div 12 = 2.5\) litres of paint. So Ruby needs 3 tins (rounding up).