Practise 37 exam-style questions on Standard form for Edexcel GCSE Maths (Calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
37 questions
1–5 marks each
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20 questions, marked as you go
Sample questions with model answers
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
Question 1
2 marks
Work out \[\sqrt{\frac{5.4 \times 10^{7}}{2.4 \times 10^{-3}}}\] Give your answer in standard form.
Work out the fraction first, then take the square root of the whole result. The square root of \(10^{10}\) is \(10^{5}\) because square rooting halves the power. Make sure the square root covers the whole fraction on your calculator.
Mark scheme
1 mark
M1 for \(2.25 \times 10^{10}\) or 22 500 000 000 seen
1 mark
A1 for \(1.5 \times 10^{5}\)
cao; correct answer with no working scores full marks
Question 2
2 marks
Work out \(\left(2.4 \times 10^{-3}\right)^2 \times 5.5 \times 10^{6}\) Give your answer in standard form.
Square both parts of the bracket: \(2.4^2 = 5.76\) and \((10^{-3})^2 = 10^{-6}\). An ordinary number such as 31.68 must still be written in standard form when asked, with a power of \(10^1\). A common mistake is squaring only the 2.4.
Mark scheme
1 mark
M1 for \(5.76 \times 10^{-6}\) or 31.68 seen
1 mark
A1 for \(3.168 \times 10^{1}\)
cao; correct answer with no working scores full marks
Question 3
3 marks
Human hair grows at about \(1.2 \times 10^{-8}\) metres per second.
Work out how many centimetres hair grows in 30 days. Give your answer correct to 2 significant figures.
Model answer
Seconds in 30 days \(= 30 \times 24 \times 60 \times 60 = 2\,592\,000\) Growth \(= 1.2 \times 10^{-8} \times 2\,592\,000 = 0.031104\) m \(0.031104 \times 100 = 3.1104\) cm = 3.1 cm (2 s.f.)
Explanation
The rate is per second, so find the number of seconds in 30 days and multiply. The answer is in metres, so multiply by 100 to get centimetres. A common mistake is to divide by 100 instead, or to forget one of the conversions (days to hours, hours to minutes, minutes to seconds).
Mark scheme
1 mark
M1 for the number of seconds in 30 days: \(30 \times 24 \times 60 \times 60\) (= 2 592 000)
1 mark
M1 for \(1.2 \times 10^{-8} \times\) their seconds (= 0.0311... m)
1 mark
A1 for 3.1 cm
awrt 3.1 (3.1104); correct answer with no working scores full marks
Question 4
4 marks
During a storm, 1.8 cm of rain falls on a town of area 2.4 km². One raindrop has a volume of \(3.3 \times 10^{-8}\) m³.
Work out an estimate for the number of raindrops that fell on the town. Give your answer in standard form correct to 2 significant figures.
Model answer
Area: 1 km² = 1000 m × 1000 m = \(10^{6}\) m², so 2.4 km² = \(2.4 \times 10^{6}\) m² Depth = 1.8 cm = 0.018 m Volume of rain \(= 2.4 \times 10^{6} \times 0.018 = 43\,200\) m³ Number of raindrops \(= 43\,200 \div (3.3 \times 10^{-8}) = 1.309... \times 10^{12}\) = \(1.3 \times 10^{12}\) (2 s.f.)
Explanation
The rain forms a very thin layer, so its volume is area × depth, with both in metres. 1 km² is \(10^6\) m², not 1000 m². Then divide the total volume by the volume of one drop.
Mark scheme
1 mark
P1 for the area in m²: \(2.4 \times 10^{6}\) m²
2.4 × 1000 × 1000; correct answer with no working scores full marks
1 mark
P1 for 1.8 cm = 0.018 m and the volume of rain = 43 200 m³
1 mark
P1 for their volume \(\div 3.3 \times 10^{-8}\)
1 mark
A1 for \(1.3 \times 10^{12}\)
awrt \(1.3 \times 10^{12}\) (1.309... × 10¹²)
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