1.12 Calculating with standard form
9 exam questions worth 19 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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Work out (2 \times 10^4) \times (3 \times 10^5).
Choose one answer.
Correct Not quite: the answer is \( 6 \times 10^9 \)
Mark scheme
C: 6 \times 10^9
Model answer
6 \times 10^9 (C). 2 × 3 = 6 and 10⁴ × 10⁵ = 10⁹.
Work out (4 \times 10^6) \times (5 \times 10^3). Give your answer in standard form.
Mark scheme
M1: 20 × 10⁹; A1: 2 × 10¹⁰
Model answer
4 × 5 = 20 and 10⁶ × 10³ = 10⁹. So 20 × 10⁹ = 2 × 10¹⁰.
Work out (6.4 \times 10^8) \div (1.6 \times 10^3). Give your answer in standard form.
Mark scheme
M1: 6.4 ÷ 1.6 = 4 or 10⁸ ÷ 10³ = 10⁵; A1: 4 × 10⁵
Model answer
6.4 ÷ 1.6 = 4 and 10⁸ ÷ 10³ = 10⁵, so 4 × 10⁵.
Work out (3 \times 10^{-4}) \times (2 \times 10^{-3}). Give your answer in standard form.
Mark scheme
M1: 6 and 10⁻⁷ (or 3 × 2 and -4 + -3); A1: 6 × 10⁻⁷
Model answer
3 × 2 = 6 and 10⁻⁴ × 10⁻³ = 10⁻⁷, so 6 × 10⁻⁷.
Work out 4.2 \times 10^5 + 3.5 \times 10^4. Give your answer in standard form.
Mark scheme
M1: writes with the same power (42 × 10⁴ + 3.5 × 10⁴ or 4.2 × 10⁵ + 0.35 × 10⁵); A1: 4.55 × 10⁵
Model answer
3.5 × 10⁴ = 0.35 × 10⁵. So 4.2 × 10⁵ + 0.35 × 10⁵ = 4.55 × 10⁵.
Work out 7.2 \times 10^{-3} - 9 \times 10^{-4}. Give your answer in standard form.
Mark scheme
M1: 72 × 10⁻⁴ - 9 × 10⁻⁴ (same powers); A1: 6.3 × 10⁻³
Model answer
7.2 × 10⁻³ = 72 × 10⁻⁴. So 72 × 10⁻⁴ - 9 × 10⁻⁴ = 63 × 10⁻⁴ = 6.3 × 10⁻³.
The Earth is 1.5 \times 10^{11} m from the Sun. Light travels at 3 \times 10^{8} m/s. Work out the time, in seconds, for light to travel from the Sun to the Earth.
Mark scheme
M1: 1.5 × 10¹¹ ÷ 3 × 10⁸; A1: 500 (5 × 10²)
Model answer
Time = distance ÷ speed = 1.5 × 10¹¹ ÷ 3 × 10⁸ = 0.5 × 10³ = 5 × 10² = 500 s.
A bacterium is 2.5 \times 10^{-6} m long. How many bacteria placed end to end make a length of 1 cm?
Mark scheme
B1: 1 cm = 10⁻² m; M1: 10⁻² ÷ 2.5 × 10⁻⁶; A1: 4000 (4 × 10³)
Model answer
1 cm = 10⁻² m. 10⁻² ÷ (2.5 × 10⁻⁶) = 0.4 × 10⁴ = 4 × 10³ = 4000 bacteria.
The mass of the Earth is 5.97 \times 10^{24} kg and the mass of the Moon is 7.35 \times 10^{22} kg. How many times heavier is the Earth than the Moon? Give your answer to 3 significant figures.
Mark scheme
M1: 5.97 × 10²⁴ ÷ 7.35 × 10²²; M1: 0.8122... × 10² or calculator value; A1: 81.2
Model answer
5.97 × 10²⁴ ÷ 7.35 × 10²² = (5.97 ÷ 7.35) × 10² = 0.8122... × 100 = 81.2 (3 s.f.).
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