Maths — Higher, Unit 2 — IGCSE

13 markshard

1 mark

(a)

Write $640000000$ in standard form.

Your answer

2 marks

(b)

Work out $(3\times10^{7})\div(6\times10^{4})$ Give your answer in standard form.

Your answer

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22 marksmedium

Work out $\frac{3\times10^{5}-2.7\times10^{4}}{6\times10^{-2}}$

Your answer

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32 markseasy

1 mark

(a)

Write $7.8\times10^{-4}$ as an ordinary number.

Your answer

1 mark

(b)

Write $95600000$ as a number in standard form.

Your answer

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44 markshard

1 mark

(a)

Write $5400000$ as a number in standard form.

Your answer

1 mark

(b)

Write $3.2\times10^{-4}$ as an ordinary number.

Your answer

2 marks

(c)

The mass of the Sun is $2\times10^{30}$ kg. The mass of the largest known star is $315$ times the mass of the Sun.

Work out the mass of this star. Give your answer in kg in standard form.

Your answer

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52 marksmedium

An approximation for the value of $π$ is given by

$4 ( 1 - \frac{22}{57} + \frac{22}{85} - \frac{22}{105} + \frac{22}{117} - \frac{22}{242} )$

Use your calculator to show that this approximation is within 0.1 of 3.14

Your answer

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62 markseasy

Work out the value of $(7.5\times10^{4})\times(2.5\times10^{3})$ Give your answer in standard form.

Your answer

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73 markshard

1 mark

(a)

Write $7.97\times10^{-6}$ as an ordinary number.

Your answer

2 marks

(b)

Work out the value of $(2.52\times10^{5})\div(4\times10^{-3})$ Give your answer in standard form.

Your answer

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81 markmedium

Use a calculator to find the decimal value of $\frac{\sqrt{29-3\times32^{0.4}}}{3}$ .

Your answer

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91 markeasy

Write 0.000068 in standard form.

Your answer

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103 markshard

$p^{2}=\frac{x-y}{xy}$

$x=8.5\times10^{9}\,y=4\times10^{8}$

Find the value of $p$ . Give your answer in standard form correct to $2$ significant figures.

Your answer

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112 markseasy

1 mark

(a)

Write $0.000423$ in standard form.

Your answer

1 mark

(b)

Write $4.5\times10^{4}$ as an ordinary number.

Your answer

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124 markshard

2 marks

(a)

$T=\sqrt{\frac{w}{d^{3}}}$

$w=5.6\times10^{-5}\,d=1.4\times10^{-4}$

Work out the value of $T$ . Give your answer in standard form correct to $3$ significant figures.

Your answer

2 marks

(b)

$w$ is increased by $10 \%$ $d$ is increased by $5 \%$

Lottie says, "The value of $T$ will increase because both $w$ and $d$ are increased."

Lottie is wrong. Explain why.

Your answer

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132 markseasy

1 mark

(a)

Write $0.00562$ in standard form.

Your answer

1 mark

(b)

Write $1.452\times10^{3}$ as an ordinary number.

Your answer

How did you do?/ 2

144 markshard

1 mark

(a)

Write 8.2 x 10⁵ as an ordinary number.

Your answer

1 mark

(b)

Write 0.000 376 in standard form.

Your answer

2 marks

(c)

Work out the value of (2.3 x 10¹²) ÷ (4.6 x 10³) Give your answer in standard form.

Your answer

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152 markseasy

1 mark

(a)

Write $2.46\times10^{6}$ as an ordinary number.

Your answer

1 mark

(b)

Write $0.00074$ in standard form.

Your answer

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162 markshard

Work out the value of (3.5 x 10⁶) ÷ (5 x 10^-3). Give your answer in standard form.

Your answer

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171 markeasy

Circle the number that is written in standard form.

0.9 × 10^–3	6 × 10^0.5	5.2 × 10^–4	12 × 10⁷

Your answer

How did you do?/ 1

183 markshard

(b)

Find 4% of 4.5 × 10¹⁵⁷ Give your answer in standard form

Your answer

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193 markseasy

2 marks

(a)

Write these numbers in standard form.

i) 6500

(1 mark)

ii) 0.0584

(1 mark)

Your answer

1 mark

(b)

Work out $( 4.2 \times 10^{5 ) \times ( 1.8 \times 10^{-2} } )$ giving your answer in standard form.

Your answer

How did you do?/ 3

203 markseasy

2 marks

(a)

A grain of salt weighs $6.48\times10^{-5}$ kg on average.

A packet contains 0.35 kg of salt.

Use this information to calculate the number of grains of salt in the packet.

Your answer

1 mark

(b)

Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.

Your answer

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214 markseasy

Tom researches the weights of plant seeds.

One poppy seed weighs $3\times10^{-4}$ grams
250 pumpkin seeds weigh 21 grams.
One sesame seed weighs $3.64\times10^{-6}$ kilograms.

Write the three types of seed in order according to the weight of one seed. Write the lightest type of seed first. You must show how you decide.

Your answer

How did you do?/ 4

225 markseasy

A newborn baby has an approximate mass of 3.5 kilograms.

A human cell has an approximate mass of 2.7 × 10^–11 grams.

Use these values to estimate the number of human cells in a newborn baby. Give your answer in standard form, correct to 2 significant figures.

Your answer

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232 markseasy

1 mark

(a)

Write 76 000 000 in standard form.

Your answer

1 mark

(b)

Write 5.4 × 10^–4 as an ordinary number.

Your answer

How did you do?/ 2

244 markseasy

1 mark

(a)

Write $5.87\times10^{-4}$ as an ordinary number

Your answer

1 mark

(b)

Write 84 000 000 in standard form.

Your answer

2 marks

(c)

The number of neurons in a human brain is $8.5\times10^{10}$ The number of neurons in a monkey brain is $1.47\times10^{9}$

The number of neurons in a human brain is $K\times$ the number of neurons in a monkey brain.

Work out the value of $K$ Give your answer correct to one decimal place

Your answer

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252 markseasy

Work out $(5.6\times10^{6})+(2.3\times10^{5})$

Your answer

How did you do?/ 2

263 marksmedium

One sheet of paper is $9\times10^{-3}$ cm thick.

Mark wants to put $500$ sheets of paper into the paper tray of his printer. The paper tray is $4$ cm deep.

Is the paper tray deep enough for $500$ sheets of paper? You must explain your answer.

Your answer

How did you do?/ 3

272 markseasy

(c)

Work out $4.2\times10^{3}+5.3\times10^{2}$

Give your answer in standard form.

Your answer

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282 marksmedium

Write the following numbers in order of size. Start with the smallest number.

$0.038\times10^{2}$	$3800\times10^{-4}$	$380$	$0.38\times10^{-1}$

Your answer

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292 marksmedium

(c)

Write these numbers in order of size. Start with the smallest number.

$2.73\times10^{3}$	$27.3\times10^{-3}$	$273\times10^{2}$	$0.00273$

Your answer

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304 marksmedium

1 mark

(a)

The table shows some information about eight planets.

Planet	Distance from Earth (km)	Mass (kg)
Earth	$0$	$5.97\times10^{24}$
Jupiter	$6.29\times10^{8}$	$1.898\times10^{27}$
Mars	$7.83\times10^{7}$	$6.42\times10^{23}$
Mercury	$9.17\times10^{7}$	$3.302\times10^{23}$
Neptune	$4.35\times10^{9}$	$1.024\times10^{26}$
Saturn	$1.28\times10^{9}$	$5.68\times10^{26}$
Uranus	$2.72\times10^{9}$	$8.683\times10^{25}$
Venus	$4.14\times10^{7}$	$4.869\times10^{24}$

Write down the name of the planet with the greatest mass.

Your answer

1 mark

(b)

Find the difference between the mass of Venus and the mass of Mercury.

Your answer

2 marks

(c)

Nishat says that Neptune is over a hundred times further away from Earth than Venus is.

Is Nishat right? You must show how you get your answer.

Your answer

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312 marksmedium

Work out $(13.8\times10^{7})\times(5.4\times10^{-12})$ Give your answer as an ordinary number.

Your answer

How did you do?/ 2

323 marksmedium

1 mark

(b)

Write 6.7 x 10^-5 as an ordinary number.

Your answer

2 marks

(c)

Work out the value of (3 x 10⁷) x (9 x 10⁶).

Give your answer in standard form.

Your answer

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332 marksmedium

(c)

Calculate $9\times10^{4}\times3\times10^{3}$ . Give your answer in standard form.

Your answer

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342 marksmedium

Work out the value of $(9\times10^{-4})\times(3\times10^{7})$ . Give your answer in standard form.

Your answer

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352 marksmedium

(b)

Work out the value of 350³. Give your answer in standard form.

Your answer

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363 marksmedium

2 marks

(a)

The table shows information about the surface area of each of the world’s oceans.

Ocean	Surface area in square kilometres
Pacific	$1.56\times10^{8}$
Indian	$6.86\times10^{7}$
Southern	$2.03\times10^{7}$
Arctic	$1.41\times10^{7}$
Atlantic	$1.06\times10^{8}$

Work out the difference, in square kilometres, between the surface area of the Atlantic Ocean and the surface area of the Indian Ocean. Give your answer in standard form.

.......................square kilometres

Your answer

1 mark

(b)

The surface area of the Pacific Ocean is $k$ times the surface area of the Arctic Ocean.

Work out the value of $k$ . Give your answer correct to the nearest whole number.

$k=$ ...........................

Your answer

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379 marksmedium

2 marks

(a)

A company makes sweets. The sweets are put into packets.

Here are some facts.

$1.47\times10^{7}$ sweets are made every day	$3.5\times10^{5}$ packets of sweets are produced every day

Calculate the mean number of sweets in one packet.

Your answer

3 marks

(b)

Sweets are made on 288 days each year.

Calculate the number of sweets made each year. Give your answer in standard form.

Your answer

4 marks

(c)

The company has 152 machines making the sweets. Each machine operates for 15 hours each day.

i) Calculate the number of sweets made by one machine each hour. Give your answer as an ordinary number correct to the nearest 10.

(3 marks)

ii) State one assumption you have made in part (c)(i).

(1 mark)

Your answer

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384 marksmedium

1 mark

(a)

The table shows the population, correct to two significant figures, of each of six countries in April 2016.

Country	Population (April 2016)
Hungary	9.8×10⁶
Mexico	1.3×10⁸
Thailand	6.8×10⁷
Nigeria	1.9×10⁸
Singapore	5.7×10⁶
Egypt	9.3×10⁷

Write 9.3×10⁷ as an ordinary number.

Your answer

1 mark

(b)

Which of these countries had the least population?

Your answer

2 marks

(c)

The population of China was 1.382×10⁹ in April 2016. The population of India was 1.327×10⁹ in April 2016.

Work out the difference between the population of China and the population of India in April 2016. Give your answer in standard form.

Your answer

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