STANDARD FORM[ESTIMATED TIME: 80 minutes] GCSE TOPIC PRACTICE

(+ IGCSE) EXAM QUESTION PRACTICELeaveblank

10 *N23069A01020*

10. The table shows the populations of five countries.

(a) Which of these countries has the largest population?

........................................(1)

(b) Calculate the difference between the population of Kenya and the population ofNigeria.Give your answer in standard form.

..........................(2)

(c) The population of South Africa is 30 times the population of The Gambia.Calculate the population of South Africa.Give your answer in standard form.

........................................(1) Q10

(Total 4 marks)

CountryThe GambiaKenyaMaliNigeriaSwaziland

Population

1.4 106

3.2 107

1.2 107

1.4 108

1.2 106

1. [4 marks]

Note that these questions are sorted in date order (most recent questions first).

November 2005, 4H Q10: 4 Marks

Questions compiled by @Maths4Everyone

9

*P41038A0920* Turn over

9 The table shows the diameters, in kilometres, of five planets.

Planet Diameter (km)Venus 1.2 ! 104

Jupiter 1.4 ! 105

Neptune 5.0 ! 104

Mars 6.8 ! 103

Saturn 1.2 ! 105

(a) Which of these planets has the smallest diameter?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Calculate the difference, in kilometres, between the diameter of Saturn and the diameter of Neptune.

Give your answer in standard form.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km(2)

The diameter of the Moon is 3.5 ! 103 km. The diameter of the Sun is 1.4 ! 106 km.

(c) Calculate the ratio of the diameter of the Moon to the diameter of the Sun. Give your answer in the form 1 : n

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 9 is 5 marks)

2. [5 marks]

Note that these questions are sorted in date order (most recent questions first).

January 2013, 3H Q9: 5 Marks

12

*P44388A01228*

10 The table shows some information about the five Great Lakes in North America.

Name Surface area (m2) Volume of water (m3)

Lake Erie 2.57 × 1010 4.80 × 1011

Lake Huron 6.01 × 1010 3.52 × 1012

Lake Michigan 5.80 × 1010 4.87 × 1012

Lake Ontario 1.91 × 1010 1.64 × 1012

Lake Superior 8.21 × 1010 1.22 × 1013

(a) Work out the total surface area of the five Great Lakes. Give your answer in standard form.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2

(2)

Loch Ness is the largest lake in Scotland. The lake has a volume of water of 7.45 × 109 m3

The volume of water in Lake Superior is k times the volume of water in Loch Ness.

(b) Work out the value of k. Give your answer correct to 3 significant figures.

k = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)(Total for Question 10 is 4 marks)

3. [4 marks]

Note that these questions are sorted in date order (most recent questions first).

May 2015, 3H Q10: 4 Marks

10

*P46917A01024*

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10 The table gives the surface areas, in square kilometres, of five seas.

Sea Surface area in square kilometres

Mediterranean Sea 2.97 × 106

East China Sea 1.25 × 106

Baltic Sea 4.22 × 105

Red Sea 4.38 × 105

Okhotsk Sea 1.59 × 106

(a) Write 1.59 × 106 as an ordinary number.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

(b) Work out the difference, in square kilometres, between the largest surface area and the smallest surface area for these five seas.

Give your answer in standard form.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km2

(2)

The surface area of the East China Sea is k times the surface area of the Baltic Sea.

(c) Work out the value of k. Give your answer to the nearest whole number.

k = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 10 is 5 marks)

4. [5 marks]

Note that these questions are sorted in date order (most recent questions first).

January 2016, 4HR Q10: 5 Marks

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9

10. The table shows the annual world production of four foods.

(a) Calculate the total annual world production of coffee and sugar.

.................................. tonnes(2)

(b) Brazil produces 9.7% of the world’s sugar.Calculate the annual production of sugar from Brazil.

.................................. tonnes(2)

(c) Express the world production of wheat as a percentage of the total production of allfour foods.

..................................%(3)

Turn over

Q10

(Total 7 marks)

*N22125A0920*

Food

CocoaCoffeeSugarWheat

Annual worldproduction, in tonnes

1.75 106

1.85 106

9.72 107

4.98 108

5. [7 marks]

Note that these questions are sorted in date order (most recent questions first).

May 2005, 4H Q10: 7 Marks

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9

Turn over*N24646A0920*

The capsules move in a circle of diameter 135 m.

(c) Calculate the distance moved by a capsule in making a complete revolution. Give your answer correct to 3 significant figures.

........................... m(2)

The capsules move at an average speed of 0.26 m/s.

(d) Calculate the time taken for a capsule to make a complete revolution. Give your answer in minutes, correct to the nearest minute.

........................... min(3)

11. Write as ordinary numbers

(i) 3.6 ! 105

...........................

(ii) 2.9 ! 10–3

...........................

Q10

(Total 9 marks)

Q11

(Total 2 marks)

6. [2 marks]

Note that these questions are sorted in date order (most recent questions first).

May 2006, 3H Q11: 2 Marks

10.

The diagram shows a shape.

AB is an arc of a circle, centre O.

Angle AOB = 90&.

OA =OB = 6 cm.

Calculate the perimeter of the shape.

Give your answer correct to 3 significant figures.

......................... cm

(Total 4 marks)

11. The distance between the Earth and the Sun is 150 000 000 km.

(a) Write the number 150 000 000 in standard form.

...............................

(1)

The distance between Neptune and the Sun is 30 times greater than the distance between the

Earth and the Sun.

(b) Calculate the distance between Neptune and the Sun.

Give your answer in standard form.

........................ km

(2)

(Total 3 marks)

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7. [3 marks]

Note that these questions are sorted in date order (most recent questions first).

May 2004, 3H Q11: 3 Marks71+O1!

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C;&/,<)S)-,:O0E8. [3 marks]

Note that these questions are sorted in date order (most recent questions first).

November 2006, 4H Q13: 3 Marks

11

*P43131A01124* Turn over

(c) Given also that BY = SY, find the bearing of S from B.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °

(2)

(Total for Question 10 is 5 marks)

11 The table shows the population of each of three countries in 2012.

Country Population

India 1.21 × 109

Turkey 7.48 × 107

Singapore 5.2 × 106

(a) Find the total population of India, Turkey and Singapore in 2012. Give your answer in standard form.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

Population density is calculated by the formula

Population density = Population ÷ Land area

The land area of India is 3.29 × 106 km2

(b) Calculate the population density of India in 2012. Give your answer correct to 3 significant figures.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . people/km2

(2)

(Total for Question 11 is 4 marks)

9. [4 marks]

Note that these questions are sorted in date order (most recent questions first).

January 2014, 4HR Q11: 4 Marks

12

*P45863A01224*

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11 The table gives the populations of each of five countries in 2014

Country Population

China 1.4 × 109

India 1.3 × 109

USA 3.2 × 108

Ethiopia 9.7 × 107

Mexico 1.2 × 108

(a) Write 9.7 × 107 as an ordinary number.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

The population of Russia in 2014 was 140000000

(b) Write 140000000 in standard form.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

In 2014, there were more people living in China than were living in the USA.

(c) How many more? Give your answer in standard form.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

In 2014, the population of India was k times the population of Mexico.

(d) Work out the value of k. Give your answer to the nearest whole number.

k = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 11 is 6 marks)

10. [6 marks]

Note that these questions are sorted in date order (most recent questions first).

June 2016, 4H Q11: 6 Marks

10

*P42933A01020*

11

Calculate the value of x. Give your answer correct to 3 significant figures.

x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 11 is 3 marks)

12 (a) Write as an ordinary number

(i) 4.2 ! 106

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) 3.82 ! 10–4

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(b) Here are three numbers written in standard form. Arrange these numbers in order of size. Start with the smallest number.

5.6 ! 10–7 8.6 ! 10–9 5.64 ! 10–8

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 12 is 4 marks)

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11. [4 marks]

Note that these questions are sorted in date order (most recent questions first).

May 2013, 3HR Q12: 4 Marks

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12. [4 marks]

Note that these questions are sorted in date order (most recent questions first).

May 2009, 3H Q12: 4 Marks

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13. [4 marks]

Note that these questions are sorted in date order (most recent questions first).

November 2008, 4H Q12: 4 Marks

12

*P44614A01220*

13 (a) Write 0.000076 in standard form.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

The area covered by the Pacific Ocean is 1.6 × 108 km2

The area covered by the Arctic Ocean is 1.4 × 107 km2

(b) Write 1.6 × 108 as an ordinary number.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

The area covered by the Pacific Ocean is k times the area covered by the Arctic Ocean.

(c) Find, correct to the nearest integer, the value of k.

k= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 13 is 4 marks)

14 Kwo invests HK$ 40000 for 3 years at 2.5% per year compound interest. Work out the value of the investment at the end of 3 years.

HK$... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 14 is 3 marks)

14. [4 marks]

Note that these questions are sorted in date order (most recent questions first).

January 2015, 4H Q13: 4 Marks

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15. [6 marks]

Note that these questions are sorted in date order (most recent questions first).

November 2010, 4H Q15: 6 Marks

16

*P42940A01620*

18 (a) x = 9 × 102m where m is an integer.

Find, in standard form, an expression for x

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(b) y = 9 × 102n where n is an integer.

Find, in standard form, an expression for y32

Give your answer as simply as possible.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

(Total for Question 18 is 5 marks)

19 Factorise completely (12x – y)2 – (4x – 3y)2

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 19 is 2 marks)

16. [5 marks]

Note that these questions are sorted in date order (most recent questions first).

January 2014, 3H Q18: 5 Marks

19

*P38579A01924* Turn over

19 P is directly proportional to the cube of Q. When Q = 15, P = 1350

(a) Find a formula for P in terms of Q.

P = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

(b) Calculate the value of P when Q = 20

P = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(Total for Question 19 is 4 marks)

20 x = a×10n where n is an integer and 10 10a! <

Find, in standard form, an expression for x2. Give your expression as simply as possible.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 20 is 3 marks)

17. [3 marks]

Note that these questions are sorted in date order (most recent questions first).

June 2011, 3H Q20: 3 Marks

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18. [5 marks]

Note that these questions are sorted in date order (most recent questions first).

May 2008, 4H Q20: 5 Marks

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19. [4 marks]

Note that these questions are sorted in date order (most recent questions first).

June 2010, 4H Q22: 4 Marks

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20. [5 marks]

Note that these questions are sorted in date order (most recent questions first).

June 2009, 4H Q22: 5 Marks