x = y = z =

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1 Q1. x, y and z are standard form numbers x = y = z = (a) Calculate x y (b) Calculate x (c) Calculate (Total 3 marks) Q2. A company produces 35 million packets of crisps and snacks each week. Production is 7 days a week, 24 hours a day. (a) On average, how many packets are produced in one day? Give your answer in standard form. Answer... Page 1 of 14

2 (b) Each packet makes an average profit of 12p. Calculate the average hourly profit for this company. Answer... (Total 4 marks) Q3. For each calculation circle the answer that is correct and is in standard form. (a) (3 10 ) (4 10 ) Answer (b) (4 10 ) (8 10 ) Answer (Total 2 marks) Q4. A builder has 7200 kg of sand. (a) Write 7200 kg in grams. Give your answer in standard form... g (b) One grain of this sand weighs g. Write the weight of one grain of sand in standard form.. g Page 2 of 14

3 (c) How many grains of sand are there in 7200 kg of sand? Give your answer in standard form.... (Total 5 marks) Q5. In 2002 the number of visitors to four tourist attractions is shown in the table. Blackpool Pleasure Beach 6.2 million Edinburgh Castle Giant s Causeway Tate Modern 4.6 million (a) Write the number of visitors to Edinburgh Castle in standard form. (b) Blackpool Pleasure Beach claimed that it had more visitors than the other three added together. Is this claim true? You must show your working. (Total 3 marks) Page 3 of 14

4 Q6. (a) The star Alpha Centauri is approximately kilometres from Earth. Write this number in standard form to 3 significant figures. (b) Light travels at approximately kilometres per second. There are seconds in a day. How many days will light take to reach the Earth from Alpha Centauri? Give your answer to an appropriate degree of accuracy. days (4) (Total 6 marks) Q7. The population of France is people. The area of France is square kilometres. Mean number of people = Calculate the mean number of people per square kilometre in France. Give your answer to a suitable degree of accuracy (Total 3 marks) Page 4 of 14

5 Q8. The table gives the diameter, in metres, of planets in the solar system. The diameters are given to an accuracy of 3 significant figures. Planet Diameter (metres) Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto (a) Which planet has the largest diameter? (b) Which planet has the smallest diameter? (c) Which planet has a diameter approximately 10 times that of Venus? (d) Write as an ordinary number. Page 5 of 14

6 (e) What is the diameter of Pluto in kilometres? Give your answer in standard form. km (Total 6 marks) Q9. Some large numbers are written below. 1 million = billion = trillion = (a) How many millions are there in one trillion?... (b) Write 8 billion in standard form.... (c) Work out 8 billion multiplied by 3 trillion. Give your answer in standard form.... (Total 4 marks) Page 6 of 14

7 Q10. (a) A calculator displays a number in standard form as Which of the following numbers does the display show? Circle the correct answer (b) Use your calculator to work out cos (tan ) (i) Give all the figures in your calculator display. (ii) Write your answer to an appropriate degree of accuracy. (c) Use your calculator to work out (Total 4 marks) Page 7 of 14

8 Q11. Astronomers measure distances in the solar system in astronomical units (AU). One AU is kilometres. The distance from the Sun to Pluto is 39.5 AU. How many kilometres is the Sun from Pluto? Give your answer in standard form to a sensible degree of accuracy km (3) (Total 3 marks) Page 8 of 14

9 (b) M1. (a) or (c) [3] M2. (a) M A1 (b) Their (a) M ft their answer to (a) A1ft [4] M3. (a) Circles (b) Circles [2] Page 9 of 14

10 M4. Incorrect standard form notation Eg or Penalise first time only (a) or eg = B0 ft (b) (c) ( ) ( )oe Or their (a) their (b) oe or ? M Ft for ? Only A1 ft [5] M5. (a) Allow (b) Attempt to add , and 4.6 million Numbers all in same form with at least two correct M (oe) and Yes Must have both A1 [3] M6. (a) if incorrect rounding 10 13, is is B0 B2 Page 10 of 14

11 (b) their (a) ( or 86400) Dividing by or at any point gets M1 their (a) Dividing by other value gets DM1 = 1576 to 1584 Use of original value gives = 1580 or 1600 This mark is independent and can be given for any value greater than 3 s.f. seen or implied rounded to 2 or 3 s.f. M1 DM1 A1 ft ft [6] M ( ) Condone invisible brackets Allow if not in standard form and at least one correct or both 2 zeros out (5.83 7) (5.47 5) M M0 M1 A1 110 or 107 ft to 2 sf or 3 sf Allow but no ft to 4 sf ft [3] Page 11 of 14

12 M8. (a) Jupiter (b) (c) Pluto Saturn (d) (e) or oe A1 [6] M9. (a) 10 6 oe (b) (c) or 22 as power or oe e.g B2 [4] M10. (a) (b) (i) (052) (ii) 0.9, 0.91, 0.912, 9 or 9.1 or ft their answer for (b)(i) to 1, 2 or 3sf eg Gradians (b)(i) B0 (b)(ii) 0.02, , etc ft ft Page 12 of 14

13 (c) or [4] M11. Sight of digits 5925, 593, 59 or 6 M or oe from award of M A1 Rounded to 5.93, 5.9 or ft. their value if 4 s.f if rounded to 3, 2 or 1 s.f. NB If A0 awarded and final answer correctly rounded but not in standard form still give. ft [3] Page 13 of 14

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