Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Q1. x, y and z are standard form numbers. 5 x = 2.5 × 10 (a) Calculate 4 y = 3.8 × 10 6 z = 1.9 × 10 x–y ........................................................................................................................ ........................................................................................................................ Answer .................................................. (1) (b) Calculate x 2 ........................................................................................................................ ........................................................................................................................ Answer .................................................. (1) (c) Calculate ........................................................................................................................ ........................................................................................................................ Answer .................................................. (1) (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 ................................................ (2) Page 1 of 14 (b) Each packet makes an average profit of 12p. Calculate the average hourly profit for this company. ......................................................................................................................... ......................................................................................................................... Answer £............................................. (2) (Total 4 marks) Q3. For each calculation circle the answer that is correct and is in standard form. (a) 5 7 (3 × 10 ) × (4 × 10 ) Answer 12 × 10 12 1.2 × 10 36 35 12 × 10 13 1.2 × 10 (1) (b) –8 –2 (4 × 10 ) ÷ (8 × 10 ) Answer –6 0.5 × 10 5 × 10 4 –7 5 × 10 5 × 10 –5 (1) (Total 2 marks) Q4. A builder has 7200 kg of sand. (a) Write 7200 kg in grams. Give your answer in standard form. .......................................................................................................................... .......................................................................................................................... Answer ................................................. g (2) (b) One grain of this sand weighs 0.0006 g. Write the weight of one grain of sand in standard form. .......................................................................................................................... Answer ................................................. g (1) Page 2 of 14 (c) How many grains of sand are there in 7200 kg of sand? Give your answer in standard form. .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ................................................. (2) (Total 5 marks) Q5. In 2002 the number of visitors to four tourist attractions is shown in the table. (a) Blackpool Pleasure Beach 6.2 million Edinburgh Castle 1 153 000 Giant’s Causeway 4.07 × 105 Tate Modern 4.6 million Write the number of visitors to Edinburgh Castle in standard form. ......................................................................................................................... Answer ................................................. (1) (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. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (Total 3 marks) Page 3 of 14 Q6. (a) The star Alpha Centauri is approximately 40 653 230 000 000 kilometres from Earth. Write this number in standard form to 3 significant figures. ......................................................................................................................... ......................................................................................................................... Answer ................................................. (2) (b) Light travels at approximately 298 000 kilometres per second. There are 86 400 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. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... Answer ................................................. days (4) (Total 6 marks) Q7. The population of France is 5.83 × 107 people. The area of France is 5.47 × 105 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. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. Answer ................................................. (Total 3 marks) Page 4 of 14 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. (a) Planet Diameter (metres) Mercury 4.88 × 106 Venus 1.21 × 107 Earth 1.28 × 107 Mars 6.79 × 106 Jupiter 1.43 × 108 Saturn 1.21 × 108 Uranus 5.11 × 107 Neptune 4.95 × 107 Pluto 2.39 × 106 Which planet has the largest diameter? Answer ................................................. (1) (b) Which planet has the smallest diameter? Answer ................................................. (1) (c) Which planet has a diameter approximately 10 times that of Venus? Answer ................................................. (1) (d) Write as an ordinary number. Answer ................................................. (1) Page 5 of 14 (e) What is the diameter of Pluto in kilometres? Give your answer in standard form. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... Answer ................................................. km (2) (Total 6 marks) Q9. Some large numbers are written below. 1 million = 106 1 billion = 109 1 trillion = 1012 (a) How many millions are there in one trillion? ......................................................................................................................... ......................................................................................................................... Answer .................................................... (1) (b) Write 8 billion in standard form. ......................................................................................................................... Answer .................................................... (1) (c) Work out 8 billion multiplied by 3 trillion. Give your answer in standard form. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... Answer .................................................... (2) (Total 4 marks) Page 6 of 14 Q10. (a) A calculator displays a number in standard form as Which of the following numbers does the display show? Circle the correct answer. 7000 0.700 0.007 700 0.0007 (1) (b) Use your calculator to work out cos (tan–10.45) (i) Give all the figures in your calculator display. Answer ................................................. (1) (ii) Write your answer to an appropriate degree of accuracy. Answer ................................................. (1) (c) Use your calculator to work out Answer ................................................. (1) (Total 4 marks) Page 7 of 14 Q11. Astronomers measure distances in the solar system in astronomical units (AU). One AU is 150 000 000 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. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. Answer ................................................. km (3) (Total 3 marks) Page 8 of 14 M1. (a) 2.12 × 105 or 212 000 B1 (b) 6.25 × 1010 62 500 000 000 B1 (c) 5000 5 × 103 B1 [3] M2. (a) 35 000 000 ÷ 7 5 000 000 M1 5 × 106 A1 (b) Their (a) × 0.12 ÷ 24 M1 25 000 ft their answer to (a) A1ft [4] M3. (a) Circles 1.2 × 1013 B1 (b) Circles 5 × 10–7 B1 [2] Page 9 of 14 M4. Incorrect standard form notation Eg. 7.2 6 or 7.26 Penalise first time only (a) 7200 × 1000 7.2 × 103 × 1000 or 7200 × 103 B1 7.2 × 106 eg. 7200 × 100 = 7.2 × 105... B0 B1 B1 ft (b) 6 × 10-4 B1 (c) (7.2 × 106) ÷ (6 × 10-4)oe Or their (a) ÷ their (b) oe or 1.2 × 10? M1 1.2 × 1010 Ft for 1.2 × 10? Only A1 ft [5] M5. (a) 1.153 × 106 Allow 1.153000 × 106 B1 (b) Attempt to add 1 153 000, 4.07 × 105 and 4.6 million Numbers all in same form with at least two correct M1 6 160 000 (oe) and Yes Must have both A1 [3] M6. (a) 4.07 × 1013 B1 if incorrect rounding × 1013, 4.0713 is B1 4.07 × 10–13 is B0 B2 Page 10 of 14 (b) their (a) ÷ (298000 or 86400) Dividing by 86400 or 298000 at any point gets M1 M1 their (a) ÷ 298000 ÷ 86400 Dividing by other value gets DM1 DM1 = 1576 to 1584 Use of original value gives 1578.93….. A1 ft = 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. B1 ft [6] M7. 5.83 × 107 ÷ (5.47 × 105) 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) M0 40.81 ÷ 27.35 M0 M1 106.58... A1 110 or 107 ft to 2 sf or 3 sf Allow 106.6 but no ft to 4 sf B1 ft [3] Page 11 of 14 M8. (a) Jupiter B1 (b) Pluto B1 (c) Saturn B1 (d) 4 880 000 B1 (e) or 2 390 oe B1 A1 [6] M9. (a) 106 oe B1 (b) 8 × 109 B1 (c) 2.4 × 1022 B1 2.4 or 22 as power or 24000000000000000000000 oe e.g. 24 × 1021 B2 [4] M10. (a) 0.007 B1 (b) (i) 0.9119215(052) B1 (ii) 0.9, 0.91, 0.912, 9 or 9.1 or 9.12 × 10-1 ft their answer for (b)(i) to 1, 2 or 3sf eg Gradians (b)(i) 0.02221673729 B0 (b)(ii) 0.02, 2 × 10–2, etc B1 ft B1 ft Page 12 of 14 (c) 0.00805 or 8.05 × 10-3 B1 [4] M11. Sight of digits 5925, 593, 59 or 6 M1 5 925 000 000 or 5.925 × 109 oe from award of M A1 Rounded to 5.93, 5.9 or 6 × 109 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 B1. B1 ft [3] Page 13 of 14 Page 14 of 14