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Edexcel GCSE Maths - Collins Education images/GCSEMaths/Answers...Edexcel GCSE Maths 209732 Edexcel Higher Teacher Pack title page.indd 1 3/27/15 2:38 PM Higher Student Book Answers

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  • Edexcel GCSE

    Maths

    209732 Edexcel Higher Teacher Pack title page.indd 1 3/27/15 2:38 PM

    Higher Student Book Answers

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  • 719

    Answers

    Chapter 1 Number: Basic number

    Exercise 1A

    1 a 6000 b 5 cans cost 1.95, so 6 cans cost 1.95.

    32 = 5 6 + 2. Cost is 10.53.

    2 a 288 b 16

    3 a 38 b Coach price for adults = 8, coach price for

    juniors = 4, money for coaches raised by tickets = 12 400, cost of coaches = 12 160, profit = 240

    4 (18.81...) Kirsty can buy 18 models.

    5 8.40 per year, 70p per copy

    6 450

    7 15

    8 3 weeks

    9 248.75

    10 Gavin pays 2926.25 1840 = 1086.25

    11 a Col is correct b Abi has multiplied 30 50 as 150 instead of

    1500. Baz has lined up the columns wrongly when adding. Instead of lining up the units he has lined up the first digits. Des has forgotten to add a zero on the second line of the multiplication, it should be 1530.

    Exercise 1B

    1 a 4.6 b 0.08 c 45.716 d 94.85 e 602.1 f 671.76 g 7.1 h 6.904 i 13.78 j 0.1 k 4.002 l 60.0

    2 a 0.028 b 0.09 c 50.96 d 46.512

    3 a 35, 35.04, 0.04 b 16, 18.24, 2.24 c 60, 59.67, 0.33 d 140, 140.58, 0.58

    4 a 18 b 140 c 1.4 d 12 e 6.9

    5 a 280 b 12 c 240 d 450 e 0.62

    6 a 572 b i 5.72 ii 1.43 iii 22.88

    7 a Incorrect as should end in the digit 2 b Incorrect since 9 5 = 45, so answer must be

    less than 45

    8 300

    9 a 27 b i 27 ii 0.027 iii 0.27

    10 Mark bought a DVD, some jeans and a pen.

    11 Headline A does not give the exact figure so does

    not convey any useful information. Headline B is accurate and records should be given accurately. Headline C may be correct but without the previous record does not convey any useful information.

    Exercise 1C

    1 a 50 000 b 90 000 c 30 000 d 200 e 0.5 f 0.006 g 0.3 h 10 i 0.05 j 1000

    2 a 56 000 b 80 000 c 31 000 d 1.7 e 0.066 f 0.46 g 4.1 h 8.0 i 1.0 j 0.80

    3 a 60 000 b 5300 c 89.7 d 110 e 9 f 1.1 g 0.3 h 0.7

    4 a 65, 74 b 95, 149 c 950, 1499

    5 Elsecar 750, 849; Hoyland 1150, 1249; Barnsley

    164 500, 165 499

    6 18 to 23 inclusive

    7 1, because there could be 450 then 449

    8 Donte has rounded to 2 significant figures or

    nearest 10 000

    9 a Advantage quick. Disadvantage assumes

    3 penguins a square metre which may not be accurate

    b Advantage. Quite accurate as 5 by 5 is a big

    enough area to give a reliable estimate. Disadvantage takes a long time.

    Exercise 1D

    1 a 60 000 b 120 000 c 10 000 d 15 e 140 f 100 g 200 h 0.08 i 0.09 j 45

    2 a 5 b 25 c 3000 d 600 e 2000 f 5000 g 400 h 8000 i 4 000 000

    3 30 90 000 = 2 700 000

    600 8000 = 4 800 000 5000 4000 = 20 000 000 200 000 700 = 140 000 000

    4 a 54 400 b 16 000

    5 1400 million

    6 His answer is correct but he had one too many

    zeros on each value, which cancel each other

    out. Matt wrote 600,000 rather than 60,000 and

    2000 rather than 200. The two mistakes

    cancelled themselves out due to the zeros

    involved.

    7 a Value of the money is about 66 000 000 0.2

    = 13 200 000, so it is enough to buy the yacht.

    b Weight is 66 000 000 5 = 330 000 000

    grams = 330 tonnes, so they do not weigh as much as the yacht.

    8 1420 000 000 000 64 000 000 22 200, so the

    National Debt per person is approximately

    22 200.

  • 720

    Exercise 1E

    1 a 35 000 b 15 000 c 960 d 5 e 1200 f 500

    2 a 39 700 b 17 000 c 933 d 4.44 e 1130 f 550

    3 a 1.74 m b 6 minutes c 240 g d 83C e 35 000 people f 15.5 miles g 14 m2

    4 a 10 b 1 c 3

    5 a 8.79 b 1.03 c 3.07

    6 82F, 5 km, 110 min, 43 000 people, 6.2

    seconds, 67th, 1788, 15 practice walks, 5

    seconds

    The answers will depend on the approximations made. Your answers should be to the same order as these.

    7 a 15 000 b 18 000 c 17 500

    8 $1000

    9 a 40 miles per hour b 10 gallons c 70

    10 a 80 000 b 2000 c 1000 d 30 000 e 5000 f 2500 g 75 h 100

    11 a 86 900 b 1760 c 1030 d 29 100 e 3960 f 2440 g 84.8 h 163

    12 Approximately 500

    13 1 million pounds is 20 million 5p coins. 20 000

    000 4.2 = 84 000 000 grams = 84 tonnes, so 5

    lorries needed.

    14 22.5 C 18.2 C = 4.3 Celsius degrees

    15 a i 27.571 428 57 ii 27.6 b i 16.896 516 39 ii 16.9 c i 18 672.586 16 ii 18 700

    16 a 37.5 48.6 40 50 = 2000 21.7 103.6 20

    100 = 2000 985 0.54 1000 0.5 = 2000

    b as both values are rounded down the actual

    answer must be bigger than 2000. The other two must be less than 2000.

    c Pete is correct it is not possible to tell. 37.5

    48.6 = 1822.5 985 0.54 = 1824.074

    17 149 000 000 300 000 = 496.67 500 seconds

    18 a 58.9 4.8 60 5 = 300 b Lower as both values are rounded up to get

    the estimate.

    19 Macaus population density is approximately 710

    000 times the population density of Greenland.

    20 26.8 3.1 27 3 = 9 36.2 3.9 36

    4 = 9. Second calculation must be biggest as first

    is smaller than 27 3 and second is bigger than

    36 4.

    Exercise 1F

    1 a 12 b 9 c 6 d 13 e 15 f 14 g 16 h 10 i 18 j 17 k 8 or 16 l 21

    2 4 packs of sausages and 5 packs of buns (or

    multiples of these)

    3 30 seconds

    4 12 minutes; Debbie will have run 4 laps; Fred will

    have run 3 laps.

    5 1 + 3 + 5 + 7 + 9 = 25, 1 + 3 + 5 + 7 + 9 + 11 =

    36, 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49, 1 + 3 + 5 + 7

    + 9 + 11 + 13 + 15 = 64

    6 a 2 b 7 c 12 d 1 e 30

    7 a 1 b 3 c 4 d 2 e 4

    8 a 400 b 900 c 2500 d 0.25 e 16

    9 a Students own explanation b 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91,

    105 c Adding consecutive pairs gives you square

    numbers.

    10

    Square number Factor of 56

    Cube number 64 8

    Multiple of 7 49 28

    11 2, 3 and 12

    12 a 1, 64, 729, 4096, 15 625 b 1, 8, 27, 64, 125

    c 3 a a a

    d Square numbers

    13 a 0.2 b 0.5 c 0.6 d 0.9 e 1.5 f 2.1 g 0.8 h 0.7

    14 The answers will depend on the approximations

    made. Your answers should be to the same order

    as these.

    a 60 b 1500 c 150

    Exercise 1G

    1 a 84 = 2 2 3 7 b 100 = 2 2 5 5 c 180 = 2 2 3 3 5 d 220 = 2 2 5 11 e 280 = 2 2 2 5 7 f 128 = 2 2 2 2 2 2 2 g 50 = 2 5 5

    2 a 84 = 22 3 7 b 100 = 22 52 c 180 = 22 32 5 d 220 = 22 5 11 e 280 = 23 5 7 f 128 = 27 g 50 = 2 52

    3 1, 2, 3, 22, 5, 2 3, 7, 23, 32, 2 5, 11, 22 3, 13,

    2 7, 3 5, 24, 17, 2 32, 19, 22 5, 3 7, 2

    11, 23, 23 3, 52, 2 13, 33, 22 7, 29, 2 3 5,

    31, 25, 3 11, 2 17, 5 7, 22 32, 37, 2 19,

    3 13, 23 5, 41, 2 3 7, 43, 22 11, 32 5,

    2 23, 47, 24 3, 72, 2 52

    4 a 2 is always the only prime factor b 64, 128 c 81, 243, 729 d 256, 1024, 4096 e 3, 32, 33, 34, 35, 36; 4, 42, 43, 44, 45, 46

  • 721

    5 a 2 2 3 5 b 22 3 5 c 120 = 23 3 5, 240 = 24 3 5,

    480 = 25 3 5

    6 a 72 112 132 b 73 113 133 c 710 1110 1310

    7 Because 3 is not a factor of 40 so it does not

    divide exactly.

    8 a = 2, b = 7

    9 a 2ab a2 4b b 8a3b 4a3b2

    Exercise 1H

    1 a 20 b 56 c 6 d 28 e 10 f 15 g 24 h 30

    2 They are the two numbers multiplied together.

    3 a 8 b 18 c 12 d 30

    4 No. The numbers have a common factor.

    Multiplying them together would mean using this

    factor twice, thus increasing the size of the

    common multiple. It would not be the least

    common multiple.

    5 a 16