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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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Edexcel GCSE Maths (4th Edition) 1 HarperCollinsPublishers Ltd 2015 Higher Student Book 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.

8.40 per year, 70p per copy

6 450

7 15

8 3 weeks

9 250.74

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, 2.2 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 22 000, so the National Debt per person is approximately 22 000.

Edexcel GCSE Maths (4th Edition) 2 HarperCollinsPublishers Ltd 2015 Higher Student Book Answers

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 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 /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 180

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

Edexcel GCSE Maths (4th Edition) 3 HarperCollinsPublishers Ltd 2015 Higher Student Book Answers

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 168 b 105 c 84 d 84 e 96 f 54 g 75 h 144

6 3 packs of cheese slices and 4 packs of bread rolls