Link to examining board: http://www.edexcel.com The question paper associated with these solutions is available to download for free from the Edexcel website. The navigation around the website sometimes changes. However one possible route is to follow the above link, then SUBJECTS Mathematics, QUALIFICATIONS (from the LH Panel), under INTERNATIONAL GCSE FROM 2003 choose MATHEMATICS. Otherwise you can order the paper from the Edexcel Publications by phoning them on +44 (0)1623 467467 These solutions are for your personal use only. DO NOT photocopy or pass on to third parties. If you are a school or an organisation and would like to purchase these solutions please contact Chatterton Tuition for further details. Question 1 a) Hong Kong has the largest number with 9624 b) eight thousand and nine c) 4 hundred or 400 d) 6727 to the nearest 100 is 6700 e) to be an even number then the number must end in 0, 2, 4, 6 or 8 the smallest even number is Dubai with 5492 f) to be a multiple of five then the number must end with 0 or 5 Larnaca is the only airport with a number that is a multiple of 5, this is 3275 g) 8709 when rounded to the nearest thousand gives 9000 answer is 8709 www.chattertontuition.co.uk 0775 950 1629 Page 1
Question 2 a) 22 million tonnes b) the USA produced 7 million tonnes c) Australia produced 5 million tonnes twice this is 10 million tonnes China produced 10 million tonnes China d) e) i) Brazil produced 30 million tonnes the fraction that Brazil produced is = = ii) = 0.2 www.chattertontuition.co.uk 0775 950 1629 Page 2
Question 3 a) 10, 7 b) we are taking away 3 each time 13 3 = 10 10 3 = 7 c) just take away another 3 10 th term -3 = 11 th term -2 3 = -5 d) this time we need to work backwards 20 th term 3 = 21 st term 20 th term 3 = -35 add 3 to both sides 20 th term = -35 + 3 = -32 Question 4 a) and b) parallel lines are always the same distance away from each other they will never meet perpendicular lines are at right angles to each other www.chattertontuition.co.uk 0775 950 1629 Page 3
c) to find the area we could simply count the squares (full and partial) but this is difficult as the shape is fairly awkward. Instead separate off the shape into sections of rectangles or triangles area of a triangle is ½ x base x height Area A ½ x 2 x 1 = 1 Area B ½ x 1 x 1 = ½ Area C ½x 2 x 1 = = 1 Area D ½ x 1 x ½ = Area E ½ x 3 x 1 = 1 Area F 5 Total area = 1 + + 1+ + 1+ 5 = 9 = 9.5 cm2 www.chattertontuition.co.uk 0775 950 1629 Page 4
Question 5 a) 3n b) 5p c) 8q Question 6 a) 100% is all of the students 56% are the girls 100 56 = 44% are boys b) 56% of 725 = x 725 = 406 c) of 725 = 725 5= 145 so of 725 will be 3 x 145 = 435 alternatively key straight into calculator x 725 = 435 Question 7 a) a six sided polygon is called a hexagon it is called a regular hexagon if all the sides are the same length b) an acute angle is between 0 and 90⁰ an obtuse angle is between 90⁰and 180⁰ a reflex angle is more than 180⁰ i) angle x is an acute angle ii) angle y is a reflex angle c) order of rotational symmetry is how many times the shape can rotate and still look exactly the same before it gets back to the original position order of symmetry of 3 d) 3.4 cm e) all the sides are 3.4 cm and there are 6 sides so the perimeter will be 6 x 3.4 6 x 3.4 = 20.4 cm www.chattertontuition.co.uk 0775 950 1629 Page 5
Question 8 a) there is one 5 cent coin out of a possible six coins b) there are no coins worth less than 5 cents so the probability will be zero 0 c) all of the coins are worth more than 1 cent so this will definitely happen with probability of 1 1 d) there are two 10 cent coins out of a possible 6 coins = e) there are four coins that are not 10 cent coins = Question 9 a) cube of 8 means 8 to the power of 3 (8 3 or 8 x 8 x 8) 512 b) i) 3 4 = 81 ii) 2 3 x 5 2 = 8 x 25 = 200 c) i) 6 0.7 2 = 12.24489796 ii) 12.2 (to 3 significant figures) www.chattertontuition.co.uk 0775 950 1629 Page 6
Question 10 a) x -1 0 1 2 3 4 y -5 note 1-3 note 2 Note 1: (2 x -1) 3 = -2 3 = -5 Note 2: (2 x 0) 3 = 0 3 = -3 Note 3: (2 x 2) 3 = 4 3 = 1 Note 4: (2 x 3) 3 = 6 3 = 3 b) -1 1 note 3 3 note 4 5 www.chattertontuition.co.uk 0775 950 1629 Page 7
Question 11 a) area of a rectangle is length x width 45 x 29 = 1305 cm 2 b) we need to know how many times 150 goes into 1305 1305 150 = 8.7 we then round this number down 8 fish c) volume of a cuboid is area of cross section (area of surface water) x depth 1305 x 32 = 41760 cm 3 d) area of a circle is πr 2 (given in formulae sheet) radius is half of diameter so in this case the radius is 8 cm area = π x 8 2 = 201.0619 = 201 (3 significant figures) Question 12 Apple Fool For 6 people For 1 person note 1 For 15 people note 2 Cooking apples 900 g 150 g 2250 g 750 g Sugar 100 g 16.67 g 250 g Double cream 300 ml 50 ml 750 ml For 5 people note 3 Note 1: we have the ingredients for 6 people so divide each of these figures by 6 Note 2: we now have the ingredients for 1 person so multiply each of these figures by 15 Note 3: from the ingredients for 1 person, multiply by 5 a) for 15 people we need: 2250 g of cooking apples 250 g of sugar 750 ml of double cream b) for 5 people we need: 750 g of cooking apples www.chattertontuition.co.uk 0775 950 1629 Page 8
Question 13 a) i) for this we need to ignore the line PR altogether x = 62⁰ ii) alternate angles are equal b)i) here we need to ignore the line PQ altogether y = 71⁰ ii) corresponding angles are equal Question 14 a) 5(n + 6) = 5n + 30 b) y 6 c) 4(x 2) = 3 4x 8 = 3 add 8 to both sides 4x = 11 divide both sides by 4 x = 2.75 Question 15 a) we want to find of = x = x = x = b) if are women then this means that the total number must be a multiple of 12 (otherwise would give us a part of a person!) if wear glasses then this means that the total number must be a multiple of 8 (otherwise would give us a part of a person!) so our total number must be a multiple of both 12 and 8. We want the least common multiple. Multiple of 12 are 12, 24, 36, Multiples of 8 are 8, 16, 24, 32 The least common multiple is 24 www.chattertontuition.co.uk 0775 950 1629 Page 9
Question 16 a) the modal class is the class that has the highest frequency. This is 400 V 500. b) Volume of water (V m 3 ) Frequency Mid point Midpoint x frequency 0 V 100 2 50 100 100 V 200 4 150 600 200 V 300 6 250 1500 300 V 400 18 350 6300 400 V 500 44 450 19800 500 V 600 6 550 3300 Total 80 31600 Mean = 31600 80 = 395 Question 17 i) 8.3 correct to 2 significant figures could be as low as 8.25 cm ii) 20 correct to 1 significant figure could be as low as 15 cm www.chattertontuition.co.uk 0775 950 1629 Page 10
Question 18 We have a right angled triangle so we can use SOHCAHTOA Label all the sides from the point of view of the angle hyp 6.8 cm opp 41⁰ x cm adj We have hyp (H) and we are trying to find Adj (A). We don t have Opp (O) and don t want it. SOHCAHTOA this leaves CAH (cosine) cos 41⁰ = =. multiply both sides by 6.8 6.8cos 41⁰ = x x = 6.8 cos 41⁰ = 5.13 cm (3 significant figures) www.chattertontuition.co.uk 0775 950 1629 Page 11
Question 19 a) this is a reflection in the mirror line y = -x b) Question 20 a) the three numbers have a median of 4 and as there are only three numbers then the middle number must equal 4 if we put a + 2, b + 2 and c + 2 in order of size, they will have the same order as a, b and c when in size order the median will be the middle number. This is 2 more than the previous median. Median = 4 + 2 = 6 b) the range of the numbers will be the largest take away the smallest this will be the same as the original range (7) as we have simply added 2 to the highest and to the lowest. The range is still 7. www.chattertontuition.co.uk 0775 950 1629 Page 12
Question 21 a) -4 x 3 (as there is a full circle above the -4 we use, and as there is an open circle about the 3 we use ) b) i) subtract 9 from both sides 2x -8 divide both sides by 2 x -4 ii) integer means whole number n could be -3, -2, or -1 If you found this paper helpful then visit www.chattertontuition.co.uk/maths-revision-papers where you will find plenty more. It should be noted that Chatterton Tuition is responsible for these solutions. The solutions have not been produced nor approved by Edexcel. In addition these solutions may not necessarily constitute the only possible solutions. www.chattertontuition.co.uk 0775 950 1629 Page 13