Cambridge International Examinations Cambridge International General Certificate of Secondary Education

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1 Cambridge IGCSE Cambridge International Examinations Cambridge International General Certificate of Secondary Education CANDIDATE NAME CENTRE NUMBER CANDIDATE NUMBER MATHEMATICS Paper (Core) SPECIMEN PAPER 0580/0 For Examination from 205 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Tracing paper (optional) Geometrical instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For n, use either your calculator value or At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 56. The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level /Level 2 Certificate. This document consists of printed pages and blank page. u c le s 202 S CAMBRIDGE [Turn over

2 2 The diagram shows the map of part of an orienteering course. Sanji runs from the start, S, to the point A. Write as a column vector. Answer [] 4 2 When Ali takes a penalty, the probability that he will score a goal is Ali takes 30 penalties. Find how many times he is expected to score a goal. Answer... [2] 3 The ratio of Anne s height : Ben s height is 7 : 9. Anne s height is.4 m. Find Ben s height. Answer... m [2] UCLES /0/SP/5

3 4 The distance between the centres of two villages is 8 km. A map on which they are shown has a scale of : Calculate the distance between the centres of the two villages on the map. Give your answer in centimetres. 3 Answer, cm [2] 5 Frequency Favourite colour The bar chart shows the favourite colours of students in a class. (a) How many students are in the class? (b) Write down the modal colour. Answer(a) [] Answer(b) [] UCLES /0/SP/5 [Turn over

4 4 6 Use your calculator to find 45 x Answer [2] 7 (a) Calculate 60% of 200. Answer (a)... [] (b) Write 0.36 as a fraction. Give your answer in its lowest terms. Answer(b)... [2] 8 A circle has a radius of 50 cm. (a) Calculate the area of the circle in cm2. Answer(a)... cm2 [2] (b) Write your answer to p a rt (a) in m2. Answer(b)... m2 [] UCLES /0/SP/5

5 5 9 Temperature ( C) Time The graph shows the temperature in Paris from 6 am to 6 pm one day. (a) What was the temperature at 9 am? Answer(a)... C [] (b) Between which two times was the temperature decreasing? Answer(b)... and [] (c) Work out the difference between the maximum and minimum temperatures shown. Answer(c) C [] 0 (a) Write down the mathematical name of a quadrilateral that has exactly two lines o f symmetry. Answer (a)... [] (b) Write down the mathematical name of a triangle with exactly one line o f symmetry. (c) Write down the order o f rotational symmetry of a regular pentagon. Answer(b)... [] Answer (c)... [] UCLES /0/SP/5 [Turn over

6 6 2 Without using your calculator, work out 2 V j Show all your working clearly and give your answer as a fraction. Answer [3] 2 y x The diagram shows the graph of y = (x + )2 for -4 Y x (a) On the same grid, draw the line y = 3. [] (b) Use your graph to find the solutions of (x + )2 = 3. Give each solution correct to decimal place. Answer(b) x =... orx = [2] UCLES /0/SP/5

7 7 3 NOT TO SCALE The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size. Calculate the size of one of these angles. Answer... [3] 4 (a) Expand and simplify. 2(3x - 2) + 3(x - 2) Answer(a)... [2] (b) Expand. x(2x2-3) Answer(b)... [2] UCLES /0/SP/5 [Turn over

8 >< s \ A 30 X X- X >< <D ^ on a 20 W Mathematics test mark The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an English test by 5 students. (a) Describe the correlation. Answer(a) [] (b) The mean for the Mathematics test is The mean for the English test is Plot the mean point (47.3, 30.3) on the scatter diagram above. [] (c) (i) Draw the line of best fit on the diagram above. [] (ii) One student missed the English test. She received 45 marks in the Mathematics test. Use your line to estimate the mark she might have gained in the English test. Answer(c)(u) [] UCLES /0/SP/5

9 9 6 (a) NOT TO SCALE E In the diagram, AB is parallel to DE. Angle ABC = 0. Find angle BDE. Answer(a) Angle BDE = [2] (b) TA is a tangent at A to the circle, centre O. Angle OAB = 50. Find the value of (i) y, Answer(b)(i) y = [] (ii) z, Answer(b)(ii) z = [] (iii) t. Answer(b)(iii) t = [] UCLES /0/SP/5 [Turn over

10 0 7 NOT TO SCALE The diagram shows a ladder, of length 8 m, leaning against a vertical wall. The bottom of the ladder stands on horizontal ground, 3 m from the wall. (a) Find the height of the top of the ladder above the ground. Answer(a) m [3] (b) Use trigonometry to calculate the value of y. Answer(b) y = [2] UCLES /0/SP/5

11 8 (a) Lucinda invests $500 at a rate of 5% per year simple interest. Calculate the interest Lucinda has after 3 years. Answer(a) $... [2] (b) Andy invests $500 at a rate of 5% per year compound interest. Calculate how much more interest Andy has than Lucinda after 3 years. Answer(b) $... [4] UCLES /0/SP/5

12 2 BLANK PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. UCLES /0/SP/5

13 Cambridge IGCSE C am b rid g e International E xam inations Cambridge International General Certificate of Secondary Education MATHEMATICS 0580/0 Paper (Core) For Examination from 205 SPECIMEN MARK SCHEME hour MAXIMUM MARK: 56 The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level /Level 2 Certificate. This document consists of 4 printed pages. u c le s 202 S CAMBRIDGE [Turn over

14 Types of m ark M marks are given for a correct method. A marks are given for an accurate answer following a correct method. B marks are given for a correct statement or step. D marks are given for a clear and appropriately accurate drawing. P marks are given for accurate plotting o f points. E marks are given for correctly explaining or establishing a given result. SC marks are given for special cases that are worthy of some credit. A bbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied Qu. Answers M ark P a rt M arks r- 3j 4 J 2 24 or 24 out of M for x M for.4 t 7 or SC for answer B for cm to 0.5km oe or (cm) or figs 6 5 (a) 25 (b) Green cao 6 7.5(0) cao 2 7 (a) M for (b) cao 25 8 (a) 7853 to 7855 or 7850 or 7860 www 2 B f for-----or M for n x 502 (b) to or or ft Their (a) t evaluated 9 (a) 5 (b) 2 (pm), 6 (pm) (c) 5 Allow -5 0 (a) Rectangle or rhombus (b) Isosceles (triangle) (c) 5 cao Either one or both given UCLES /0/SM/5

15 3 k final answer www 24k Method (Addition first) B M or oe x their 2 x their 2 A Method 2 (Multiplication first) B M A 2 + or + oe ad + bc. a c for their + bd b d 2 (a) Correct ruled line (b) -2.7, 0.7 If M0, SC if is only followed b y 2 24 or if zero, SC if work is entirely in decimals with answer of to , ft B2ft their ruled line through (0, 3) for two intersections given to decimal place or B for to and 0.70 to 0.75 or Bft their ruled line through (0, 3) for two intersections not given to decimal place 3 35 cao 3 M for 720 or (6-2) x 80 oe seen in working and M for equation x = their 720 or M for (360-80) ^ 4 (= 45) oe seen in working and M dep for 80 - their 45 4 (a) 9x - 0 final answer (b) 2x3-3x final answer 2 2 B for 6x - 4 or 3x - 6 or for answer of 9x + j, or kx - 0 B for answer in form 2x3 + m or n - 3x 5 (a) Negative (b) Correct point (c) (i) Accurate ruled line (ii) English mark 6 (a) 70 (b) (i) (y =) 80 (ii) (z =) 40 (iii) (t =) 0 ft 2 ft Ignore embellishments Follow through their (c)(i) B for angle ABD = 70 stated or seen on the diagram Follow through 90 - their y or 50 - their z UCLES /0/SM/5 [Turn over

16 4 7 (a) 7.42 or cao 3 M2 for 2-32) orcomplete alternate method or M for x = 82 or better (b) to 68(.0) cao 2 3 M for cos (y) = oe 8 8 (a) x 5 x 3 M f o r oe 00 or SC for answer of 575 (b) 3.8(25) 4 M2 for 500 x.05 x.05 x.05 or M for 500 x.05 x.05 A for 578.8(25) or 78.8(25) seen and Aft for value of 500(.05) their (a) UCLES /0/SM/5

17 Cambridge IGCSE Cambridge International Examinations Cambridge International General Certificate of Secondary Education CANDIDATE NAME CENTRE NUMBER CANDIDATE NUMBER MATHEMATICS Paper 2 (Extended) SPECIMEN PAPER Candidates answer on the Question Paper. 0580/02 For Examination from 205 hour 30 minutes Additional Materials: Electronic calculator Tracing paper (optional) Geometrical instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For n, use either your calculator value or At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level /Level 2 Certificate. This document consists of 2 printed pages. u c le s 202 Egg CAMBRIDGE [Turn over

18 2 Use your calculator to find 45 x Answer... [2] 2 The mass of a carbon atom is 2 x 0 27 g. How many carbon atoms are there in 6 g of carbon? Answer... [2] 3 Write the following in order o f size, largest first. sin 58 cos 58 cos 38 sin 38 Answer... >... >... >... [2] 4 Express 0.23 as a fraction in its simplest form. Answer... [3] UCLES /02/SP/5

19 3 5 A circle has a radius of 50 cm. (a) Calculate the area of the circle in cm2. Answer(a) cm2 [2] (b) Write your answer to p a rt (a) in m. Answer(b) m 2 [] 6 NOT TO SCALE The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size. Calculate the size of one of these angles. Answer... [3] UCLES /02/SP/5 [Turn over

20 4 7 TA is a tangent at A to the circle, centre O. Angle OAB = 50. Find the value of (a) y, Answer(a)y =... [] (b) z, Answer(b)z=... [] (c) t. Answer (c)t=... [] 8 This is a sketch of two lines P and Q. y The two lines P and Q are perpendicular. The equation of line P is y = 2x. Line Q passes through the point (0, 0). Work out the equation of line Q. Answer... [3] UCLES /02/SP/5

21 5 9 O The point A lies on the circle centre O, radius 5 cm. (a) Using a straig h t edge and compasses only, construct the perpendicular bisector of the line OA.[2] (b) The perpendicular bisector meets the circle at the points C and D. Measure and write down the size of the angle AOD. Answer(b) Angle AOD =... [] u c l e s /02/SP/5 [Turn over

22 0 In a flu epidemic 45% of people have a sore throat. If a person has a sore throat the probability of not having flu is 0.4. If a person does not have a sore throat the probability of having flu is Calculate the probability that a person chosen at random has flu. Answer [4] Work out. (a) / \ 2 2 ' Answer(a) [2] (b) V 4 3 J Answer(b) [2] UCLES /02/SP/5

23 A English test mark Mathematics test mark The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an English test by 5 students. (a) Describe the correlation. Answer (a)... [] (b) The mean for the Mathematics test is The mean for the English test is Plot the mean point (47.3, 30.3) on the scatter diagram above. [] (c) (i) Draw the line of best fit on the diagram above. [] (ii) One student missed the English test. She received 45 marks in the Mathematics test. Use your line to estimate the mark she might have gained in the English test. Answer(c)(ii)... [] UCLES /02/SP/5 [Turn over

24 8 3 D A and B have position vectors a and b relative to the origin O. C is the midpoint of AB and B is the midpoint of AD. Find, in terms of a and b, in their simplest form (a) the position vector of C, Answer(a) [2] (b) the vector CD. Answer(b) [2] 4 (a) Find T when g = 9.8 and I = 2 Answer(a) T =... [2] (b) Make g the subject of the formula. Answer(b) g =... [3] UCLES /02/SP/5

25 9 5 A container ship travelled at 4 km/h for 8 hours and then slowed down to 9 km/h over a period of 30 minutes. It travelled at this speed for another 4 hours and then slowed to a stop over 30 minutes. The speed-time graph shows this voyage. Speed (km / h) (a) Calculate the total distance travelled by the ship. Answer(a) km [4] (b) Calculate the average speed of the ship for the whole voyage. Answer(b)... km/h [] UCLES /02/SP/5 [Turn over

26 0 6 The mass of a radioactive substance is decreasing by 0% a year. The mass, M grams, after t years, is given by the formula M = 500 x 0.9f. (a) Complete this table. t (years) M (grams) [2] (b) Draw the graph of M = 500 x 0.9(. M i \ M...I...U-;... :!... --U...f -...i...[...;-;-i I T 2 T 4 T 6 [2] (c) (i) Use your graph to estimate after how long the mass will be 350 grams. Answer(c)(\)... years [] (ii) When will the mass o f the radioactive substance be zero grams? Answer(c)(ii)... years [] UCLES /02/SP/5

27 7 f(x) = x + 4 (x * - 4 ) g(x) = x - 3x h(x) = x3 + (a) Work out fg(). Answer(a)... [2] (b) Find ho(x). Answer(b) h '(x) =... [2] (c) Solve the equation g(x) = - 2. Answer(c) x =... o rx =... [3] Question 8 is printed on the next page. UCLES /02/SP/5 [Turn over

28 2 8 The first four terms of a sequence are T= 2 T2= T3 = T4 = (a) The nth term is given by Tn = n(n + )(2n + ). 6 Work out the value of T23. Answer(a) T23 =... [2] (b) A new sequence is formed as follows. Ui = T2- Ti U 2= T3 - T2 U3 = T4 - T3... (i) Find the values of U and U2. (ii) Write down a formula for the nth term, Un. Answer(b)(\) Ui =... and U2=... [2] Answer (b){ii) U =... [] (c) The first four terms of another sequence are V = 22 V2= V3 = V4 = By comparing this sequence with the one in p a rt (a), find a formula for the nth term, Vn. Answer(c) V =... [2] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. UCLES /02/SP/5

29 Cambridge IGCSE C am b rid g e International E xam inations Cambridge International General Certificate of Secondary Education MATHEMATICS 0580/02 Paper 2 (Extended) For Examination from 205 SPECIMEN MARK SCHEME hour 30 minutes MAXIMUM MARK: 70 The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level /Level 2 Certificate. This document consists of 4 printed pages. u c le s 202 S CAMBRIDGE [Turn over

30 2 Types of m ark M marks are given for a correct method. A marks are given for an accurate answer following a correct method. B marks are given for a correct statement or step. D marks are given for a clear and appropriately accurate drawing. P marks are given for accurate plotting o f points. E marks are given for correctly explaining or establishing a given result. SC marks are given for special cases that are worthy of some credit. A bbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied Qu. Answers M ark P a rt M arks 7.5(0) cao 2 ^ M for x M for 6 t (2 x 0-27) 3 cos38 sin38 sin58 cos58 2 M correct decimals seen 0.7(88..) 0.6(5..) 0.3(74..) -0.9(27..) (a) 7853 to 7855 or 7850 or 7860 www (b) to or or ft 23 B2 f o r oe fraction 999 or M for 000[x] = oe M for n x 502 Their (a) t evaluated 6 35 cao 3 M for 720 or (6-2) x 80 oe seen in working and M for equation x = their 720 or M for (360-80) t 4 (= 45) oe seen in working and M dep for 80 - their 45 7 (a) (y =) 80 (b) (z =) 40 (c) (t =) 0 ft Follow through 90 - their y or 50 - their z UCLES /02/SM/5

31 3 8 y = - x +0 oe 2 3 M2 for - x +0 2 or M for gradient identified as (a) Correct perpendicular bisector with arcs (b) 60 2 or intercept as 0 (not on diagram) e.g. y = mx + 0 or y = ---- x + c 2 B correct line B correct construction arcs or 50 4 B 0.8, 0.6 or 0.55 then M 0.45 x their 0.6 M 0.2 x their 0.55 or M2 - (0.45 x x their 0.8) (a) f 8 5 ^ ^ B two or three entries correct f - \ (b) 2 2 oe V - 2 V 2 (a) Negative (b) Correct point (c) (i) Accurate ruled line (ii) English mark 3, x (a) a + b oe ft 2 (a c ^, / 3 - A B ^ B (k ) 2 ^b d) v \ ) Ignore embellishments Follow through their (c)(i) M unsimplified or any correct route e.g a + (b - a) or OA + AC (b) - a + b oe (a) n 2 (b) T 2 oe M unsimplified or any correct route e.g. CD = AB or b - a + (b - a) 2 2 M correct substitution of g and I seen M each correct move but third move marked on answer line 5 (a) 56 (b) 2 4 ft M intention to find area under graph B2 completely correct area statement or B two areas found correctly (or one trapezium area) Their (a)/3 UCLES /02/SM/5 [Turn over

32 4 6 (a) 500, 405, , 295 (...) 2 B2 (b) 5 points plotted within correct square P ft from table correct curve drawn within mm of points plotted (c) (i) (ii) Never oe C B ft from their curve or line reading at 350 g 7 (a) 2 2 B f(-2) seen (b) 3V(x - ) or 3 x - 2 M x - = j 3 or 3V(y - ) (c) 2 3 M2 (x - )(x - 2) = 0 or M (x + a)(x + b) = 0 where ab = 2 or a + b = -3 If 0 scored give M for x2-3x + 2 = 0 8 (a) 4324 cao 2 M x 23 x 24 x 47 or better 6 (b) (i) 4, 9 (c) (ii) (n + )2 or n2 + 2n + 2 B either correct 2 n(n+ )(2n + ) oe 2 M recognising Vn = 4Tn UCLES /02/SM/5

33 Cambridge IGCSE C am b rid g e International E xam inations Cambridge International General Certificate of Secondary Education CANDIDATE NAME CENTRE NUMBER CANDIDATE NUMBER MATHEMATICS Paper 3 (Core) SPECIMEN PAPER Candidates answer on the Question Paper. Additional Materials: Electronic calculator Tracing paper (optional) 0580/03 For Examination from hours Geometrical instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For n, use either your calculator value or At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 04. The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level /Level 2 Certificate. This document consists of 6 printed pages. u c le s 202 S CAMBRIDGE [Turn over

34 2 (a) Write twenty five m illion in figures. Answer(a) [] (b) Write the following in order of size, starting with the smallest % 0.6 Answer(b) < < [] (c) In a sale a coat costing $250 is reduced to $200. Find the percentage decrease in the cost. Answer(c) % [3] (d) NOT TO SCALE 20 students are asked to choose their favourite sport. The results are shown in the pie chart. Calculate the number of students who chose (i) basketball, Answer(d)(i) [] (ii) football. Answer(d)(ii) [2] UCLES /03/SP/5

35 2 The distance between Geneva and Gstaad is 50 km. (a) Write 50 in standard form. 3 Answer (a)... [] (b) A car took hours to travel from Geneva to Gstaad. 2 Calculate the average speed of the car. Answer(b)... km/h [] (c) A bus left Gstaad at 0 5. It arrived in Geneva at Calculate the time, in hours and minutes, that the bus took for the journey. Answer(c)... h... min [] (d) Another bus left Geneva at It travelled at an average speed of 60 km/h. Find the time it arrived in Gstaad. Answer(d)... [2] (e) The distance of 50 km is correct to the nearest 0 km. Complete the statement for the distance, d km, from Geneva to Gstaad. Answer(e)... d <... [2] UCLES /03/SP/5 [Turn over

36 Use the num bers in the list above to answer all the following questions. (a) Write down (i) two even numbers, Answer (a)(\)...,... [] (ii) two prime numbers, Answer(a)(ii)...,... [2] (iii) a square number, Answer (a)( iii)... [] (iv) two factors of 90. Answer(a)( iv)...,... [2] (b) (i) Calculate the mean of the seven numbers. Answer(b)(i)... [2] (ii) Find the median. Answer (b)( ii)... [2] (iii) Find the range. Answer(b){ iii)... [] UCLES /03/SP/5

37 5 (c) A number from the list is chosen at random. Find the probability that the number is (i) even, Answer (c)(i)... [] (ii) a multiple of 5. Answer(c)(n)... [] UCLES /03/SP/5 [Turn over

38 6 4 (a) Using the exchange rates change $ = 0.70 Euros and $ = 90 Yen (i) $00 to Euros, Answer(a)(i)... Euros [] (ii) 00 Yen to dollars. Answerlajiu) $... [2] (b) Tania went on holiday to Switzerland. The exchange rate was $ =.04 Swiss francs (CHF). She changed $500 to Swiss francs and paid % commission. (i) How much commission, in dollars, did she pay? Answer(b)(i) $... [] (ii) Show that she received CHF Answer (b)(ii) [2] (c) Tania spent CHF 950 on her holiday. She converted the remaining Swiss francs back into dollars. She paid CHF 0 to make the exchange. Calculate the amount, in dollars, Tania received. Answer(c) $... [3] UCLES /03/SP/5

39 7 5 (a) Find the gradient of the line l. Answer(a)... [2] (b) (i) Complete the table below for x + 2y = 6. x 0 2 y 0 (ii) On the grid, draw the line x + 2y = 6 for -4 Y x Y 6. [2] [3] (c) The equation of the line I is 4x + 3y = 4. Use your diagram to solve the simultaneous equations 4x + 3y = 4 and x + 2y = 6. Answer(c) x = y =... [2] u c l e s /03/SP/5 [Turn over

40 8 6 (a) A B The line AB is drawn above. Parts (i), (iii), and (v) m ust be completed using a ruler and compasses only. All construction arcs m ust be clearly shown. (i) Construct triangle ABC with AC = 7 cm and BC = 6 cm. [2] (ii) Measure angle BAC. Answer(a) (ii) Angle BA C =... [] (iii) Construct the bisector o f angle ABC. [2] (iv) The bisector of angle ABC meets AC at T. Measure the length of AT. Answer(a)(iv) A T =... cm [] (v) Construct the perpendicular bisector of the line B C. [2] (vi) Shade the region that is and nearer to B than to C nearer to BC than to AB. [] UCLES /03/SP/5

41 (b) A ship sails 40 km on a bearing of 040 from P to Q. 9 (i) Using a scale of centimetre to represent 5 kilometres, make a scale drawing of the path of the ship. Mark the point Q. North P Scale: cm = 5 km [2] (ii) At Q the ship changes direction and sails 30 km on a bearing of 60 to the point R. Draw the path of the ship. [2] (iii) Find how far, in kilometres, the ship is from the starting position P. Answer(b)(iii). km [] (iv) Measure the bearing of P from R. Answer(b)(iv) [] UCLES /03/SP/5 [Turn over

42 0 7 (a) Solve the equation 2(x + 4) = 3(x + 2) + 8. Answer(a) x =... [3] (b) Make z the subject of za + b = 3. Answer(b) z =... [2] (c) Find x when 2x3 = 54. Answer(c) x =... [2] UCLES /03/SP/5

43 (d) A rectangular field has a length of x metres. The width of the field is (2x - 5) metres. (i) Show that the perimeter of the field is (6x - 0) metres. Answer (d)(i) [2] (ii) The perimeter of the field is 50 metres. Find the length of the field. Answer(d)(ii) length =... m [2] u c l e s /03/SP/5 [Turn over

44 2 8 y The diagram shows two shapes A and B. (a) Describe fully the single transformation which maps A onto B. Answer(a)... [2] (b) On the grid, draw the line x = 2. [] (c) On the grid, draw the image of shape A after the following transformations. (i) Reflection in the line x = 2. Label the image C. [] (ii) Enlargement, scale factor 2, centre (0, 0). Label the image D. [2] UCLES /03/SP/5

45 3 9 (a) Factorise completely 3x2 + 2x. Answer(a)... [2] (b) Find the value of a3 + 3b2 when a = 2 and b = -2. Answer(b)... [2] (c) Simplify 3x4 x 2x3. Answer(c)... [2] UCLES /03/SP/5 [Turn over

46 4 0 The diagram shows a ramp in the form o f a triangular prism. The cross-section is a right-angled triangle of length 5 m and height 2 m. (a) Find the value of x. Give your answer correct to decimal place. Answer(a) x =... [3] (b) Find the area of the cross-section. Answer(b)... m2 [2] (c) The ramp is 0 m long. Calculate the volume of the ramp. Answer(c)... m3 [] UCLES /03/SP/5

47 (d) Calculate the total surface area of all five faces of the ramp. 5 Answer(d)... m2 [3] (e) Each face of the ramp is painted. Paint costs $2.25 per square metre. Calculate the total cost of the paint. Answer(e) $... [] Question is printed on the next page. u c l e s /03/SP/5 [Turn over

48 6 Diagram Diagram 2 Diagram 3 The diagrams show a sequence o f shapes. (a) On the grid, draw Diagram 4. [] (b) Complete the table showing the number o f lines in each diagram. Diagram (n) Number of lines [3] (c) Work out the number of lines in Diagram 8. Answer(c) [] (d) Write down an expression, in terms of n, for the number of lines in Diagram n. Answer (d) [2] (e) Work out the number of lines in Diagram 00. Answer (e) [] (f) The number of lines in Diagramp is 66. Find the value of p. Answer (f) p =. [2] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. UCLES /03/SP/5

49 Cambridge IGCSE C am b rid g e International E xam inations Cambridge International General Certificate of Secondary Education MATHEMATICS 0580/03 Paper 3 (Core) For Examination from 205 SPECIMEN MARK SCHEME 2 hours MAXIMUM MARK: 04 The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level /Level 2 Certificate. This document consists of 5 printed pages and blank page. u c le s 202 S CAMBRIDGE [Turn over

50 2 Types of mark M marks are given for a correct method. A marks are given for an accurate answer following a correct method. B marks are given for a correct statement or step. D marks are given for a clear and appropriately accurate drawing. P marks are given for accurate plotting o f points. E marks are given for correctly explaining or establishing a given result. SC marks are given for special cases that are worthy of some credit. Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied Qu. Answers Mark Part Marks (a) cao (b) 0.6 < 65% < - 3 (c) 20% 3 B for 50 seen M for their 50 x (d) (i) 30 or B for 0.8 or 80 seen M for - their 0.8 or 00 - their 80 (ii) 40 2 M for ( ) implied by 20 seen 2 (a).5(0) x 02 cao (b) 00 cao (c) 2 hours 5 minutes cao (d) 6(:) 25 (pm) or (0)425 pm 2 M for 2.5 (oe), 2hrs 30 min (e) 45 < d < 55 2 B for each value in correct place UCLES /03/SM/5

51 3 3 (a) (i) 36, 0 (ii) 29, 4, 3 any two 2 B for each (iii) 36 (iv) 45, 5, 0 any two 2 B for each (b) (i) 27 2 B for seen implied by 89 (ii) 29 2 M for attempting to order the numbers (iii) 35 cao (c) (i) (ii) 2 oe 7 3 oe 7 4 (a) (i) 70 cao ft Their denominator from (c)(i) 5 (a) (ii).(...) 2 B for 00-90, 0-9, 9 (b) (i) 5 cao (ii) (500-5) x.04 2 B for x.04, 560, 5.60 (c) M for (584.40) oe M indep for ^ oe, -.2 to r. rise B for attempt a t run (b) (i) 3, 2, 6 3 B for each value (ii) Correct continuous line 2ft Minimum length (0,3) to (6,0) B for plotting their 3 points (c) x = -2, y = 4 2ft B for their x, B for their y from their intersections UCLES /03/SM/5 [Turn over

52 4 6 (a) (i) Correct construction 2 B for two lines or B for accurate arcs seen or B for one correct line with two arcs SC for AC = 6 and BC = 7 with arcs (ii) 47 (45-49) ft Strict ft their (a)(i) (iii) Correct construction 2ft Their (a)(i) B for accurate arcs no line or B for accurate line drawn no arcs or B for accurate line with arcs bisecting another angle (iv) 4 ( ) ft Strict ft their (iii) with intersection on opposite side of triangle (v) Correct construction 2ft B for accurate arcs no line or B for accurate line drawn no arcs or B for accurate line with arcs, bisecting AB or AC (vi) Correct region shaded ft ft is for boundaries of correct perpendicular bisector of their BC and correct angle bisector o f their ABC, with or without arcs (b) (i) Correct scale drawing of PQ 2 B for accurate angle 40o, B for PQ 8cm (ii) Correct scale drawing of their QR 2 B for accurate angle 60o, B for QR 6cm (iii) 35 to 37 ft Measure x 5 ± km (iv) 264 to (a) -6 www 3 M2 for 8 = x or better or -x + 8 = or better M for 2x + 8 or 3x + 6 or 3x + 4 (b) 3 - b or a a I a b (c) 3 2 ft 2 B for 3 - b seen or z + = a a 54 B for or better 2 SC for embedded answer ie 2 x 33 = 54 or 2 x 3 x 3 x 3 = 54 (d) (i) x + x + 2x 5 + 2x 5 = 6x M accept 2x + 2(2x - 5) or 2(x + 2x - 5) E dep (ii) 0 2 M for 6x - 0 = 50 8 (a) Translation ' 0^, - 6 ) 2 B for translation B for column vector (b) Correct line drawn Continuous full line. Accept freehand. (c) (i) Correct reflection ft Their (b) (ii) Correct enlargement 2 B for any other enlargement scale factor 2 9 (a) 3x(x + 4) 2 B for 3(x2 + 4x) or B for x(3x + 2) or B for 3x(x + 4) seen (if not final answer) (b) 20 2 B for 8 or 2 seen (c) 6x7 2 B for kx7 or for 6xk, k ^ 0 UCLES /03/SM/5

53 5 0 (a) 5.4 cao 3 M for (= x2) implied by 29 (b) 5 2 M for 0.5 x 5 x 2 oe (c) 50 ft 0 x their (b) A 5.38(5..) or V29 or 5.39 B indep for rounding their answer to decimal place (d) 34 3ft M2 for 2 x their (b) + 0 x their (a) + 2 x x 0 or better M for any 3 faces correct (e) 30.5(0) ft Their (d) x 2.25 (a) Correct shape drawn (b) 6, 2, 26 3 B for each SC their SC their (c) 4 (d) 5n + 2 B for 5n, B for + (e) 50 ft Their (d) if linear (f) 3 2ft Their (d) if linear B for their (d) = 66 UCLES /03/SM/5

54 6 BLANK PAGE UCLES /03/SM/5

55 Cambridge IGCSE C am b rid g e International E xam inations Cambridge International General Certificate of Secondary Education CANDIDATE NAME CENTRE NUMBER CANDIDATE NUMBER MATHEMATICS Paper 4 (Extended) SPECIMEN PAPER Candidates answer on the Question Paper. Additional Materials: Electronic calculator Tracing paper (optional) 0580/0 4 For Examination from hours 30 minutes Geometrical instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For n use either your calculator value or At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 30. The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level /Level 2 Certificate. This document consists of 6 printed pages. u c le s 202 S CAMBRIDGE [Turn over

56 (a) Abdullah and Jasmine bought a car for $9000. Abdullah paid 45% of the $9000 and Jasmine paid the rest. 2 (i) How much did Jasmine pay towards the cost of the car? Answer(a){i) $... [2] (ii) Write down the ratio of the payments Abdullah : Jasmine in its simplest form. Answer (a)( ii)... :... [] (b) Last year it cost $2256 to run the car. Abdullah, Jasmine and their son Henri share this cost in the ratio 8 : 3 :. Calculate the amount each paid to run the car. Answer(b) Abdullah $... Jasmine $... Henri $... [3] (c) (i) A new truck costs $5 000 and loses 23% of its value each year. Calculate the value of the truck after three years. Answer(c)(i) $... [3] (ii) Calculate the overall percentage loss o f the truck s value after three years. Answer(c)(ii)... % [3] UCLES /04/SP/5

57 2 (a) Find the integer values for x which satisfy the inequality -3 < 2x - Y 6. 3 Answer(a)... [3] (b) Simplify x 2 + 3x - 0 x 2-25 Answer(b)... [4] (c) (i) Show t h a t = 3 can be simplified to 3x - 3x - 8 = 0. x - 3 x + Answer(c)(i) (ii) Solve the equation 3x2-3x - 8 = 0. Show all your working and give your answers correct to two decimal places. [3] Answer(c)(ii) x =... o rx =... [4] UCLES /04/SP/5 [Turn over

58 4 3 The table shows information about the heights of 20 girls in a swimming club. Height (h metres) Frequency.3 < h Y < h Y < h Y < h Y < h Y < h Y.9 6 (a) (i) Write down the modal class. Answer(a)(i)... m [] (ii) Calculate an estimate of the mean height. Show all of your working. Answer(a)(ii)... m [4] (b) Girls from this swimming club are chosen at random to swim in a race. Calculate the probability that (i) the height of the first girl chosen is more than.8 metres, Answer(b)(i)... [] (ii) the heights of both the first and second girl chosen are.8 metres or less. Answer(b)(n)... [3] UCLES /04/SP/5

59 (c) (i) Complete the cumulative frequency table for the heights. 5 Height (h metres) Cumulative frequency h Y.3 0 h Y.4 4 h Y.5 7 h Y.6 50 h Y.7 h Y.8 4 h Y.9 [] (ii) Draw the cumulative frequency graph on the grid Cumulative frequency h (d) Use your graph to find Height (m) [3] (i) (ii) the median height, the 30th percentile. Answer(d)(i)... m [] Answer (d){ii)... m [] UCLES /04/SP/5 [Turn over

60 6 4 r NOT TO SCALE The diagram shows a plastic cup in the shape of a cone with the end removed. The vertical height of the cone in the diagram is 20 cm. The height of the cup is 8 cm. The base of the cup has radius 2.7 cm. (a) (i) Show that the radius, r, of the circular top of the cup is 4.5 cm. Answer(a)(i) [2] (ii) Calculate the volume of water in the cup when it is full. 2 [The volume, V, of a cone with radius r and height h is V = nr h.] 3 Answer(a)in)... cm3 [4] UCLES /04/SP/5

61 7 (b) (i) Show that the slant height, s, of the cup is 8.2 cm. Answer(b)(i) [3] (ii) Calculate the curved surface area of the outside of the cup. [The curved surface area, A, of a cone with radius r and slant height l is A = nrl.] Answer(b)(ii) cm2 [5] UCLES /04/SP/5 [Turn over

62 8 5 (a) Complete the table for the function f(x) = x x f(x) [3] (b) On the grid draw the graph of y = f(x) for 3 Y x Y 3.5. y A x _4- [4] UCLES /04/SP/5

63 9 (c) Use your graph to (i) solve f(x) = 0.5, Answer(c)(i) x =... or x = or x = [3] (ii) find the inequalities for k, so that f(x) = k has only answer. Answer(c)(ii) k < k > [2] (d) (i) On the same grid, draw the graph of y = 3x - 2 for Y x Y 3.5. [3] 3 X 3 (ii) The e q u a tio n x - = 3x - 2 can be written in the form x + ax + b = 0. 2 Find the values of a and b. Answer(d)(n) a=... and b =... [2] 3 x (iii) Use your graph to find the positive answers t o x - = 3x - 2 for 3 Y x Y Answer(d)(m) x =... o rx =... [2] UCLES /04/SP/5 [Turn over

64 0 6 C NOT TO SCALE The quadrilateral ABCD represents an area o f land. There is a straight road from A to C. AB = 79 m, AD = 20 m and CD = 95 m. Angle BCA = 26 and angle CDA = 77. (a) Show that the length of the road, AC, is 35 m correct to the nearest metre. Answer(a) [4] (b) Calculate the size of the obtuse angle ABC. Answer(b) Angle ABC =... [4] UCLES /04/SP/5

65 (c) A straight path is to be built from B to the nearest point on the road AC. Calculate the length of this path. Answer(c)... m [3] (d) Houses are to be built on the land in triangle ACD. Each house needs at least 80 m2 of land. Calculate the maximum number of houses which can be built. Show all of your working. Answer(d)... [4] UCLES /04/SP/5 [Turn over

66 2 7 y (a) Describe fully the single transformation which maps (i) triangle A onto triangle B, Answer (a){ i)... [2] (ii) triangle A onto triangle C, Answer (a)( ii)... [3] (iii) triangle A onto triangle D. Answer(a)( iii)... [3] UCLES /04/SP/5

67 3 (b) Draw the image of (i) triangle B after a translation of <- 5 ^ V 2, [2] (ii) triangle B after a transformation by the matrix ( 2 0 N v 2y [3] (c) Describe fully the single transformation represented by the matrix Answer(c) [3] UCLES /04/SP/5 [Turn over

68 8 Mr Chang hires x large coaches andy small coaches to take 300 students on a school trip. Large coaches can carry 50 students and small coaches 30 students. There is a maximum of 5 large coaches. (a) Explain clearly how the following two inequalities satisfy these conditions. (i) x Y 5 4 Answer (a)( i)... [] (ii) 5x + 3y [ 30 Answer (a)(ii)... Mr Chang also knows that x + y Y 0. (b) On the grid, show the information above by drawing three straight lines and shading the unw anted regions. y I L x [5] UCLES /04/SP/5

69 (c) A large coach costs $450 to hire and a small coach costs $ (i) Find the number of large coaches and the number of small coaches that would give the minimum hire cost for this school trip. Answer(c)(i) Large coaches... Small coaches... [2] (ii) Calculate this minimum cost. Answer(c)in) $... [] 9 The number, P, of penguins in a colony, t years after the year 2000, is given by P = 2500 x.02'. (a) (i) How many penguins were in the colony in the year 2000? Answer (a){ i)... [] (ii) What information is given by.02 in the formula? Answer (a)(ii)... (b) Using trial and improvement, or otherwise, find in which year the number of penguins in the colony will first be greater than Answer(b)... [3] Question 0 is printed on the next page. UCLES /04/SP/5 [Turn over

70 6 0 (a) John wants to estimate the value of n. He measures the circumference of a circular pizza as 05 cm and its diameter as 34 cm, both correct to the nearest centimetre. Calculate the lower bound of his estimate of the value of n. Give your answer correct to 3 decimal places. Answer (a)... [4] (b) The volume of a cylindrical can is 550 cm3, correct to the nearest 0 cm3. The height of the can is 2 cm correct to the nearest centimetre. Calculate the upper bound of the radius of the can. Give your answer correct to 3 decimal places. Answer (b)... cm [5] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. UCLES /04/SP/5

71 Cambridge IGCSE C am b rid g e International E xam inations Cambridge International General Certificate of Secondary Education MATHEMATICS 0580/0 4 Paper 4 (Extended) For Examination from 205 SPECIMEN MARK SCHEME 2 hours 30 minutes MAXIMUM MARK: 30 The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level /Level 2 Certificate. This document consists of 7 printed pages and blank page. u c le s 202 S CAMBRIDGE [Turn over

72 2 Types of m ark M marks are given for a correct method. A marks are given for an accurate answer following a correct method. B marks are given for a correct statement or step. D marks are given for a clear and appropriately accurate drawing. P marks are given for accurate plotting o f points. E marks are given for correctly explaining or establishing a given result. SC marks are given for special cases that are worthy of some credit. A bbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied Qu. Answers M ark P a rt M arks (a) (i) 4950 (ii) 9 : (b) (c) (i) or 6848 or 6850 (ii) 54.3 (54.33 to 54.35) 2 3 3ft M for 9000 x 0.55 oe Accept :.22 or 0.88 : After 4050 in (a)(i) allow SC for : 9 etc After 0 scored M for ( ) soi M2 for 5000 x oe (6847. (..)ww imp M2) or M for x oe soi (8893.5) After 0 scored SC for art 2793 or 2790 or ft their ( their (c)(i))/5000 x 00 to 3sf or better but not for negative answer or from 4650 in (c)(i) leading to 69% M2 for ( ) or their ( their (c)(i))/5000 (x 00) or SC2ft their (c)(i)/5000 x 00 correctly evaluated (45.65 to or 45.7) or M for ( ) or their (c)(i)/5000 UCLES /04/SM/5

73 3 2 (a) 0,, 2, 3 3 Additional values count as errors B2 for one error/omission or B for two errors/ omissions After B0, M2 for - < x < 3.5 seen, allow 7/2 for 3.5 or M for - < x or x < 3.5 or x = - and x = 3.5 Allow M2 for 0 < x < 4 or M for x > 0 or x < 4 (b) 2 www final answer x - 5 (c) (i) 5(x + ) + 2(x - 3) = 3(x + )(x - 3) oe x2-3x + x - 3 or better seen 3x2-3x - 8 = 0 4 M l B l E l M3 for (x + 5)(x - 2) (x + 5)(x - 5) or M2 for (x + 5)(x - 2) seen or M for (x + a)(x + b) where ab = -0 or a + b = 3 and M for (x + 5)(x - 5) seen Allow if still over common denominator Allow x2-2x - 3 seen or 3x2 - ^ + 3x - 9 or better seen With no errors seen and brackets correctly expanded on both sides (ii) i (-3) ± V (-3)2-4(3)(-8) 2(3) B l B l In square root B for (-3)2-4(3)(-8) or better (265) If in form r r 4.88 and cao B lb l B for - (-3) and 2(3) or better SC for 4.88 and seen or and 4.9 or and to UCLES /04/SM/5 [Turn over

74 4 3 (a) (i).6 < h <.7 Condone alternative notation used for class (ii) {.35 x x x x x x 6}- 20 M3 (94/20) M for mid-values soi (allow one slip) and M for use of YJX with x in correct interval (allow one more slip) and M depend on 2nd M for dividing by or.66 to.67 A www4 (b) (i) 6 20 oe Accept dec/% to 3 sf or better but not ratio isw cancelling/conversion (also for (ii)) (ii) oe (0.902(..)) 3 k k - k M2 f o r -----x w h e re----- is - their (b)(i) or i f k = 4 or M for - their (b)(i) or for 4/20 seen After 0 scored SC2 for ans /476 oe or SC for 6/20 x 5/9 (c) (i) 95, 20 (ii) Plots 7 points correctly exact or in correct square P2ft Pft for 5 or 6 correct plots Curve or lines through 7 points Cft ft their increasing curve within mm of points (d) (i).6 to.63 ft ft their 60th reading on inc. curve to nearest 0.0 (ii).555 to.57 ft ft their 36th reading on inc. curve 4 (a) (i) 2.7 x oe = E2 M for (SF =) 20/2 or 2/20 (but not from 2.7/4.5 or 4.5/2.7) (ii) /3n x 4.52 x 20 - /3n x 2.72 x 2 or ( - (3/5)3) x /3n x 4.52 x 20 oe M3 M for /3n x 4.52 x 20 ( or 35n) and M for /3n x 2.72 x 2 (9.6..or 29.6n) to or 332 or 333 A (b) (i) 82 + ( )2 oe M e.g. Alt: and sq root M Dep on st M Alt: Other complete correct methods are M2 8.2 E No errors seen (ii) 85 or 86 or 85.5 or to M4 for n x 4.5 x n x 2.7 x 2.3 or other complete correct method or M3 for n x 4.5 x 20.5 or n x 2.7 x 2.3 (290 or 92.25n) ( or 33.2n) or B2 for (slant height of large cone =) 20.5 or (slant height of removed cone =) 2.3 or M forv4t o r V 2 ^ or 2/8 x 8.2 oe or 20/8 x 8.2 oe UCLES /04/SM/5

75 5 5 (a), -, 3.5,, (b) 0 correct points plotted P3ft P2ft for 8 or 9 correct Pft for 6 or 7 correct Allow points to be implied from curve Smooth curve through at least 8 points and correct shape (c) (i) -2.2 to to Cft ft ft Correct cubic shape, not ruled Correct or ft their x values 2.5 to 2.7 ft If ft and more than 3 solns then 2 marks maximum (ii) (k <) -4 to -3.7 ft Correct or ft their graph for y values at max and min (k >).7 to 2 ft After 0 scored SC for both correct but reversed (d) (i) Ruled line gradient 3 and jy-intercept -2 over the range - to B2 for correct but freehand or short or M for a ruled line of gradient 3 or passes through (0, -2) (but not y = -2) (ii) (a =) -2, (b =) 2, After 0, M for x3-6x- 6x (=0) or better (iii) 0. to 0.2 and 3.3 to 3.4 cao, 6 (a) x 20 x 95 x cos77 M2 M for implicit version or 35.3 E2 A for 8295 to 8297 (b),.. their35 x sin26 (sin#) = M2 ~ sin# sin26 M f o r = oe their to 48.7 isw A 3 or 3.3 to 3.5 www4 Bft ft for 80 - their 48.5 to 48.7 dep on sine rule or sine used (c) (Angle A =) 22.5 to 22.7 Bft ft 54 - their (b), also accept angle B = 67.3 to 67.5 (ft their (b) - 64) Path /79 = sin (their A) oe M Dep on B and their A < 90 eg 79 cos to 30.5 www3 A (d) x 20 x 95 x sin 77 oe 2 M (5554) Their area + 80 M Dep on area attempt 30.8 to 30.9 A 30 Bft ft their 30.8 to 30.9 truncated dep on at least M earned After M2 answer 30 www scores AB Answer 30 ww scores 0 UCLES /04/SM/5 [Turn over

76 6 7 (a) (a) (i) Reflection only B Spoilt if extras y = -2 (ii) Enlargement only B Spoilt if extras 2 B B (, 4) B (iii) Rotation only B Spoilt if extras 90 clockwise oe B Accept -90 or (+)270 Around (, -3) (b) (i) Triangle at (-4, 4), (-, 4), (-, 5) 2 B ( - 5 ^ ( k ^ B for translation of or V k J V2 J After B0, SC for translation of 5 small squares to the left and 2 small squares up (ii) Triangle at (2, 4), (8, 4), (8, 6) 3 B for each correct co-ordinate (max B2) plotted If no/wrong plots allow SC2 for 3 correct co-ordinates shown in working or SC for any 2 correct co-ordinates shown or M for "2 0N (c) Rotation or Enlargement 80 oe or SF - v0 2, origin Accept (0, 0) or O UCLES /04/SM/5

77 7 8 (a) (i) There are up to 5 large coaches oe (b) (c) E.g. cannot hire more than 5 large coaches The maximum is 5 large coaches The large coaches are less than or equal to 5 (ii) 50x + 30y > 300 oe E2 No errors Allow in words provided clear e.g. 50 in large coaches and 30 in small coaches must equal 300 seats or more M for associating 50 with x or large coaches and 30 with y or small coaches x = 5 ruled x + y = 0 ruled L L Freehand lines - penalise once. All lines must be long enough to make full boundary of their region accept dashed or solid lines 5x + 3jy = 30 ruled L2 L for ruled line with intercepts at (0, 0) or (6, 0) within 2mm by eye at intercepts (extend if line is short) Correct region indicated cao R Allow if slight inaccuracy(s) in diagonal lines Allow any clear indication o f region (a) (i) 2500 After 5 and 2 in working ignore attempts to calculate costs (ii) 2950 ft ft their 5 x their 2 x 350 provided positive integers (ii) Increase of 2% (per year) (b) 2036 (accept 2035) 3 M2 for t = 35 to 36 (inclusive) identified e.g =.999,.0236 = or equivalent with values of P OR M for one correct trial of P (or.02*) with t [ 20 (condone t not an integer) 0 (a) or cao 4 B3 for (85...) or M for their 05/their 34 (their 05 in range 04 to 06 and their 34 in range 33 to 35) and B for 04.5 or 34.5 or selected (b) nr2 their h = their V M Where V is in range 540 to 560 and h is in range to 3 2 their V (r = ) n x their h M Implies previous method (5.36 implies M2) If using 545 and 2.5 then 3.88 (leading to 3.73) If using 550 and 2 then 4.59 (leading to 3.82) Sq root M Dep on M2, can be implied from answers Selects 555 or and.5 B Indep 3.99 cao A If trials then 5 or 0 UCLES /04/SM/5

78 8 BLANK PAGE UCLES /04/SM/5