1、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 a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction uid. DO NOT WRITE IN ANY BARCODES. Answer
2、 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 speci ed in the question, and if the answer is not exact, give the answer to three signi cant gures. Give answers in degrees to one deci
3、mal place. For , use either your calculator value or 3.142. 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 130. MATHEMATICS 0580/43Paper 4 (Extended
4、) May/June 20132 hours 30 minutes Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instrumentsTracing paper (optional) UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certi cate of Secondary Education This document consists of
5、19 printed pages and 1 blank page. Turn over IB13 06_0580_43/5RP UCLES 2013 *9687546924* 2 0580/43/M/J/13 UCLES 2013 For Examiners Use 1 (a) Ali and Ben receive a sum of money.They share it in the ratio 5 : 1.Ali receives $2345.Calculate the total amount.Answer(a) $ . 2(b) Ali uses 11% of his $2345
6、to buy a television.Calculate the cost of the television.Answer(b) $ . 2(c) A different television costs $330.(i) Ben buys one in a sale when this cost is reduced by 15%.How much does Ben pay?Answer(c)(i) $ . 2(ii) $330 is 12% less than the cost last year.Calculate the cost last year.Answer(c)(ii) $
7、 . 3 3 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use(d) Ali invests $1500 of his share in a bank account.The account pays compound interest at a rate of 2.3% per year.Calculate the total amount in the account at the end of 3 years.Answer(d) $ . 3(e) Ali also buys a computer for $325.He later
8、 sells this computer for $250.Calculate Alis percentage loss.Answer(e) . % 3 _ 4 0580/43/M/J/13 UCLES 2013 For Examiners Use 2 (a) In this question show all your construction arcs and use only a ruler and compasses to draw the boundaries of your region.This scale drawing shows the positions of four
9、towns, P, Q, R and S, on a map where 1 cm represents 10 km. P S R Q North Scale: 1 cm to 10 kmA nature reserve lies in the quadrilateral PQRS.The boundaries of the nature reserve are: equidistant from Q and from R equidistant from PS and from PQ 60 km from R along QR.(i) Shade the region which repre
10、sents the nature reserve. 7(ii) Measure the bearing of S from P.Answer(a)(ii) . 1 5 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use(b) A circular lake in the nature reserve has a radius of 45 m.(i) Calculate the area of the lake.Answer(b)(i) m 22(ii) NOT TO SCALEA fence is placed along part of
11、 the circumference of the lake.This arc subtends an angle of 210 at the centre of the circle.Calculate the length of the fence.Answer(b)(ii) . m 2 _ 6 0580/43/M/J/13 UCLES 2013 For Examiners Use 3 (a) Luk wants to buy x goats and y sheep.(i) He wants to buy at least 5 goats.Write down an inequality
12、in x to represent this condition.Answer(a)(i) . 1 (ii) He wants to buy at least 11 sheep.Write down an inequality in y to represent this condition.Answer(a)(ii) . 1(iii) He wants to buy at least 20 animals.Write down an inequality in x and y to represent this condition.Answer(a)(iii) . 1(b) Goats co
13、st $4 and sheep cost $8.The maximum Luk can spend is $160.Write down an inequality in x and y and show that it simpli es to x + 2y Y 40 .Answer(b) 1 7 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use(c) (i) On the grid below, draw four lines to show the four inequalities and shade the unwanted
14、regions. 40 35 30 25 20 15 10 5 y x 0 51 01 52 02 53 03 54 0 7(ii) Work out the maximum number of animals that Luk can buy.Answer(c)(ii) . 2 _ 8 0580/43/M/J/13 UCLES 2013 For Examiners Use 4 I G E F J H 40 cm 22 cm 7 cm NOT TO SCALEEFGHIJ is a solid metal prism of length 40 cm.The cross section EFG
15、is a right-angled triangle.EF = 7 cm and EG = 22 cm.(a) Calculate the volume of the prism.Answer(a) cm 32(b) Calculate the length FJ.Answer(b) FJ = . cm 4 9 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use(c) Calculate the angle between FJ and the base EGJH of the prism.Answer(c) . 3(d) The pri
16、sm is melted and made into spheres.Each sphere has a radius 1.5 cm.Work out the greatest number of spheres that can be made.The volume, V, of a sphere with radius r is V = 3 4 r 3 .Answer(d) . 3(e) (i) A right-angled triangle is the cross section of another prism.This triangle has height 4.5 cm and
17、base 11.0 cm.Both measurements are correct to 1 decimal place.Calculate the upper bound for the area of this triangle.Answer(e)(i) cm 22(ii) Write your answer to part (e)(i) correct to 4 signi cant gures.Answer(e)(ii) cm 21 _ 10 0580/43/M/J/13 UCLES 2013 For Examiners Use 5 (a) Complete this table o
18、f values for the function f(x) = x 1 x 2 , x 0. x 3 2 1 0.5 0.2 0.2 0.5 1 2 3 f(x) 9.33 4.5 2 2.25 4.96 3.5 8.67 3(b) Draw the graph of f(x) = x 1 x 2for 3 Y x Y 0.2 and 0.2 Y x Y 3. y x 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 0 1 1 2 3 23 5 11 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use(c) Use you
19、r graph to solve f(x) = 3. Answer(c) x = or x = or x = 3(d) By drawing a suitable line on your graph, solve the equation f(x) = 2x 2. Answer(d) x = or x = or x = 3(e) By drawing a suitable tangent, work out an estimate of the gradient of the curve at the point where x = 2.You must show your working.
20、Answer(e) . 3 _ 12 0580/43/M/J/13 UCLES 2013 For Examiners Use 6 In a box there are 7 red cards and 3 blue cards.A card is drawn at random from the box and is not replaced.A second card is then drawn at random from the box.(a) Complete this tree diagram. Red Blue Red Blue Blue RedFirst card Second c
21、ard 7 10 3(b) Work out the probability that the two cards are of different colours.Give your answer as a fraction.Answer(b) . 3 _ 13 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use 7 AB x y 10 9 8 7 6 5 4 3 2 1 0 12345678(a) (i) Draw the image of shape A after a stretch, factor 3, x-axis invar
22、iant. 2(ii) Write down the matrix representing a stretch, factor 3, x-axis invariant. Answer(a)(ii) eo 2(b) (i) Describe fully the single transformation which maps shape A onto shape B.Answer(b)(i) 3(ii) Write down the matrix representing the transformation which maps shape A onto shape B. Answer(b)
23、(ii) eo 2 _ 14 0580/43/M/J/13 UCLES 2013 For Examiners Use 8 (a) 27 B C O A E D NOT TO SCALEA, B, C, D and E are points on the circle centre O.Angle ABD = 27.Find(i) angle ACD,Answer(a)(i) Angle ACD = . 1(ii) angle AOD,Answer(a)(ii) Angle AOD = . 1(iii) angle AED.Answer(a)(iii) Angle AED = . 1(b) L
24、K N M 67 100 45 cm 32 cm NOT TO SCALEThe diagram shows quadrilateral KLMN.KL = 45 cm, LN = 32 cm, angle KLN = 100 and angle NLM = 67. 15 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use(i) Calculate the length KN.Answer(b)(i) KN = . cm 4(ii) The area of triangle LMN is 324 cm 2 .Calculate the l
25、ength LM.Answer(b)(ii) LM = . cm 3(iii) Another triangle XYZ is mathematically similar to triangle LMN. L N M X Z Y NOT TO SCALEXZ = 16 cm and the area of triangle LMN is 324 cm 2 .Calculate the area of triangle XYZ.Answer(b)(iii) cm 22 _ 16 0580/43/M/J/13 UCLES 2013 For Examiners Use 9 Sam asked 80
26、 people how many minutes their journey to work took on one day.The cumulative frequency diagram shows the times taken (m minutes). 80 70 60 50 40 30 20 10 m 0 10 20 30 40 50 Cumulative frequency Time (minutes)(a) Find(i) the median,Answer(a)(i) min 1(ii) the lower quartile,Answer(a)(ii) min 1(iii) t
27、he inter-quartile range.Answer(a)(iii) min 1 17 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use(b) One of the 80 people is chosen at random.Find the probability that their journey to work took more than 35 minutes.Give your answer as a fraction.Answer(b) . 2(c) Use the cumulative frequency dia
28、gram to complete this frequency table. Time (m minutes) 0 m Y 10 10 m Y 15 15 m Y 30 30 m Y 40 40 m Y 50 Frequency 30 12 18 2(d) Using mid-interval values, calculate an estimate of the mean journey time for the 80 people.Answer(d) min 3(e) Use the table in part (c) to complete the histogram to show
29、the times taken by the 80 people.One column has already been completed for you. Frequency density Time (minutes) 4 3 2 1 0 10 20 30 40 50 m 5 _ 18 0580/43/M/J/13 UCLES 2013 For Examiners Use 10 (a) (i) Solve 2(3x 7) = 13.Answer(a)(i) x = . 3(ii) Solve by factorising x 2 7x + 6 = 0. Answer(a)(ii) x =
30、 . or x = . 3(iii) Solve 5 x 32 -+ 10 2 x += 4.Answer(a)(iii) x = . 4 19 0580/43/M/J/13 UCLES 2013 Turn over For Examiners Use(b) 1 2= 11 2+ 2 2= 51 2+ 2 2+ 3 2= 141 2+ 2 2+ 3 2+ 4 2= 301 2+ 2 2+ 3 2+ 4 2+ . + n 2= an 3+ bn 2+ 6 nWork out the values of a and b.Answer(b) a = .b = . 6 _ 20 0580/43/M/J
31、/13 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 incl
32、uded the publisher will be pleased to make amends at the earliest possible opportunity. University of 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. BLANK PAGE UCLES 2013
