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This document consists of 19 printed pages and 1 blank page.IB11 06_0580_43/4RP© UCLES 2011[Turn over*8044643715*UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary EducationMATHEMATICS 0580/43Paper 4 (Extended) May/June 20112 hours 30 minutesCandidates answer on the Question Paper.Additional Materials: Electronic calculatorGeometrical instrumentsMathematical tables (optional)Tracing paper (optional)READ THESE INSTRUCTIONS FIRSTWrite 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 fluid. DO NOT WRITE IN ANY BARCODES.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 π 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.© UCLES 20110580/43/M/J/11For Examiner's Use1 Lucy works in a clothes shop.(a) In one week she earned $277.20.(i) She spent 81of this on food.Calculate how much she spent on food. Answer(a)(i) $ [1](ii) She paid 15% of the $277.20 in taxes. Calculate how much she paid in taxes. Answer(a)(ii) $ [2](iii) The $277.20 was 5% more than Lucy earned in the previous week. Calculate how much Lucy earned in the previous week. Answer(a)(iii) $ [3](b) The shop sells clothes for men, women and children.(i) In one day Lucy sold clothes with a total value of $2200 in the ratio men : women : children = 2 : 5 : 4. Calculate the value of the women’s clothes she sold. Answer(b)(i) $ [2](ii) The $2200 was 7344of the total value of the clothes sold in the shop on this day. Calculate the total value of the clothes sold in the shop on this day. Answer(b)(ii) $ [2]© UCLES 2011 0580/43/M/J/11[Turn overUsex(a) (i) Draw the reflection of shape X in the x -axis. Label the image Y . [2](ii) Draw the rotation of shape Y , 90° clockwise about (0, 0). Label the image Z . [2](iii) Describe fully the single transformation that maps shape Z onto shape X .Answer(a)(iii)[2](b) (i) Draw the enlargement of shape X , centre (0, 0), scale factor21. [2](ii) Find the matrix which represents an enlargement, centre (0, 0), scale factor 21.Answer(b)(ii)[2](c) (i) Draw the shear of shape X with the x -axis invariant and shear factor –1.[2](ii) Find the matrix which represents a shear with the x -axis invariant and shear factor –1.Answer(c)(ii)[2]© UCLES 20110580/43/M/J/11Use(x + 5) cm2x cmx cmNOT TO SCALEThe diagram shows a square of side (x + 5) cm and a rectangle which measures 2x cm by x cm. The area of the square is 1 cm 2 more than the area of the rectangle.(a) Show that x 2 – 10x – 24 = 0 . Answer(a) [3]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(b) Find the value of x . Answer(b) x = [3](c) Calculate the acute angle between the diagonals of the rectangle. Answer(c) [3]© UCLES 2011 0580/43/M/J/11For Examiner's Use4NOT TO SCALEThe circle, centre O , passes through the points A , B and C . In the triangle ABC , AB = 8 cm, BC = 9 cm and CA = 6 cm. (a) Calculate angle BAC and show that it rounds to 78.6°, correct to 1 decimal place. Answer(a) [4](b) M is the midpoint of BC .(i) Find angle BOM . Answer(b)(i) Angle BOM = [1]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(ii) Calculate the radius of the circle and show that it rounds to 4.59 cm, correct to 3 significantfigures.Answer(b)(ii) [3](c) Calculate the area of the triangle ABC as a percentage of the area of the circle. Answer(c) % [4]© UCLES 2011 0580/43/M/J/11ForExaminer's Use5 (a) Complete the table of values for the function f(x ), where f(x ) = x 2 + 21x , x ≠ 0 .xO 3 O 2.5 O 2 O 1.5 O 1 O 0.50.5 1 1.5 2 2.5 3 f(x ) 6.41 2.69 4.25 4.252.69 6.41[3](b) On the grid, draw the graph of y = f(x ) for O 3 Y x Y O 0.5 and 0.5 Y x Y 3 .[5]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(c) (i) Write down the equation of the line of symmetry of the graph.Answer(c)(i)[1](ii) Draw the tangent to the graph of y = f(x ) where x = O 1.5. Use the tangent to estimate the gradient of the graph of y = f(x ) where x = O 1.5. Answer(c)(ii) [3](iii) Use your graph to solve the equation x 2 + 21x= 3.Answer(c)(iii) x = or x = or x = or x = [2](iv) Draw a suitable line on the grid and use your graphs to solve the equation x 2 + 21x = 2x .Answer(c)(iv) x =or x =[3]© UCLES 2011 0580/43/M/J/11For Examiner's Use6CumulativefrequencyMass (kilograms)mThe masses of 200 parcels are recorded. The results are shown in the cumulative frequency diagram above.(a) Find(i) the median, Answer(a)(i) kg [1](ii) the lower quartile, Answer(a)(ii) kg [1](iii) the inter-quartile range, Answer(a)(iii) kg [1](iv) the number of parcels with a mass greater than 3.5 kg. Answer(a)(iv) [2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(b) (i) Use the information from the cumulative frequency diagram to complete the groupedfrequency table.Mass (m ) kg0 I m Y 44 I m Y 66 I m Y 77 I m Y 10Frequency 36 50[2](ii) Use the grouped frequency table to calculate an estimate of the mean. Answer(b)(ii) kg [4](iii) Complete the frequency density table and use it to complete the histogram.Mass (m ) kg 0 I m Y 4 4 I m Y 6 6 I m Y 7 7 I m Y 10Frequency density916.7FrequencydensityMass (kilograms)m[4]© UCLES 20110580/43/M/J/11ForExaminer's Use7 Katrina puts some plants in her garden.The probability that a plant will produce a flower is107. If there is a flower, it can only be red, yellow or orange.When there is a flower, the probability it is red is 32 and the probability it is yellow is 41.(a) Draw a tree diagram to show all this information. Label the diagram and write the probabilities on each branch. Answer(a) [5](b) A plant is chosen at random. Find the probability that it will not produce a yellow flower. Answer(b) [3](c) If Katrina puts 120 plants in her garden, how many orange flowers would she expect? Answer(c) [2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use8A(a) Draw accurately the locus of points, inside the quadrilateral ABCD , which are 6 cm from thepoint D . [1](b) Using a straight edge and compasses only, construct(i) the perpendicular bisector of AB , [2](ii) the locus of points, inside the quadrilateral, which are equidistant from AB and from BC . [2](c) The point Q is equidistant from A and from B and equidistant from AB and from BC .(i) Label the point Q on the diagram. [1](ii) Measure the distance of Q from the line AB . Answer(c)(ii) cm [1](d) On the diagram, shade the region inside the quadrilateral which is• less than 6 cm from Dand• nearer to A than to Band• nearer to AB than to BC . [1]© UCLES 2011 0580/43/M/J/11For Examiner's Use9 f(x ) = 3x + 1 g(x ) = (x + 2)2(a) Find the values of(i) gf(2), Answer(a)(i)[2](ii) ff(0.5). Answer(a)(ii)[2](b) Find f –1(x ), the inverse of f(x ). Answer(b)[2](c) Find fg(x ). Give your answer in its simplest form. Answer(c)[2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(d) Solve the equation x 2 + f(x ) = 0. Show all your working and give your answers correct to 2 decimal places. Answer(d) x = or x =[4]UseBABCD is a parallelogram.DC, M is the midpoint of BC and N is the midpoint of LM.pq.(i)Find the following in terms ofp and q, in their simplest form.(a)Answer(a)[1](b)Answer(a)[2](c)Answer(a)[2] (ii) N lies on the line AC.Answer(a)(ii) [1]© UCLES 2011 0580/43/M/J/11© UCLES 2011 0580/43/M/J/11[Turn overUseEH J2x°75°(x + 15)°NOT TO SCALEEFG is a triangle. HJ is parallel to FG . Angle FEG = 75°. Angle EFG = 2x ° and angle FGE = (x + 15)°.(i) Find the value of x . Answer(b)(i) x = [2](ii) Find angle HJG . Answer(b)(ii) Angle HJG = [1]© UCLES 2011 0580/43/M/J/11For Examiner's Use11 (a) (i) The first three positive integers 1, 2 and 3 have a sum of 6. Write down the sum of the first 4 positive integers. Answer(a)(i) [1](ii) The formula for the sum of the first n integers is21)(+n n . Show the formula is correct when n = 3. Answer(a)(ii) [1](iii) Find the sum of the first 120 positive integers. Answer(a)(iii) [1](iv) Find the sum of the integers121 + 122 + 123 + 124 + …………………………… + 199 + 200.Answer(a)(iv)[2](v) Find the sum of the even numbers 2 + 4 + 6 + …………………………+ 800.Answer(a)(v)[2]© UCLES 20110580/43/M/J/11For Examiner's Use(b) (i) Complete the following statements about the sums of cubes and the sums of integers.13 = 1 1 = 113 + 23 = 9 1 + 2 = 3 13 + 23 + 33 =1 +2 +3 =13 + 23 + 33 + 43 =1 +2 +3 +4 =[2](ii) The sum of the first 14 integers is 105. Find the sum of the first 14 cubes. Answer(b)(ii) [1](iii) Use the formula in part(a)(ii) to write down a formula for the sum of the first n cubes. Answer(b)(iii) [1](iv) Find the sum of the first 60 cubes. Answer(b)(iv) [1](v) Find n when the sum of the first n cubes is 278 784. Answer(b)(v) n = [2]BLANK PAGEPer mission to r epr oduce items wher e thir d-par ty owned mater ial pr otected by copyr ight is included has been sought and clear ed wher e possible. Ever y 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.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.© UCLES 2011 0580/43/M/J/11。
Turn over P42864A©2014 Pearson Education Ltd.1/1/1/1/*P42864A0120*Instructionst Use black ink or ball-point pen.t Fill in the boxes at the top of this page with your name,centre number and candidate number.t Answer all questions.t A nswer the questions in the spaces provided– there may be more space than you need.t Show all the steps in any calculations and state the units.t SInformationt The total mark for this paper is 60.t T he marks for each question are shown in brackets– use this as a guide as to how much time to spend on each question.Advicet Read each question carefully before you start to answer it.t Keep an eye on the time.t Write your answers neatly and in good English.t Try to answer every question.t Check your answers if you have time at the end.2*P42864A0220*3*P42864A0320*Turn overBLANK PAGE4*P42864A0420*5*P42864A0520*Turn over6*P42864A0620*2 Bromine, chlorine, fluorine and iodine are elements in Group 7 of the Periodic Table.(a) Which two of these elements have the darkest colours?(1)....................................................................................................................................and ....................................................................................................................................(b) The equation for the reaction between hydrogen and chlorine isH 2 + Cl 2 o 2HClDifferent names are used for the product, depending on its state symbol.(i) What are the names used for HCl(g) and HCl(aq)?(2)HCl(g) .................................................................................................................................................................................................................................................................HCl(aq) ............................................................................................................................................................................................................................................................... (ii) The presence of HCl(g) can be confirmed by adding ammonia (NH 3) gas.State the observation in the reaction between HCl(g) and ammonia gas and write a chemical equation for the reaction.(2)observation ......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................chemical equation ................................................................................................................................................................................................................................ (iii) The presence of chloride ions in HCl(aq) can be shown by mixing it with silvernitrate solution and dilute nitric acid.State the result of this test and complete the chemical equation for the reaction by adding the state symbols.(3)result .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................AgNO 3(.......................) + HCl(aq) o AgCl(.......................) + HNO 3(.......................)7*P42864A0720*Turn over8*P42864A0820*3 Tungsten is a useful metal. It has the chemical symbol W. (a) One method of extracting tungsten involves heating a tungsten compound (WO 3)with hydrogen.(i) Suggest the chemical name of WO 3(1)....................................................................................................................................................................................................................................................................................(ii) Balance the equation for the reaction between WO 3 and hydrogen.(1)WO 3 + ............................H 2 o ............................W + ............................H 2O(iii) Why is this reaction described as reduction?(1)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(b) Scheelite is an ore of tungsten. The main compound in scheelite has the percentage composition by mass Ca = 13.9%, W = 63.9%, O = 22.2%.Calculate the empirical formula of this compound.(3)empirical formula = ...................................................9*P42864A0920*Turn over(c) Tungsten can also be obtained by reacting tungsten fluoride with hydrogen.The equation for this reaction isWF 6 + 3H 2 o W + 6HF(i) In an experiment, a chemist used 59.6g of tungsten fluoride. What is the maximum mass of tungsten he could obtain from 59.6 g of tungsten fluoride?Relative formula mass of tungsten fluoride = 298(2)maximum mass = ................................................... g(ii) Starting with a different mass of tungsten fluoride, he calculates that the massof tungsten formed should be 52.0 g. In his experiment he actually obtains 47.5 g of tungsten.What is the percentage yield of tungsten in this experiment?(2)percentage yield = ................................................... %(Total for Question 3 = 10 marks)10*P42864A01020*4 A student investigated the neutralisation of acids by measuring the temperature changeswhen alkalis were added to acids of known concentrations.He used this apparatus to add different volumes of sodium hydroxide solution to a fixed volume of dilute nitric acid.He used this method. Ɣ measure the temperature of 25.0 cm 3 of the acid in the polystyrene cupƔ add the sodium hydroxide solution in 5.0 cm 3 portions until a total of 30.0 cm 3has been added(a) State two properties of the sodium hydroxide solution that should be kept constantfor each 5.0 cm 3 portion.(2)1 ...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2 ...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................polystyrene cup11*P42864A01120*Turn over12*P42864A01220*13*P42864A01320*Turn over14*P42864A01420*(f) Another student used sulfuric acid instead of nitric acid in her experiments.She started with 25.0 cm 3 of sulfuric acid of concentration 0.650 mol/dm 3. She added 0.500 mol/dm 3 sodium hydroxide solution until the acid was completely neutralised.The equation for this reaction is2NaOH + H 2SO 4 o Na 2SO 4 + 2H 2O(i) Calculate the amount, in moles, of sulfuric acid used.(2)amount = ................................. mol(ii) Calculate the amount, in moles, of sodium hydroxide needed to neutralise thisamount of sulfuric acid.(1)amount = ................................. mol(iii) Calculate the volume, in cm 3, of sodium hydroxide solution needed to neutralisethis amount of sulfuric acid.(2)volume = ................................. cm 3(Total for Question 4 = 18 marks)15*P42864A01520*Turn over16*P42864A01620*(c) The equation for one reaction that could occur in process 2 is C x H y o C 5H 12 + 2C 2H 4(i) Deduce the formula of C x H y(1)....................................................................................................................................................................................................................................................................................(ii) Give the name of the compound C 5H 12(1)....................................................................................................................................................................................................................................................................................(iii) Draw the displayed formula of C 2H 4(1)(d) The structural formula of chloroethene formed in process 3 is CH 2CHClThe polymer formed in process 4 is poly(chloroethene).Draw the displayed formula for the repeat unit of poly(chloroethene).(2)17*P42864A01720*(e) Poly(chloroethene) is formed by addition polymerisation. Nylon is formed by condensation polymerisation.(i) How does condensation polymerisation differ from addition polymerisation?(1)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii) Poly(chloroethene) and nylon do not biodegrade easily.What is meant by the term biodegrade ?(2)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(iii) What feature of addition polymers makes it difficult for them to biodegrade?(1)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(Total for Question 5 = 13 marks)(TOTAL FOR PAPER = 60 MARKS)18*P42864A01820*BLANK PAGE19*P42864A01920*BLANK PAGE20*P42864A02020*BLANK PAGE。
gmat数学真题及解析答案高中高中阶段是学生们备战升学考试的关键时期。
而在备考的过程中，数学是其中最重要的一门科目。
为了帮助高中生更好地备考GMAT数学部分，下面将介绍一些真题及其解析答案。
第一道题目是关于平面几何的。
题目如下：在平面直角坐标系中，点A(-3, 1)和点B(2, 4)分别为线段AC 和线段BC的中点，那么三角形ABC的面积是多少？解析：首先，通过计算可以得出点C的坐标为(-3,4)和(2,1)。
由于三角形ABC是平面直角坐标系中的三角形，可以利用坐标和三角形的性质来求解。
首先，通过计算AC和BC的长度，可以发现AC的长度是4，BC 的长度是3。
而既然AC和BC是以A和B为中点的线段，所以AC和BC 是等长的。
接下来，我们可以通过计算向量的差来求解三角形ABC的面积。
向量BA的坐标为(2-(-3), 4-1) = (5,3)。
根据向量的性质，如果平行四边形的邻边是向量a和向量b，那么平行四边形的面积可以通过向量a和b的叉积来求解。
而这里的三角形ABC恰好是平行四边形的一个四分之一，所以三角形ABC的面积等于平行四边形的面积的四分之一。
所以三角形ABC 的面积为(5*3)/4 = 15/4 = 3.75。
第二道题目是关于概率与组合的。
题目如下：小明参加了一个抽奖活动，需要从1至100中随机选择3个数。
那么小明中奖的概率是多少？解析：首先，计算一共有多少种可能的情况。
从1至100中选择3个数，即从100个数中选取3个数，那么一共有C(100,3)种可能的情况。
而中奖的情况只有一种，即选择出的3个数中恰好包含了中奖号码。
假设中奖号码为x、y、z，那么一共有C(3,3)种中奖情况。
所以小明中奖的概率等于中奖的情况数除以可能的情况数，即1/C(100,3)。
将这个概率换算成小数形式，即得到了小明中奖的概率。
接下来是一道关于代数和方程的题目。
题目如下：如果x^2 - 8x + 15 = 0，那么x的值是多少？解析：这是一个关于二次方程的题目。
4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010 – AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 22 questions in this question paper. The total mark for this paperis 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.N36905AIGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write down all stages in your working.1. Solve 6 y – 9 = 3 y + 7y = ................................(Total 3 marks) 2. The diagram shows two towns, A and B, on a map.(a) By measurement, find the bearing of B from A.....................................(2)C is another town.The bearing of C from A is 050.(b) Find the bearing of A from C.....................................(2)(Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will land on red is 0.5The probability that it will land on blue is 0.2Imad spins the spinner once.(a) Work out the probability that it will land on yellow......................................(2)Janet spins the spinner 30 times.(b)Work out an estimate for the number of times the spinner will land on blue......................................(2)(Total 4 marks)4. Rosetta drives 85 kilometres in 1 hour 15 minutes.(a) Work out her average speed in kilometres per hour...................................... km/h(2)Rosetta drives a total distance of 136 kilometres.(b) Work out 85 as a percentage of 136................................. %(2)Sometimes Rosetta travels by train to save money.The cost of her journe y by car is £12The cost of her journey by train is 15% less than the cost of her journey by car.(c)Work out the cost of Rosetta’s journey by train.£ ...................................(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant figures.x = ................................(Total 3 marks)6. A = {2, 3, 4, 5}B = {4, 5, 6, 7}(a)(i) List the members of A B......................................(ii) How many members are in A B?.....................................(2)ℰ = {3, 4, 5, 6, 7}P = {3, 4, 5}Two other sets, Q and R, each contain exactly three members.P Q = {3, 4}P R = {3, 4}Set Q is not the same as set R.(b)(i) Write down the members of a possible set Q......................................(ii) Write down the members of a possible set R......................................(2)(Total 4 marks)7. Rectangular tiles have width (x + 1) cm and height (5x – 2) cm.Some of these tiles are used to form a large rectangle.The large rectangle is 7 tiles wide and 3 tiles high.The perimeter of the large rectangle is 68 cm.(a) Write down an equation in x...............................................................................................................(3)(b) Solve this equation to find the value of x.x = ................................(3)(Total 6 marks)8. Show that 121 141 = 1519. The depth of water in a reservoir increases from 14 m to 15.75 m.Work out the percentage increase.................................. %(Total 3 marks)10. Quadrilaterals ABCD and PQRS are similar.AB corresponds to PQ.BC corresponds to QR.CD corresponds to RS.Find the value of(a) xx = ...............................(2)(b) yy = ...............................(1)(Total 3 marks)11. Simplify fully6x + 43x.....................................(Total 3 marks)12.(a)Find the equation of the line L......................................(3)(b) Find the three inequalites that define the unshaded region shown in the diagram below................................................................................................................(3)(Total 6 marks)13. (a) Solve x 2– 8x + 12 = 0.....................................(3)(b) Solve the simultaneous equationsy = 2x4x – 5y = 9x = ................................y = ................................(3)(Total 6 marks)14.The area of the triangle is 6.75 cm2.The angle x° is acute.Find the value of x.Give your answer correct to 1 decimal place.x = ................................(Total 3 marks)15. The unfinished histogram shows information about the heights, h metres, ofsome trees.(a) Calculate an estimate for the number of trees with heights in theinterval 4.5 < h ≤ 10.....................................(3)(b) There are 75 trees with heights in the interval 10 < h ≤ 13Use this information to complete the histogram.(2)(Total 5 marks)16. A bag contains 3 white discs and 1 black disc.John takes at random 2 discs from the bag without replacement.(a) Complete the probability tree diagram.First disc Second disc(3)(b)Find the probability that both discs are white......................................(2)All the discs are now replaced in the bag.Pradeep takes at random 3 discs from the bag without replacement.(c)Find the probability that the disc left in the bag is white......................................(3)(Total 8 marks)17. The diagram shows a sector of a circle, radius 45 cm, with angle 84°.Calculate the area of the sector.Give your answer correct to 3 significant figures.............................. cm2(Total 3 marks) 18.Calculate the length of AC.Give your answer correct to 3 significant figures................................ cm(Total 3 marks)19. A cone has slant height 4 cm and base radius r cm.The total surface area of the cone is 433π cm 2.Calculate the value of r .r = ................................(Total 4 marks)20. f(x) = (x – 1)2(a) Find f(8).....................................(1)The domain of f is all values of x where x ≥ 7(a)Find the range of f......................................(2)xg(x) =x1(c) Solve the equation g(x) = 1.2.....................................(2)(d) (i) Express the inverse function g –1 in the form g –1(x) = .......g –1(x) = ...................................(ii) Hence write down gg(x) in terms of x.gg(x) = ....................................(6)(Total 11 marks)21.In the diagram OA= a and OC= c.(a) Find CA in terms of a and c......................................(1)The point B is such that AB=1c.2(b) Give the mathematical name for the quadrilateral OABC......................................(1)The point P is such that OP= a + k c, where k ≥ 0(c) State the two conditions relating to a + k c that must be true for OAPCto be a rhombus.(2)(Total 4 marks)22. (a) Work out 5.2 × 102+ 2.3 × 104Give your answer in standard form......................................(2)a × 102 +b × 104 =c × 104(b) Express c in terms of a and b.c = ................................(2)(Total 4 marks)TOTAL FOR PAPER = 100 MARKSEND。
4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010 – AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: . (2).There are 22 questions in this question paper. The total mark for this paperis 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.This publication may be reproduced only in accordance with Edexcel Limited copyright policy.©2010 Edexcel Limited.Printer’s Log. No. N36905AIGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write down all stages in your working.1. Solve 6 y – 9 = 3 y + 7y = ................................(Total 3 marks) 2. The diagram shows two towns, A and B, on a map.(a) By measurement, find the bearing of B from A.....................................(2)C is another town.The bearing of C from A is 050.(b) Find the bearing of A from C.....................................(2)(Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will land on red isThe probability that it will land on blue isImad spins the spinner once.(a) Work out the probability that it will land on yellow......................................(2)Janet spins the spinner 30 times.(b)Work out an estimate for the number of times the spinner will land on blue......................................(2)(Total 4 marks)4. Rosetta drives 85 kilometres in 1 hour 15 minutes.(a) Work out her average speed in kilometres per hour...................................... km/h(2)Rosetta drives a total distance of 136 kilometres.(b) Work out 85 as a percentage of 136................................. %(2)Sometimes Rosetta travels by train to save money.The cost of her journey by car is £12The cost of her journey by train is 15% less than the cost of her journey by car.(c)Work out the cost of Rosetta’s journ ey by train.£ ...................................(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant figures.x = ................................(Total 3 marks)6. A = {2, 3, 4, 5}B = {4, 5, 6, 7}(a)(i) List the members of A B......................................(ii) How many members are in A B?.....................................(2)ℰ = {3, 4, 5, 6, 7}P = {3, 4, 5}Two other sets, Q and R, each contain exactly three members.P Q = {3, 4}P R = {3, 4}Set Q is not the same as set R.(b)(i) Write down the members of a possible set Q......................................(ii) Write down the members of a possible set R......................................(2)(Total 4 marks)7. Rectangular tiles have width (x + 1) cm and height (5x – 2) cm.Some of these tiles are used to form a large rectangle.The large rectangle is 7 tiles wide and 3 tiles high.The perimeter of the large rectangle is 68 cm.(a) Write down an equation in x...............................................................................................................(3)(b) Solve this equation to find the value of x.x = ................................(3)(Total 6 marks)8. Show that 121 141 = 1519. The depth of water in a reservoir increases from 14 m to m.Work out the percentage increase.................................. %(Total 3 marks)10. Quadrilaterals ABCD and PQRS are similar.AB corresponds to PQ.BC corresponds to QR.CD corresponds to RS.Find the value of(a) xx = ...............................(2)(b) yy = ...............................(1)(Total 3 marks)11. Simplify fully6x + 43x.....................................(Total 3 marks)12.(a)Find the equation of the line L......................................(3)(b) Find the three inequalites that define the unshaded region shown in the diagram below................................................................................................................(3)(Total 6 marks)13. (a) Solve x 2– 8x + 12 = 0.....................................(3)(b) Solve the simultaneous equationsy = 2x4x – 5y = 9x = ................................y = ................................(3)(Total 6 marks)14.The area of the triangle is cm2.The angle x° is acute.Find the value of x.Give your answer correct to 1 decimal place.x = ................................(Total 3 marks)15. The unfinished histogram shows information about the heights, h metres, ofsome trees.(a) Calculate an estimate for the number of trees with heights in theinterval < h ≤ 10.....................................(3)(b) There are 75 trees with heights in the interval 10 < h ≤ 13Use this information to complete the histogram.(2)(Total 5 marks)16. A bag contains 3 white discs and 1 black disc.John takes at random 2 discs from the bag without replacement.(a) Complete the probability tree diagram.First disc Second disc(3)(b)Find the probability that both discs are white......................................(2)All the discs are now replaced in the bag.Pradeep takes at random 3 discs from the bag without replacement.(c)Find the probability that the disc left in the bag is white......................................(3)(Total 8 marks)17. The diagram shows a sector of a circle, radius 45 cm, with angle 84°.Calculate the area of the sector.Give your answer correct to 3 significant figures.............................. cm2(Total 3 marks) 18.Calculate the length of AC.Give your answer correct to 3 significant figures................................ cm(Total 3 marks)19. A cone has slant height 4 cm and base radius r cm.The total surface area of the cone is 433π cm 2.Calculate the value of r .r = ................................(Total 4 marks)20. f(x) = (x – 1)2(a) Find f(8).....................................(1)The domain of f is all values of x where x ≥ 7(a)Find the range of f......................................(2)xg(x) =x1(c) Solve the equation g(x) =.....................................(2)(d) (i) Express the inverse function g –1 in the form g –1(x) = .......g –1(x) = ...................................(ii) Hence write down gg(x) in terms of x.gg(x) = ....................................(6)(Total 11 marks)21.In the diagram OA= a and OC= c.(a) Find CA in terms of a and c......................................(1)The point B is such that AB=1c.2(b) Give the mathematical name for the quadrilateral OABC......................................(1)The point P is such that OP= a + k c, where k ≥ 0(c) State the two conditions relating to a + k c that must be true for OAPCto be a rhombus.(2)(Total 4 marks)22. (a) Work out × 102+ × 104Give your answer in standard form......................................(2)a × 102 +b × 104 =c × 104(b) Express c in terms of a and b.c = ................................(2)(Total 4 marks)TOTAL FOR PAPER = 100 MARKSEND。
1、Which of the following equations is true?( ).A.7×(2+3)=3+(7×2)B.7×(2+3)=7+(2×3)C.7×(2+3)=3×(2+7)D.7×(2+3)=7×(3+2)2、Which of the following is closest to the value of the expression below?( ).A.4B. 5C. 9D. 113、A container of soup is in the shape of a right circular cylinder. The container and its dimensions are shown below.What is the volume, in cubic centimeters, of the container?( ).A.200πB. 160πC. 80πD. 40π4、Which of the following is equivalent to the expression below? ( ).A.P2-2p-8B.p2-4p-2C. p2-8D. p2-25、Which of the following values of x is a solution of the equation below? ( ).A.4B. 16C. 128D. 5126、A waiter received a 15% tip for a restaurant bill of $59.14. Which of the following estimates is closest to the tip the waiter received? ( ).A.$5.00B. $7.50C. $9.00D. $12.007、The weights, in pounds, of 7 packages are listed below.The weight of an 8th package is added to the list. The mean weight of the 8 packages is 12 pounds. What is the weight, in pounds, of the 8th package?( ).A.19B. 16C. 11D. 108、Point S is the midpoint of RT. The coordinates of point R and point T are listed below.What are the coordinates of point S ?( ).R(-11, -12) T(-7, -4)A.(-2, -4)B. (-8, -10)C. (-9, -8)D. (-18, -16)9、Which of the following is equivalent to the expression below?( ).A.(x-1)(x-144)B. (x-1)(x+144)C. (x-12)(x-12)D. (x-12)(x+12)10、A rug in the shape of a square has an area of 33 square feet. Which of the following estimates is closest to the length of each side of the rug?( ).A.415feetB. 435feetC.436feetD. 418feet11、A set of data is shown in the scatterplot below,Which of the following equations best represents the line of best fit for the data in the scatterplot?( ).A.221--=x yB. 121+-=x yC.221-=x yD. 121+=x y12、A parallelogram and some of its dimensions are shown below.The area of the parallelogram is 90 square inches. What is h, the height in inches of the parallelogram?( ).A. 6B. 8C. 10D. 12 13、Which of the following expressions is equivalent to 17?( ). A.3173⋅ B.31731⋅ C.3317 D. 3317 14、Two groups are going on a trip to a theater. The first group has 30 students and 4 adult chaperones. The second group has 25 students and 4 adult chaperones. The cost, in dollars, for each student ticket, s, and each adult ticket, a, can be determined using the system of equations below. ( ).What is the cost for each student ticket?A. $5B. $20C. $25D. $30Questions 15 and 16 are short -answer questionsWhat is the value of the expression below?16、The line plot below shows the number of red items of clothing owned by each student in a class.What is the median number of red items of clothing owned by the students in the class?17、Rectangle ABCD is similar to rectangle EFGH. The rectangles and some of their dimensions are shown in the diagram below.Based on the dimensions in the diagram, what is the value of x?18、The equation below has two solutions.One solution of the equation is 3. What is the other solution of the equation?19、A company packages fruit baskets of different weights and ships them to customers. The company charges a flat fee for packaging the baskets. The total packaging and shipping cost in dollars, y, of a fruit basket weighing x pounds is represented by the line on the graph below.a.What is the y-intercept of the line on the graph?b. What does the y-intercept of the line represent in this situation?c. What is the slope of the line on the graph? Show or explain how you got your answer.d. What does the slope of the line represent in this situation?e. Write an equation that represents the line on the graph.f. Use the equation you wrote in part (e) to determine the weight, in pounds, of the heaviest fruit basket that could be packaged and shipped for $50. Show or explain how you got your answer.。
一、选择题（每题3分，共30分）1. 下列各数中，绝对值最小的是（）A. -3B. -2C. 0D. 12. 如果a < b，那么下列不等式中一定成立的是（）A. a + 1 < b + 1B. a - 1 < b - 1C. a + 2 < b + 2D. a - 2 < b - 23. 一个等腰三角形的底边长为10cm，腰长为8cm，那么这个三角形的周长是（）A. 24cmB. 26cmC. 28cmD. 30cm4. 下列哪个图形是中心对称图形（）A. 正方形B. 等边三角形C. 等腰三角形D. 长方形5. 已知一个正方形的边长为4cm，那么它的对角线长度是（）A. 4cmB. 6cmC. 8cmD. 10cm6. 一个长方体的长、宽、高分别为6cm、4cm、3cm，那么它的体积是（）A. 72cm³B. 96cm³C. 108cm³D. 120cm³7. 如果sin∠A = 0.5，那么∠A的大小是（）A. 30°B. 45°C. 60°D. 90°8. 下列哪个数是实数（）A. √(-1)B. √4C. √-4D. √09. 下列哪个方程有唯一解（）A. 2x + 3 = 5B. 3x + 2 = 5C. 4x + 1 = 7D. 5x - 3 = 710. 下列哪个函数是线性函数（）A. y = x²B. y = 2x + 1C. y = x³D. y = 3x - 2二、填空题（每题5分，共25分）11. 如果sin∠A = 0.8，那么cos∠A = _______。
12. 一个圆的半径是5cm，那么它的周长是 _______ cm。
13. 一个等腰三角形的底边长为12cm，腰长为15cm，那么这个三角形的面积是_______ cm²。
14. 下列数列中，下一个数是：2, 4, 8, 16, _______。
4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010 – AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 22 questions in this question paper. The total mark for this paperis 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.This publication may be reproduced only in accordance with Edexcel Limited copyright policy.©2010 Edexcel Limited.Printer’s Log. No. N36905AIGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write down all stages in your working.1. Solve 6 y – 9 = 3 y + 7y = ................................(Total 3 marks) 2. The diagram shows two towns, A and B, on a map.(a) By measurement, find the bearing of B from A.....................................︒(2)C is another town.The bearing of C from A is 050︒.(b) Find the bearing of A from C.....................................︒(2) (Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will land on red is 0.5The probability that it will land on blue is 0.2Imad spins the spinner once.(a) Work out the probability that it will land on yellow......................................(2)Janet spins the spinner 30 times.(b)Work out an estimate for the number of times the spinner will land on blue......................................(2)(Total 4 marks)4. Rosetta drives 85 kilometres in 1 hour 15 minutes.(a) Work out her average speed in kilometres per hour...................................... km/h(2)Rosetta drives a total distance of 136 kilometres.(b) Work out 85 as a percentage of 136................................. %(2)Sometimes Rosetta travels by train to save money.The cost of her journey by car is £12The cost of her journey by train is 15% less than the cost of her journey by car.(c)Work out the cost of Rose tta’s journey by train.£ ...................................(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant figures.x = ................................(Total 3 marks)6. A = {2, 3, 4, 5}B = {4, 5, 6, 7}(a)(i) List the members of A ⋂B......................................(ii) How many members are in A ⋃B?.....................................(2)ℰ = {3, 4, 5, 6, 7}P = {3, 4, 5}Two other sets, Q and R, each contain exactly three members.P ⋂Q = {3, 4}P ⋂R = {3, 4}Set Q is not the same as set R.(b)(i) Write down the members of a possible set Q......................................(ii) Write down the members of a possible set R......................................(2)(Total 4 marks)7. Rectangular tiles have width (x + 1) cm and height (5x – 2) cm.Some of these tiles are used to form a large rectangle.The large rectangle is 7 tiles wide and 3 tiles high.The perimeter of the large rectangle is 68 cm.(a) Write down an equation in x...............................................................................................................(3)(b) Solve this equation to find the value of x.x = ................................(3)(Total 6 marks)8. Show that 121 141 = 1519. The depth of water in a reservoir increases from 14 m to 15.75 m.Work out the percentage increase.................................. %(Total 3 marks) 10. Quadrilaterals ABCD and PQRS are similar.AB corresponds to PQ.BC corresponds to QR.CD corresponds to RS.Find the value of(a) xx = ...............................(2)(b) yy = ...............................(1)(Total 3 marks)11. Simplify fully6x + 43x.....................................(Total 3 marks)12.(a)Find the equation of the line L......................................(3)(b) Find the three inequalites that define the unshaded region shown in the diagram below................................................................................................................(3)(Total 6 marks)13. (a) Solve x 2– 8x + 12 = 0.....................................(3)(b) Solve the simultaneous equationsy = 2x4x – 5y = 9x = ................................y = ................................(3)(Total 6 marks)14.The area of the triangle is 6.75 cm2.The angle x° is acute.Find the value of x.Give your answer correct to 1 decimal place.x = ................................(Total 3 marks)15. The unfinished histogram shows information about the heights, h metres, ofsome trees.(a) Calculate an estimate for the number of trees with heights in theinterval 4.5 < h ≤ 10.....................................(3)(b) There are 75 trees with heights in the interval 10 < h ≤ 13Use this information to complete the histogram.(2)(Total 5 marks)16. A bag contains 3 white discs and 1 black disc.John takes at random 2 discs from the bag without replacement.(a) Complete the probability tree diagram.First disc Second disc(3)(b)Find the probability that both discs are white......................................(2)All the discs are now replaced in the bag.Pradeep takes at random 3 discs from the bag without replacement.(c)Find the probability that the disc left in the bag is white......................................(3)(Total 8 marks)17. The diagram s hows a sector of a circle, radius 45 cm, with angle 84°.Calculate the area of the sector.Give your answer correct to 3 significant figures.............................. cm2(Total 3 marks) 18.Calculate the length of AC.Give your answer correct to 3 significant figures................................ cm(Total 3 marks)19. A cone has slant height 4 cm and base radius r cm.The total surface area of the cone is 433π cm 2.Calculate the value of r .r = ................................(Total 4 marks)20. f(x) = (x – 1)2(a) Find f(8).....................................(1)The domain of f is all values of x where x ≥ 7(a)Find the range of f......................................(2)xg(x) =x1(c) Solve the equation g(x) = 1.2.....................................(2)(d) (i) Express the inverse function g –1 in the form g –1(x) = .......g –1(x) = ...................................(ii) Hence write down gg(x) in terms of x.gg(x) = ....................................(6)(Total 11 marks)21.In the diagram = a and = c.(a) Find CA in terms of a and c......................................(1)The point B is such that AB=1c.2(b) Give the mathematical name for the quadrilateral OABC......................................(1)The point P is such that = a + k c, where k ≥ 0(c) State the two conditions relating to a + k c that must be true for OAPCto be a rhombus.(2)(Total 4 marks)22. (a) Work out 5.2 × 102+ 2.3 × 104Give your answer in standard form......................................(2)a × 102 +b × 104 =c × 104(b) Express c in terms of a and b.c = ................................(2)(Total 4 marks)TOTAL FOR PAPER = 100 MARKS END。
IGCSE Additional Math题库随着国际教育的普及，越来越多的学生选择参加IGCSE考试。
IGCSE Additional Math作为其中的一门科目，备受学生们的关注。
为了帮助学生更好地备考，我们整理了一份IGCSE Additional Math题库，供学生参考。
一、代数1. 求解方程组：2x + 3y = 7，3x - 2y = 82. 求解二次方程：x² - 5x + 6 = 03. 计算多项式的值：3x² + 5x - 2，当x = 2时4. 求解不等式：2x + 5 > 135. 解决复合函数：f(g(x))二、几何1. 求解三角形的面积，已知两边长和夹角2. 计算圆的面积和周长3. 求解平行线和垂直线的性质4. 计算多边形内角和5. 解决空间几何问题：体积、表面积等三、微积分1. 求函数的导数和不定积分2. 计算定积分：∫(3x² + 2)dx3. 求解微分方程：dy/dx = 3x² - 44. 解决最值和极值问题5. 计算定积分和面积四、统计1. 计算平均数、中位数和众数2. 分析频数分布表和直方图3. 计算标准差和方差4. 解决概率问题：排列、组合、事件概率等5. 进行抽样调查和统计推断五、概率1. 计算事件的概率与概率分布2. 解决条件概率和独立事件问题3. 根据概率分布表求期望值和方差4. 进行排列和组合问题5. 计算生日问题和齐次概率问题通过这份题库的学习和练习，相信学生们能更全面地掌握IGCSE Additional Math的知识点，为考试取得好成绩打下坚实的基础。
希望学生们能够认真对待每一道题目，通过不断的练习和思考，提高自己的解题能力和应试技巧。
祝愿所有参加IGCSE Additional Math考试的学生都能取得优异的成绩！由于篇幅有限，上述的IGCSE Additional Math题库并不能涵盖所有可能出现的题目类型。
