Igcse 数学 历年真题

The line x-2y = 6 intersects the curve x2 + xy+ 10＞，+4)^ = 156 at the points A and B.Find the length of AB. [7]The area of the tri angle is 6.75 an2.The angle x°is acute.Find tlie value of x.Give your answer coirect to 1 decimal place.Tlie diagram shows a sector of a circle, radius 45 cm. witli angle 84°.卜_Diagram NOT 45 cry/84° \ accurately drawnCalculate tlie aiea of tlie sector.Give your answer collect to 3 significant figures.Diagram NOT accurately drawnCalculate tlie lengtli of AC.Give your answer collect to 3 significant figures.A cone has slant height 4 cm and base radius r cm.In the diagram the lines AB and CD are parallel. The lines AD and BC intersect at X.Angle XDC = 35。

and angle CXD = 120°. (a) (i) Write down the size of angle BAX.Answer(a)( i) Angle BAX = .................................. [........................................................................... 1 ](ii) Write down the size of angle ABX.Answer(a)( ii) Angle ABX = ............................... [1 .............................................................................. ](b) Complete the statementTriangle AXB is .................................................... t o triangle DXC. [1 ](c) AB — 8.3cm, BX — 5.5cm and CD — 16.6cm.Calculate the length of CX.Diagram NOT accurately drawnTlie total surface area of tlie cone is33 2—兀 cnr.4Calculate the value of r.NOT TOSCALEIn quadrilateral ABCD, AB = 77 m, BC = 120 m, CD = 60 m and diagonal AC = 55 m. Angle CAD = 45°, angle BAC = x° and angle ADC = y°. (a) Calculate the value of x. (b) Calculate the value of y.(c) The bearing of D from A is 090°. Find the bearing of(i) A from C, (ii) B from A.NOTTG SCALEDiagram NOT accurately drawnA, B, C and D are four points on the circumference of a circle. The chords AC and BDintersect at E.AE =3.6 ctn. CE = 2.8 cm, DE = 2.4 cm and AD = 4.9 cm. (a' Calculate the length of BE.(b‘ Calculate the size of angle AED.Give your answer correct to 3 significant figures, cABCD is a cyclic quadrilateral.AB = 9.5cm, ffC=lLlcm, angle ABC = 70°and angle CAD = 37°. (a) Calculate the length of AC. (b) Explain why angle ADC = Il0°. (c) Calculate the length of AD.(d) A point E lies on the circle such that triangle ACE is isosceles, with EA = EC.(i) Write down the size of angle A£C. <(ii) Calculate the area of triangle ACE.NOT TO SCALE44°Diagram NOTaccurately drawnL08°Q, R, sand y are points on the circumference of a circle. PU is a tangent io the circle at J.PQR is a straight line.Angle PQT=L08°.Angle STR = 44。

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。

Tuesday,July8,2014 Problem1.Let a0<a1<a2<···be an in nite sequence of positive integers.Prove that there exists a unique integer n≥1such thata n<a0+a1+···+a nn≤a n+1.Problem2.Let n≥2be an integer.Consider an n×n chessboard consisting of n2unit squares.A con guration of n rooks on this board is peaceful if every row and every column contains exactly one rook.Find the greatest positive integer k such that,for each peaceful con guration of n rooks, there is a k×k square which does not contain a rook on any of its k2unit squares.Problem3.Convex quadrilateral ABCD has∠ABC=∠CDA=90◦.Point H is the foot of the perpendicular from A to BD.Points S and T lie on sides AB and AD,respectively,such that H lies inside triangle SCT and∠CHS−∠CSB=90◦,∠T HC−∠DT C=90◦.Prove that line BD is tangent to the circumcircle of triangle T SH.Wednesday,July 9,2014Problem 4.Points P and Q lie on side BC of acute-angled triangle ABC so that ∠P AB =∠BCA and ∠CAQ =∠ABC .Points M and N lie on lines AP and AQ ,respectively,such that P is the midpoint of AM ,and Q is the midpoint of AN .Prove that lines BM and CN intersect on the circumcircle of triangle ABC .Problem 5.For each positive integer n ,the Bank of Cape Town issues coins of denomination 1n .Given a nite collection of such coins (of not necessarily di erent denominations)with total value atmost 99+12,prove that it is possible to split this collection into 100or fewer groups,such that each group has total value at most 1.Problem 6.A set of lines in the plane is in general position if no two are parallel and no three pass through the same point.A set of lines in general position cuts the plane into regions,some of which have nite area;we call these its nite regions .Prove that for all su ciently large n ,in any set of n lines in general position it is possible to colour at least √n of the lines blue in such a way that none of its nite regions has a completely blue boundary.Note:Results with √n replaced by c √n will be awarded points depending on the value of theconstant c .。

This document consists of 15 printed pages and 1 blank page.IB10 06_0620_12/RP© UCLES 2010[Turn over*8778752636*UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary EducationCHEMISTRY 0620/12Paper 1 Multiple Choice May/June 201045 MinutesAdditional Materials: Multiple Choice Answer Sheet Soft clean eraserSoft pencil (type B or HB is recommended)READ THESE INSTRUCTIONS FIRSTWrite in soft pencil.Do not use staples, paper clips, highlighters, glue or correction fluid.Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided unless this has been done for you.There are forty questions on this paper. Answer all questions. For each question there are four possibl e answers A , B , C and D .Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.Read the instructions on the Answer Sheet very carefully.Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet. A copy of the Periodic Table is printed on page 16. You may use a calculator.© UCLES 2010 0620/12/M/J/101 The diagram shows a cup of tea.Which row describes the water particles in the air above the cup compared with the water particles in the cup?moving fastercloser togetherA B C D2 Which row shows the change that takes place when element X gains the new particle shown?particle gained changeA electron an isotope of element X is formedB electron the element one place to the right of X in the Periodic Table is formedC proton an isotope of element X is formedDprotonthe element one place to the right of X in the Periodic Table is formed3 The symbols of two atoms may be written as shown.X 5223Y5224Which statement about these atoms is correct?A They are different elements because they have different numbers of neutrons.B They are different elements because they have different numbers of protons.C They are isotopes of the same element because they have the same nucleon number.D They are isotopes of the same element because they have the same proton number.4The diagram shows an atom.electronnucleus containingnine particles What is the proton number and neutron number of the atom?proton number neutron numberA 4 5B 4 9C 5 4D 5 95 A frui t dri nk coloured orange contai ns a di ssolved mi xture of red and yellow colouri ng agents.One of these colouring agents is suspected of being illegal.Which method could be used to show the presence of this illegal colouring agent?A chromatographyB distillationC evaporationD filtration6 A student carries out an experiment to find how fast 3cm pieces of magnesium ribbon dissolve in10cm3 samples of sulfuric acid at different temperatures.Which piece of apparatus does the student not need?A balanceB measuring cylinderC stop-clockD thermometer© UCLES 2010 0620/12/M/J/10 [Turn over© UCLES 2010 0620/12/M/J/10The electrolytes are listed below.cell 1 aqueous sodium chloride cell 2concentrated hydrochloric acid cell 3molten lead(II ) bromideIn which cells is a gas formed at both electrodes? A 1 and 2B 1 and 3C2 onlyD 3 only8 The diagram shows apparatus for plating a spoon with silver.Which statement is not correct?A Silver would stick to the spoon because it is a very reactive metal.B The electrolyte would be a silver salt dissolved in water.C The metal electrode would be made from silver.D The spoon would be connected to the negative of the power supply.9 Aqueous copper(II ) sulfate solution is electrolysed using inert electrodes.Copper(II ) i ons (Cu 2+), hydrogen i ons (H +), hydroxi de i ons (OH –) and sulfate i ons (−24SO ) are present in the solution.To which electrodes are the ions attracted during this electrolysis?attracted to anodeattracted to cathodeA Cu 2+ and H + OH – and −24SOB Cu 2+ and −24SOH + and OH –C H + and OH – Cu 2+ and −24SOD OH – and −24SO Cu 2+ and H +© UCLES 2010 0620/12/M/J/10[Turn over10 In which compounds are pairs of electrons shared between atoms?1 sodium chloride2 me t hane3 lead bromideA 1 onlyB 2 onlyC 1 and 3D 1, 2 and 311 Element X has six electrons in its outer shell.= electronkeyeHow could the element react?A by gaining two electrons to form a positive ionB by losing six electrons to form a negative ionC by sharing two electrons with two electrons from another element to form two covalent bondsD by sharing two electrons with two electrons from another element to form four covalent bonds12 Hydrogen and chlorine react as shown.1 molecule of hydrogen + 1 molecule of chlorine →2 moleculesof hydrogen chlorideWhat is the equation for this reaction?A 2H + 2C l → 2HC lB 2H + 2C l → H 2C l 2 C H 2 + C l 2 → 2HC lD H 2 + C l 2 → H 2C l 213 Which name is given to mixtures of metals?A alloysB compoundsC oresD salts14Iron is extracted from iron oxide using carbon monoxide as shown in the equation.iron oxide + carbon monoxide → iron + carbon dioxide What does the equation show?A Carbon monoxide is oxidised to carbon dioxide.B Carbon monoxide is reduced to carbon dioxide.C Iron is oxidised to iron oxide.D Iron oxide is oxidised to iron.15 A student investigates the rate of reaction between marble chips and hydrochloric acid.The loss in mass of the reaction flask is measured.The graph shows the results of two experiments, P and Q.mass ofreaction flaskWhich change explains the difference between P and Q?A A catalyst is added in P.B A higher temperature is used in P.C Bigger marble chips are used in Q.D Hydrochloric acid is more concentrated in Q.© UCLES 2010 0620/12/M/J/10© UCLES 2010 0620/12/M/J/10[Turn over16clouds seawater vapourWha t is the energy cha nge a nd wha t na me is given to the type of cha nge when wa ter evaporates?energy change type of change A energy given out endothermic B energy given out exothermic C energy taken in endothermic Denergy taken inexothermic17 Which process is not exothermic?A burning a fossil fuelB obtaining lime from limestoneC radioactive decay of 235UD reacting hydrogen with oxygen18 When pink cobalt(II ) sulfate crystals are heated, they form steam and a blue solid.When water is added to the blue solid, it turns pink and becomes hot.Which terms describe the pink cobalt(II ) sulfate crystals and the reactions?pink cob lt sulf te re ctionsA aqueous irreversible B aqueous reversible C hydr ted irreversible D hydr ted reversible19 An element melts at 1455°C, has a density of 8.90g/cm3 and forms a green chloride.Where in the Periodic Table is this element found?A BCD20An excess of copper(II) oxide is a dded to dilute sulfuric a cid to ma ke crysta ls of hydra ted copper(II) sulfate.The processes listed may be used to obtain crystals of hydrated copper(II) sulfate.1 concentrate the resulting solution2 filter3 heat the crystals4 wash the crystalsWhich processes are needed and in which order?A1, 2, 3 and 4B1, 2, 4 and 3C2, 1, 2 and 3D2, 1, 2 and 421 Which is not a property of Group I metals?A They are soft and can be cut with a knife.B They corrode rapidly when exposed to oxygen in the air.C They produce an acidic solution when they react with water.D They react rapidly with water producing hydrogen gas.© UCLES 2010 0620/12/M/J/1022Aqueous sodium hydroxide is added to a solid, X, and the mixture is heated.A green precipitate is formed and an alkaline gas is given off.Which ions are present in X?NH and Fe2+A +4NH and Fe3+B +4C OH– and Fe2+D OH– and Fe3+23An aqueous solution of the organic compound methylamine has a pH greater than 7.Which statement about methylamine is correct?A It neutralises an aqueous solution of sodium hydroxide.B It reacts with copper(II) carbonate to give carbon dioxide.C It reacts with hydrochloric acid to form a salt.D It turns blue litmus red.24The positions in the Periodic Table of four elements are shown.Which element is most likely to form an acidic oxide?ABCD© UCLES 2010 0620/12/M/J/10 [Turn overgas XWhat is gas X?A carbon dioxideB chlorineC hydrogenD oxygen26 A student added dilute hydrochloric acid to four metals and recorded the results.Not all of the results are correct.resultsmetal gas given off1 copper yes2 iron yes3 magnesium no4 zinc yesWhich two results are correct?A 1 and 3B 1 and 4C 2 and 3D 2 and 4© UCLES 2010 0620/12/M/J/101127 An element does not conduct electricity and exists as diatomic molecules. In which area of the Periodic Table is the element to be found?BAC D28 Copper, iron and zinc are all used as pure metals.Which of these three metals are also used in alloys?c o pper ir o n zincAB C D29 Solutions of a halogen and a sodium halide are mixed.Which mixture darkens in colour because a reaction occurs?A bromine and sodium chlorideB bromine and sodium fluorideC chlorine and sodium fluorideD chlorine and sodium iodide30 Some properties of four elements are shown in the table.Which element is a metal?melting point / °Celectrical conductivitywhen liquid electrical conductivitywhen solidA –7 l o w l o wB 801 high l ow C 1535 high high D 3550 l o w l ow31The diagram shows three types of item.cutlery cooking pan instruments used in hospitalsWhich method of rust prevention can be used for all three types of item?A coating with plasticB covering with greaseC galvanisingD using stainless steel32Aluminium is an important metal with many uses.Some of its properties are listed.1It is a good conductor of heat.2It is a reactive metal.3It has a low density.4It has an oxide layer that prevents corrosion.Which set of properties help to explain the use of aluminium for cooking and storing food?A 1, 2 and 3B 1, 2 and 4C 1, 3 and 4D 2, 3 and 433To grow roses, a fertiliser containing nitrogen, phosphorus and potassium is needed.For the best flowers, the fertiliser should contain a high proportion of potassium.Which fertiliser is best for roses?proportion by massfertiliserN P KA 9 0 25B 13 13 20C 29 5 0D 29 15 534 Which statements about water are correct?1 Water is treated with chlorine to kill bacteria.2 Household water may contain salts in solution.3 Water is used in industry for cooling.4Water for household use is filtered to remove soluble impurities.A 1, 2 and 3B 1 and 4C 2, 3 and 4D 1, 2, 3 and 435 Which statement about methane is not correct?A It is a liquid produced by distilling petroleum.B It is produced as vegetation decomposes.C It is produced by animals such as cows.D It is used as a fuel.36 Which compound in polluted air can damage stonework and kill trees?A carbon dioxideB carbon monoxideC lead compo undsD s u lf ur dioxide37 Diesel, petrol and bitumen are allA fuels.B hydrocarbons.C lubricants.D waxes.38 A macromolecule is a very large molecule.Macromolecules can be made by joining smaller molecules together. This is called polymerisation.Which row in the table describes the formation of a polymer?monomer polymerA ethane poly(ethane)B ethene poly(ethene)C ethane poly(ethene) Dethene poly(ethane)39 Which structure shows a compound that belongs to a different homologous series to propane?A B C DCC HH H H HC H HHHC H HHC C C H HH HH HHC H H HCC C H H H H H HHHH40 Which structure is incorrect ?HH H HHHC C C A HH H HHHC C BHH O HOC CHD HH H HOC C HHBLANK PAGE16Per 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. G r o u p140C eC e r i u m 58141P rP r a s e o d y m i u m 59144N d N e o d y m i u m 60P mP r o m e t h i u m61150S mS a m a r i u m62152E uE u r o p i u m63157G dG a d o l i n i u m64159T bT e r b i u m65162D yD y s p r o s i u m66165H oH o l m i u m67167E rE r b i u m68169T mT h u l i u m69173Y bY t t e r b i u m70175L uL u t e t i u m71232T hT h o r i u m 90P aP r o t a c t i n i u m 91238UU r a n i u m92N pN e p t u n i u m93P uP l u t o n i u m94A mA m e r i c i u m95C mC u r i u m96B kB e r k e l i u m97C fC a l i f o r n i u m98E sE i n s t e i n i u m99F mF e r m i u m100M dM e n d e l e v i u m101N oN o b e l i u m102L rL a w r e n c i u m1031HH y d r o g e n17L iL i t h i u m 323N aS o d i u m 1124M gM a g n e s i u m1240C aC a l c i u m 2045S c S c a n d i u m 2148T i T i t a n i u m2251V V a n a d i u m 2352C r C h r o m i u m 2455M n M a n g a n e s e 2556F e I r o n 2659C o C o b a l t 2759N i N i c k e l 2864C u C o p p e r 2965Z n Z i n c3070G aG a l l i u m3127A l A l u m i n i u m1311B B o r o n 512C C a r b o n614NN i t r o g e n716OO x y g e n819FF l u o r i n e928S iS i l i c o n1431PP h o s p h o r u s1532SS u l f u r1635.5C lC h l o r i n e1740A rA r g o n1820N eN e o n104H eH e l i u m273G eG e r m a n i u m3275A sA r s e n i c3379S eS e l e n i u m3480B rB r o m i n e3584K rK r y p t o n3639KP o t a s s i u m 1988S rS t r o n t i u m 3889Y Y t t r i u m 3991Z r Z i r c o n i u m4093N b N i o b i u m 4196M o M o l y b d e n u m 42T c T e c h n e t i u m 43101R u R u t h e n i u m 44103R h R h o d i u m 45106P d P a l l a d i u m 46108A g S i l v e r47112C dC a d m i u m48115I nI n d i u m49119S nT i n50122S bA n t i m o n y51128T eT e l l u r i u m52127II o d i n e53131X eX e n o n54137B aB a r i u m 56139L a L a n t h a n u m 57*178H fH a f n i u m72181T a T a n t a l u m 73184W T u n g s t e n 74186R e R h e n i u m 75190O s O s m i u m 76192I rI r i d i u m 77195P t P l a t i n u m78197A uG o l d79201H gM e r c u r y80204T lT h a l l i u m81207P bL e a d82209B iB i s m u t h83P oP o l o n i u m84A tA s t a t i n e85R nR a d o n86F rF r a n c i u m 87227A cA c t i n i u m899B eB e r y l l i u m4II I I I II V V V I V I I 085R bR u b i d i u m 37133C sC a e s i u m 55226R a R a d i u m 88T h e v o l u m e o f o n e m o l e o f a n y g a s i s 24d m 3a t r o o m t e m p e r a t u r e a n d p r e s s u r e (r .t .p .).a Xb a = r e l a t i v e a t o m ic m a s sX = a t o m i c s y m b o lb = p r o t o n (a t o m ic ) n u m b e rK e y *58-71 L a n t h a n o i d s e r i e s 90-103 A c t i n o i d s e r i e s D A T A S H E E T T h e P e r i o d i c T a b l e o f t h e E l e m e n t s。

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 paper is 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.This publication may be reproduced only in accordance withEdexcel 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, of some trees.(a) Calculate an estimate for the number of trees with heights in the interval 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 OAPC to 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: 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数学练习题在本文中，将为您提供一系列IGCSE数学练习题，以帮助您巩固和提高数学知识和技能。

这些练习题的题型多样，涵盖了IGCSE数学考试的各个知识点和难度级别。

一、选择题1. 在下列数中，哪个数是一个自然数？A. -3B. 2/3C. 0D. √22. 将下列分数化为最简形式：8/12A. 1/2B. 4/6C. 2/3D. 3/43. 当x = 2时，下列哪个等式成立？A. 5x - 3 = 7B. 3x + 2 = 10C. 4x + 1 = 8D. 2x + 5 = 124. 一个三角形的面积是36平方单位，底边长为6单位，高边长为x单位。

求x的值。

A. 3B. 9C. 12D. 18二、填空题1. 用两个相邻整数的平方的和表示一个奇数的方式是：_________。

2. 一个长方形的长为x+2，宽为x-3，其面积可以表示为_________。

三、解答题1. 求解方程：2x + 5 = 17。

2. 计算:(a + b)^2，其中a = 3，b = -2。

3. 解决以下三角形相似问题：两个三角形ABC和DEF之间的关系是：∠A = ∠D，∠B = ∠E，BC/DE = 4/7。

如果BC = 12，求EF的值。

四、应用题1. 在某个城市的人口数量从2018年的1000万人增长到2020年的1200万人。

求2019年该城市的人口数量，并计算增长的百分比。

2. 一辆汽车以每小时60公里的速度行驶，行驶时间为2小时。

计算该车行驶的距离。

以上是一些IGCSE数学练习题的示例，希望能够帮助您巩固数学知识和应对考试。

建议您在解答这些问题时，尽量使用适当的计算方法和策略，以提高解题效率和准确性。

祝您取得优异的成绩！。

This document consists of 19 printed pages and 1 blank page.DC (NH/JG) 130218/2© UCLES 2017[Turn over*0731247115*MATHEMATICS 0580/43Paper 4 (Extended) May/June 20172 hours 30 minutesCandidates answer on the Question Paper.Additional Materials: Electronic calculator Geometrical instrumentsTracing 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 an HB pencil for any diagrams or graphs.Do not use staples, paper clips, 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.Cambridge International ExaminationsCambridge International General Certificate of Secondary Education1 (a) In 2016, a company sold 9600 cars, correct to the nearest hundred.(i) Write down the lower bound for the number of cars sold. (1)(ii) The average profit on each car sold was $2430, correct to the nearest $10.Calculate the lower bound for the total profit.Write down the exact answer.$ (2)(iii) Write your answer to part (a)(ii) correct to 4 significant figures.$ (1)(iv) Write your answer to part (a)(iii) in standard form.$ (1)(b) In April, the number of cars sold was 546.This was an increase of 5% on the number of cars sold in March.Calculate the number of cars sold in March. (3)© UCLES 20170580/43/M/J/17(c) The price of a new car grows exponentially by 3% per year.A new car has a price of $3000 in 2013.Find the price of a new car 4 years later.$ (2)© UCLES 2017[Turn over0580/43/M/J/170580/43/M/J/17© UCLES 20172 (a)y °x °z °DABPQSRCE NOT TO SCALE24°38°PQ is parallel to RS .ABC and ADE are straight lines. Find the values of x , y and z .x = ..................................................y = ..................................................z = ..................................................[3] (b)ABDCNOT TOSCALE42°The points A , B , C and D lie on the circumference of the circle. AB = AD , AC = BC and angle ABD = 42°. Find angle CAB .Angle CAB = (3)(c)NOT TOSCALEThe points P, Q, R and S lie on the circumference of the circle, centre O.Angle QOS =146°.Find angle QRS.QRS = . (2)Angle© UCLES 2017[Turn over0580/43/M/J/170580/43/M/J/17© UCLES 20173The table shows some values for 24y x x 32=+.x –2.2–2–1.5–1–0.500.50.8y–1.940.753.58(a) Complete the table.[4](b) Draw the graph of 24y x x 32=+ for 2.20.8x G G - .[4] (c) Find the number of solutions to the equation 243x x 32+=. (1)0580/43/M/J/17© UCLES 2017[Turn over(d) (i) The equation 241x x x 32+-= can be solved by drawing a straight line on the grid.Write down the equation of this straight line.y = ..................................................[1] (ii) Use your graph to solve the equation 241x x x 32+-=.x = ............................ or x = ............................ or x = ............................[3] (e) The tangent to the graph of 24y x x 32=+ has a negative gradient when x k =. Complete the inequality for k ....................... 1 k 1 . (2)0580/43/M/J/17© UCLES 20174 (a) The diagram shows a solid metal prism with cross section ABCDE .BGFKJ DCAEH2 cm7 cm4 cm8 cm 4 cmNOT TOSCALE(i) Calculate the area of the cross section ABCDE .............................................cm 2 [6](ii) The prism is of length 8 cm.Calculate the volume of the prism.............................................cm 3 [1](b) A cylinder of length 13 cm has volume 280 cm3.(i) Calculate the radius of the cylinder..............................................cm [3] (ii) The cylinder is placed in a box that is a cube of side 14 cm.Calculate the percentage of the volume of the box that is occupied by the cylinder................................................% [3]© UCLES 2017[Turn over0580/43/M/J/175 (a) Haroon has 200 letters to post.The histogram shows information about the masses, m grams, of the letters.Mass (grams)mFrequencydensity(i) Complete the frequency table for the 200 letters.Mass (m grams)0 1m G 1010 1m G 2020 1m G 2525 1m G 3030 1m G 50Frequency5017[3](ii) Calculate an estimate of the mean mass.................................................g [4]0580/43/M/J/17© UCLES 2017(b) Haroon has 15 parcels to post.The table shows information about the sizes of these parcels.Size Small LargeFrequency96Two parcels are selected at random.Find the probability that(i) both parcels are large, (2)(ii) one parcel is small and the other is large. (3)(c) The probability that a parcel arrives late is 803.4000 parcels are posted.Calculate an estimate of the number of parcels expected to arrive late. (1)6(a) Describe fully the single transformation that maps shape A onto(i) shape B,...................................................................................................................................................... (2)(ii) shape C....................................................................................................................................................... (3)(b) Draw the image of shape A after rotation through 90° anticlockwise about the point (3, -1). [2]y=. [2] (c) Draw the image of shape A after reflection in 1f p.(d) Describe fully the single transformation represented by the matrix 3003.............................................................................................................................................................. (3)7 (a) Solve the simultaneous equations. You must show all your working.x y 2311+=x y 3550-=- x = ..................................................y = (4)(b) 12x x a x b 22-+=+^h Find the value of a and the value of b .a = ..................................................b = (3)(c) Write as a single fraction in its simplest form.x x x x 25132-+-+ (4)8 (a)The table shows the marks gained by 10 students in their physics test and their mathematics test.The first six points have been plotted for you.MathematicsmarkPhysics mark[2](ii) What type of correlation is shown in the scatter diagram? (1)(b) The marks of 30 students in a spelling test are shown in the table below.Mark012345Frequency245568Find the mean, median, mode and range of these marks.Mean = ..................................................Median = ..................................................Mode = ..................................................Range = (7)(c) The table shows the marks gained by some students in their English test.Mark 527591Number of students x4511The mean mark for these students is 70.3 .Find the value of x.= (3)x9ACQ B525 m872 m104°NOT TO SCALEABC is a triangular field on horizontal ground. There is a vertical pole BQ at B .AB = 525 m, BC = 872 m and angle ABC = 104°.(a) Use the cosine rule to calculate the distance AC .AC = ..............................................m [4] (b) The angle of elevation of Q from C is 1.0°.Showing all your working, calculate the angle of elevation of Q from A . (4)(c) (i) Calculate the area of the field.............................................. m2 [2] (ii) The field is drawn on a map with the scale 1 : 20 000.Calculate the area of the field on the map in cm2.............................................cm2 [2]10 = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30} A = { x : x is a multiple of 3} B = { x : x is prime} C = { x : x G 25}(a) Complete the Venn diagram.ABCᏱ[4] (b) Use set notation to complete the statements. (i) 26 ..................... B [1](ii) A + B = .....................[1](c) List the elements of B , (C + A ). (2)(d) Find (i) n(C ),...................................................[1] (ii) B B C n ,+l ^^h h ....................................................[1] (e)A C +^h is a subset of A C ,^h . Complete this statement using set notation.A C +^h ..................... A C ,^h [1]11 The table shows the first four terms in sequences A, B, C and D.Complete the table.BLANK PAGEPermission 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.To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at after the live examination series.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.。