澳大利亚数学竞赛cat往年真题11-12年级2017 answers

2015INTERMEDIATE DIVISIONAUSTRALIAN S CHOOL YEARS 9 and 10TIME ALLOWED: 75 MINUTESINSTRUCTIONS AND INFORMATIONGENERAL1. Do not open the booklet until told to do so by your teacher.2. NO calculators, maths stencils, mobile phones or other calculating aids are permitted. Scribbling paper, graphpaper, ruler and compasses are permitted, but are not essential. 3. Diagrams are NOT drawn to scale. They are intended only as aids.4. There are 25 multiple-choice questions, each with 5 possible answers given and 5 questions that require awhole number answer between 0 and 999. The questions generally get harder as you work through the paper. There is no penalty for an incorrect response.5. This is a competition not a test; do not expect to answer all questions. You are only competing against yourown year in your own country/Australian state so different years doing the same paper are not compared. 6. Read the instructions on the answer sheet carefully. Ensure your name, school name and school year areentered. It is your responsibility to correctly code your answer sheet. 7. When your teacher gives the signal, begin working on the problems.THE ANSWER SHEET 1. Use only lead pencil.2. Record your answers on the reverse of the answer sheet (not on the question paper) by FULLY colouring thecircle matching your answer.3. Your answer sheet will be scanned. The optical scanner will attempt to read all markings even if they are inthe wrong places, so please be careful not to doodle or write anything extra on the answer sheet. If you want to change an answer or remove any marks, use a plastic eraser and be sure to remove all marks and smudges.INTEGRITY OF THE COMPETITIONThe AMT reserves the right to re-examine students before deciding whether to grant official status to their score.©AMT P ublishing 2015 AMTT liMiTed Acn 083 950 341A ustrAliAn M AtheMAtics c oMpetitionsponsored by the c oMMonweAlth b AnkAn AcTiviTy of The AusTrAliAn MATheMATics TrusTNAMEYEA TEACHE RA u s T r A l i A n M A T h e M A T i c s T r u s TIntermediate Division Questions1to10,3marks each1.What is the area of this triangle in squarecentimetres?(A)10(B)12(C)14(D)7(E)62cm2.A movie lasts for213hours.The movie is shown in two equal sessions.For how many minutes does each session last?(A)85(B)70(C)80(D)65(E)753.If p=11and q=−4,then p2−q2equals(A)105(B)137(C)117(D)115(E)944.2015−20.15equals(A)1984.85(B)1995.15(C)1994.85(D)1995.85(E)2035.155.What is the value of2015twenty-cent coins?(A)$2015(B)$107.50(C)$17.50(D)$403(E)$436.Ana,Ben,Con,Dan and Eve are sitting around a ta-ble in that order.Ana calls out the number1,thenBen calls out the number2,then Con calls out thenumber3,and so on.After a person calls out a num-ber,the next person around the table calls out thenext number.Anyone who calls out a multiple of7must immediatelyleave the table.Who is the last person remaining at the table?(A)Ana(B)Ben(C)Con(D)Dan(E)Eve7.On a farm the ratio of horses to cows is3:2and ratio of cows to goats is4:3.The ratio of goats to horses is(A)5:7(B)3:8(C)3:5(D)5:18(E)1:28.Warren the window washer starts on the38thfloor of a building that has12windowsperfloor.He washes all of the windows on eachfloor before moving down to thefloor below.Whichfloor is Warren on after he has washed141windows?(A)25th(B)24th(C)28th(D)27th(E)26th9.A packet of lollies contains5blue lollies,15yellow lollies and some red lollies.One-third of the lollies are red.What fraction of the lollies are yellow?(A)13(B)56(C)12(D)16(E)2310.The diagram shows two small squares in opposite corners ofa large square.The squares have sides of length1cm,2cmand7cm.What is the area of the shaded pentagon?(A)18cm2(B)16cm2(C)22cm2(D)24cm2(E)20cm2Questions 11to 20,4marks each11.Jenna measures three sides of a rectangle and gets a total of 80cm.Dylan measuresthree sides of the same rectangle and gets a total of 88cm.What is the perimeter of the rectangle?(A)112cm(B)132cm(C)96cm(D)168cm(E)156cm12.A bar-tailed godwit was recorded by satellite tag in 2007tohave flown 11500km in eight days.On average,approximately how many kilometres per hour is that?(A)120(B)6(C)1(D)24(E)6013.A cube has the letters A,C,M,T,H and S on its six faces.Here are two views ofthis cube.CMAA MTWhich one of the following could be a third view of the same cube?(A)MHT(B)ATC(C)T SC(D)HTA (E)SCM 14.Two ordinary dice are rolled.The two resulting numbers are multiplied together tocreate a score.The probability of rolling a score that is a multiple of six is(A)16(B)512(C)14(D)13(E)1218.A strip of paper1cm wide is folded4times to make a regular octagon as shown.If the ends of the strip meet exactly when folded,how many centimetres long is the strip?√2(B)8(C)4+4√2(D)16(E)16−4√2(A)819.The country of Numismatica has six coins of thefollowing denominations:1cent,2cents,4cents, 10cents,20cents and40cents.Using the coins in my pocket,I can pay exactly for any amount up to and including200cents.What is the smallest number of coins I could have?(A)12(B)10(C)11(D)9(E)820.What fraction of the large triangle is shaded?(A)16(B)13(C)49(D)12(E)25Questions21to25,5marks each21.A student noticed that in a list offive integers,the mean,median and mode wereconsecutive integers in ascending order.What is the largest range possible for these five integers?(A)5(B)9(C)8(D)7(E)622.The square P QRS has sides of length2units andJ is the midpoint of P S.The line QJ intersectsthe diagonal P R at L.The length of LP is(A)√23(B)√33(C)√22(D)2√33(E)2√23SQ211PRJ23.For each integer from0to999,Andr´e wrote down the sum of its digits.What is theaverage of the numbers that Andr´e wrote down?(A)13.5(B)15(C)12(D)12.5(E)10.524.Max’s journey around this grid starts on a grid pointon side AB.He visits a grid point on each of sides BC,CD and DA in order before returning to his starting point, forming a quadrilateral.Max does not visit corner points A,B,C or D.How many journeys are possible which are not rect-angles?(Note that a square is a rectangle.)(A)256(B)252(C)64(D)248(E)76C B25.It takes Nicolai one and a half hours to paint the walls of a room and two hours topaint the ceiling.Elena needs exactly one hour to paint the walls of the same room and one hour to paint the ceiling.If Nicolai and Elena work together,what is the shortest possible time in minutes in which they can paint the walls and the ceiling of the room?(A)72(B)60(C)83(D)75(E)76For questions26to30,shade the answer as an integer from0to999in the space provided on the answer sheet.Question26is6marks,question27is7marks,question28is8marks, question29is9marks and question30is10marks.26.Mike has2015matches and uses them to builda triangular pattern like the one shown,but asbig as possible.How many matches does he haveleft over?27.How many positive integers n less than 2015have the property that 13+1ncan besimplified to a fraction with denominator less than n ?28.A rectangle has all sides of integer length.When 3units are added to the heightand 2units to the width,the area of the rectangle is tripled.What is the sum of the original areas of all such rectangles?29.At Berracan station,northbound trains arrive every three minutes starting at noonand finishing at midnight,while southbound trains arrive every five minutes starting at noon and finishing at midnight.Each day,I walk to Berracan station at a random time in the afternoon and wait for the first train in either direction.On average,how many seconds should I expect to wait?30.In a 14×18rectangle ABCD ,points P,Q,R and Sare chosen,one on each side of ABCD as pictured.The lengths AP ,P B ,BQ ,QC ,CR ,RD ,DS and SA are all positive integers and P QRS is a rectangle.What is the largest possible area that P QRS could have?DCB AQSIntermediate 2015 Answers Question Answer 1B2B3A4C5D6D7E8D9C10C11A12E13A14B15E16C17E18C19B20B21D22E23A24D25A2637272242844297430150。

THURSDAY 1 AUGUST 2013SENIOR DIVISIONAUSTRALIAN S CHOOL YEARS 11 and 12TIME ALLOWED: 75 MINUTES©AMT P ublishing 2013 AMTT liMiTed Acn 083 950 341A ustrAliAn M AtheMAtics c oMpetitionsponsored by the c oMMonweAlth b AnkAn AcTiviTy of The AusTrAliAn MATheMATics TrusTNAMEYEAR TEACHERA u s T r A l i A n M A T h e M A T i c s T r u s T姓 名： 年 级： 监考老师：意事项一般规定1.未获监考老师许可之前不可翻开此测验题本。

2.各种通讯器材一律不得携入考场，不准使用电子计算器、计算尺、对数表、数学公式等计算器具。

作答时可使用直尺与圆规，以及两面全空白的草稿纸。

3.题目所提供之图形只是示意图，不一定精准。

4.最前25题为选择题，每题有五个选项。

最后题要求填入的答案为000至999的正整数。

题目一般而言是依照越来越难的顺序安排，对于错误的答案不会倒扣分数。

5.本活动是数学竞赛而不同于学校测验，别期望每道题目都会作。

考生只与同地区同年级的其它考生评比，因此不同年级的考生作答相同的试卷将不作评比。

6.请依照监考老师指示，谨慎地在答案卡上填写您的基本数据。

若因填写错误或不详所造成之后果由学生自行负责。

7.进入试场后，须等待监考老师宣布开始作答后，才可以打开题本进行答题。

作答须知1.限用B 或2B 铅笔填写答案。

2.请用B 或2B 铅笔在答案卡上（不是在题本上）将您认为正确选项的圆圈涂满。

3.您的答案卡将由计算机阅卷，为避免计算机误判，请不要在答案卡上其它任何地方涂划任何记号。

填写答案卡时，若需要修改，可使用软性橡皮小心擦拭，并确定答案卡上无残留痕迹。

SATURDAY 6 AUGUST 2011初级卷（7—8 年级）考试时间：75 分钟注意事项一般规定1.未获监考老师许可之前不可翻开此测验题本。

2.各种通讯器材一律不得携入考场，不准使用电子计算器、计算尺、对数表、数学公式等计算器具。

作答时可使用直尺与圆规，以及两面全空白的草稿纸。

3.题目所提供之图形只是示意图，不一定精准。

4.最前25 题为选择题，每题有五个选项。

最后5 题要求填入的答案为000 至999 的正整数。

题目一般而言是依照越来越难的顺序安排，对于错误的答案不会倒扣分数。

5.本活动是数学竞赛而不同于学校测验，别期望每道题目都会作。

考生只与同地区同年级的其它考生评比，因此不同年级的考生作答相同的试卷将不作评比。

6.请依照监考老师指示，谨慎地在答案卡上填写您的基本数据。

若因填写错误或不详所造成之后果由学生自行负责。

7.进入试场后，须等待监考老师宣布开始作答后，才可以打开题本进行答题。

作答须知1.限用B 或2B 铅笔填写答案。

2.请用B或2B铅笔在答案卡上将您认为正确选项的圆圈涂满（不是在题本上）。

3.您的答案卡将由计算机阅卷，为避免计算机误判，请不要在答案卡上其它任何地方涂划任何记号。

填写答案卡时，若需要修改，可使用软性橡皮小心擦拭，并确定答案卡上无残留痕迹。

特别约定O─────────────────────────────────────────────────初级卷(7-8 年级)─────────────────────────────────────────────────1-10 题，每题 3 分1. 算式 2011－1102 等于（A ）1111 （B ）1191 （C ）1001 （D ）989 （E ）909 ───────────────────────────────────────────────── 2. 右图中，x 之值等于（A ）75 （B ）80 （C ）85 （D ）90 （E ）95───────────────────────────────────────────────── 3. 我在下午 2：15 出门散步，于下午 3：20 返家。

A u s t r A l i A n M At h e M At i c s c o M p e t i t i o na n a c t i v it y o f t h e a u s t r a l i a n m a t h e m a t i c s t r u s tT H U R S D AY 31 J U LY 2008SENIOR DIVISION COMPETITION PAPERINSTRUCTIO NS AND INFO RMATIO NGENERAL1. Do not open the booklet until told to do so by your teacher.2. NO calculators, slide rules, log tables, maths stencils, mobile phones or other calculating aids arepermitted. Scribbling paper, graph paper, ruler and compasses are permitted, but are not essential. 3. Diagrams are NOT drawn to scale. They are intended only as aids.4. There are 25 multiple-choice questions, each with 5 possible answers given and 5 questions thatrequire a whole number between 0 and 999. The questions generally get harder as you work through the paper. There is no penalty for an incorrect response.5. This is a competition not a test; do not expect to answer all questions. You are only competingagainst your own year in your own State or Region so different years doing the same paper are not compared.6. Read the instructions on the Answer Sheet carefully. Ensure your name, school name and schoolyear are filled in. It is your responsibility that the Answer Sheet is correctly coded. 7. When your teacher gives the signal, begin working on the problems.THE ANSWER SHEET 1. Use only lead pencil.2. Record your answers on the reverse of the Answer Sheet (not on the question paper) by FULLYcolouring the circle matching your answer.3. Your Answer Sheet will be read by a machine. The machine will see all markings even if they arein the wrong places, so please be careful not to doodle or write anything extra on the Answer Sheet. If you want to change an answer or remove any marks, use a plastic eraser and be sure to remove all marks and smudges.INTEGRITY OF THE COMPETITIONThe AMC reserves the right to re-examine students before deciding whether to grant official status to their score.A U S T R A L I A N S C H O O L Y E A R S 11 A N D 12T I M E A L L O W E D : 75 M I N U T E SSenior DivisionQuestions 1to 10,3marks each1.The value of 8002−2008is (A)200(B)8(C)6006(D)1060(E)59942.The difference between 120and 210is (A)0(B)110(C)35(D)310(E)3203.In the diagram,x equals................................................................................................................................................................................ (x)◦100◦110◦80◦(A)100(B)110(C)120(D)130(E)1404.The value of 200×8200÷8is(A)1(B)8(C)16(D)64(E)2005.The smallest value that x 2−4x +3can have is (A)−1(B)−3(C)1(D)3(E)26.$3is shared between two people.One gets 50cents more than the other.The ratio of the larger share to the smaller share is (A)6:1(B)7:5(C)4:3(D)5:3(E)7:4S 27.When 10002008is written as a numeral,the number of digits written is (A)2009(B)6024(C)6025(D)8032(E)20128.A semicircle is drawn on one side of an equilateral triangle.The ratio of the area of the semicircle to the area of the triangle is(A)1:1(B)π:2√3(C)π:√3(D)√3:π(E)3:π................................................................................................................................................................................................................................................................................................................................................................................................................................................................9.Given that cos x =0.5and 0◦<x <90◦,which of the following has the greatestvalue?(A)cos 2x(B)cos x(C)0.75(D)sin x(E)tan x10.A fishtank with base 100cm by 200cm and depth 100cm contains water to a depthof 50cm.A solid metal rectangular prism with dimensions 80cm by 100cm by 60cm is then submerged in the tank with an 80cm by 100cm face on the bottom..................................................................................................................6.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................100100200501006080The depth of water,in centimetres,above the prism is then (A)12(B)14(C)16(D)18(E)20Questions 11to 20,4marks each11.Which of the following numbers is the largest?(A)2500(B)3400(C)4300(D)5200(E)610012.A normal die is thrown 100times.The sum of the numbers obtained will mostlikely be(A)200(B)250(C)300(D)350(E)400S 313.What is the smallest whole number which gives a square number when multipliedby 2008?(A)2(B)4(C)251(D)502(E)200814.A cross is made up of five squares,each with side length 1unit.Two cuts aremade,the first from X to Y and the second from Z to T ,so that ZT X is a right angle.The three pieces are then arranged to form a rectangle...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ZYX T IIIIII.................................................................... (II)IIIIWhat is the ratio of the length to the width of the rectangle?(A)3:1(B)√10:1(C)2:1(D)2√3:1(E)5:215.A function is said to be a toggle function on (p,q,r )if f (p )=q ,f (q )=r andf (r )=p .The function f (x )=ax 2+bx +c is a toggle function on (1,2,3).What is the value of c ?(A)−2(B)0(C)3(D)9(E)1416.Two conical rollers with perpendicu-lar axes touch on a line that is 30◦to the axis of the smaller roller and 60◦to the axis of the larger roller.If the larger roller makes 1revolution per sec-ond and there is no slipping,how many revolutions per second does the smaller roller make?(A)12(B)1(C)√2(D)√3(E)2...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................60◦30◦S 417.Consider the set X ={1,2,3,4,5,6}.How many subsets of X ,with at least one element,do not contain two consecutive integers?(A)16(B)18(C)20(D)21(E)2418.Farmer Taylor of Burra has two tanks.Water from the roof of his farmhouse iscollected in a 100kL tank and water from the roof of his barn is collected in a 25kL tank.The collecting area of his farmhouse roof is 200square metres while that of his barn is 80square metres.Currently,there are 35kL in the farmhouse tank and 13kL in the barn tank.Rain is forecast and he wants to collect as much water as possible.He should:(A)empty the barn tank into the farmhouse tank (B)fill the barn tank from the farmhouse tank(C)pump 10kL from the farmhouse tank into the barn tank (D)pump 10kL from the barn tank into the farmhouse tank (E)do nothing19.A sequence {u 1,u 2,...,u n }of real numbers is defined byu 1=√2,u 2=π,u n =u n −1−u n −2forn ≥3.What is u 2008?(A)−√2(B)2008(√2−2008π)(C)1003√2−1004π(D)π(E)√220.In the diagram,RU is equal in lengthto ST .What is the ratio of the area of QRU to the area of QST ?(A)√3:1(B)2:1(C)√6:1(D)√3:2(E)√6:2......................................................................................................................................................................................................................... (45)◦30◦UT Q RSQuestions 21to 25,5marks each21.P ,Q ,R ,S and T are consecutive vertices of a regular polygon.When extended,the lines P Q and T S meet at U with QUS =160◦.How many sides has the polygon?(A)36(B)42(C)48(D)52(E)54S522.How many numbers from1,2,3,4,...,2008have a cubic number other than1asa factor?(A)346(B)336(C)347(D)251(E)39323.The numbers828and313are3-digit palindromes where828−313=515,whichis also a palindrome.How many pairs(a,b)of3-digit palindromes are there witha>b and with a−b also a3-digit palindrome?(A)1972(B)1980(C)1988(D)1996(E)200824.The centres of all faces of a cube are joined to form an octahedron.The centresof all faces of this octahedron are now joined to form a smaller cube.What is the ratio of an edge of the smaller cube to an edge of the original cube?(A)1:√2(B)1:√3(C)1:2(D)1:3(E)1:425.In thefigure,all line segments are par-allel to one of the sides of the equi-lateral triangle P QR which has sidelength1unit.How long should P Xbe to maximise the smallest of the tenareas defined?(A)13(B)4−√214(C)14(D)15(E)1√10.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................PQ RXFor questions26to30,shade the answer as an integer from0to999inthe space provided on the answer sheet.Question26is6marks,question27is7marks,question28is8marks, question29is9marks and question30is10marks.26.All possible straight lines joining the vertices of a cube with mid-points of its edgesare drawn.At how many points inside the cube do two or more of these lines meet?S 627.Let us call a sum of integers cool if the first and last terms are 1and each termdiffers from its neighbours by at most 1.For example,the sum 1+2+3+4+3+2+3+3+3+2+3+3+2+1is cool.How many terms does it take to write 2008as a cool sum if we use no more terms than necessary?28.The positive integers x and y satisfy3x 2−8y 2+3x 2y 2=2008.What is the value of xy ?29.A point O is inside an equilateral triangleP QR and the perpendiculars OL ,OM and ON are drawn to the sides P Q ,QR and RP respectively.The ratios of lengths of the perpendiculars OL :OM :ON is 1:2:3.If area of LONP area of P QR =a b,where a and b are integers with no common factors,what is the value of a +b ?...............................................................................................................................................................................................................................................................................................................................................................................................................................................RPQLMNO.......................................................................................................................................................................................................................................................................................30.What is the smallest value that49+a 2−7√2a + a 2+b 2−√2ab +√50+b 2−10bcan have for positive real numbers a and b ?***Senior 2008 Answers Question Answer 1E2E3D4D5A6B7C8B9E10B11B12D13D14C15A16D17C18D19A20D21E22B23B24D25C26142789282829473013。

国际数学竞赛试题及答案一、选择题（每题3分，共15分）1. 下列哪个数是最小的正整数？A. 0B. 1C. 2D. 3答案：B2. 一个圆的半径为5，它的面积是多少？A. 25πB. 50πC. 100πD. 25答案：B3. 如果一个数的平方等于它本身，这个数可能是：A. 1B. -1C. 2D. 3答案：A B4. 一个数列的前三项是1, 1, 2，如果这个数列是等差数列，那么第四项是：A. 3B. 4C. 5D. 6答案：A5. 以下哪个表达式是正确的？A. sin²θ + cos²θ = 1B. sinθ + cosθ = 1C. sinθ * cosθ = 1D. tanθ = sinθ / cosθ答案：A D二、填空题（每题4分，共20分）6. 如果一个三角形的两边长分别是3和4，且这两边夹角为60度，那么第三边的长度是________。

答案：√137. 一个函数f(x) = 2x³ - 3x² + x - 5，求导后得到的导函数是________。

答案：6x² - 6x + 18. 一个数的立方根等于它本身，这个数可以是________。

答案：1, -1, 09. 一个正六边形的内角和是________。

答案：720°10. 如果一个等差数列的首项是2，公差是3，那么第10项是________。

答案：37三、解答题（每题10分，共30分）11. 证明：对于任意实数x，等式e^x ≥ x + 1成立。

证明：考虑函数f(x) = e^x - (x + 1)。

对f(x)求导得到f'(x) = e^x - 1。

当x > 0时，f'(x) > 0，说明f(x)在此区间单调递增；当x < 0时，f'(x) < 0，说明f(x)在此区间单调递减。

因此，f(x)的最小值出现在x = 0处，此时f(0) = e^0 - (0 + 1) = 1 - 1 = 0。

第一届2D01_01题目简介：题目：请参照图绘制图形，注意其中的同心、对称等几何关系。

参数：A=92， B=50， C=36， D=39， E=18问题：上色区域的面积是多少？与标准答案相对误差在正负0.5%以内视为正确。

（标准答案：4894.19）2D01_02题目简介：题目：参照图绘制图形，注意其中的对称、同心、相切等几何关系。

参数：A=22， B=132， C=15， D=15问题：图中上色部分的面积是多少？与标准答案相对误差在正负0.5%以内视为正确。

（标准答案：6120.23）2D01_03题目简介：题目：参照图绘制图形，注意其中的竖直、水平、相切等几何关系。

参数：A=108， B=42， C=25， D=14问题：图形中上色区域的面积是多少？与标准答案相对误差在正负0.5%以内视为正确。

（标准答案：8309.27）2D01_04题目简介：题目：参照图绘制图形，注意其中的同心、相切等几何关系。

参数：A=130， B=50， C=30， D=15问题：图形上色区域的面积是多少？与标准答案相对误差在正负0.5%以内视为正确。

（标准答案：85337.90）2D01_05题目简介：题目：参照图绘制图形，注意其中的同心、相切等几何关系。

参数：A=52， B=32， C=98， D=15问题：图形绿色区域的面积是多少？与标准答案相对误差在正负0.5%以内视为正确。

（标准答案：3799.62）2D01_06题目简介：题目：参照图绘制图形，注意其中的中点、水平、同心、相切等几何关系。

参数：A=100， B=80， C=5， D=50问题：图中上色部分的面积是多少？与标准答案相对误差在正负0.5%以内视为正确。

（标准答案：8616.73）题目简介：题目：参照下图绘制图形，注意其中的水平、竖直、相切等几何关系。

参数：A=189， B=145， C=29， D=96问题：图中绿色区域的面积是多少？与标准答案相对误差在正负0.5%以内视为正确。

澳大利亚数学竞赛小学高年级（5—6）（2012年）澳大利亚数学竞赛小学高年级（5—6）（2012年）1. 算式 101－2＋1＋102 等于（）（A ）0 （B ）100 （C ）198 （D ）200 （E ）2022. 小马足球隊在某場比賽贏对手二球，而在此場比賽中两队共踢进 8 球。

请問小马足球队在此场比赛共踢进几球？（）（A ）3 （B ）4 （C ）5 （D ）6 （E ）83. 请问以下哪一項的转轮转到兔子的机会较大？（）4. 一小罐的柠檬汁容量为 250 ml 。

请问需要用多少罐這樣这样的柠檬汁才能注满個容量为2.5 L 的水壶？（）（A ）3 （B ）4 （C ）6 （D ）8 （E ）105. 下列哪一项的值介于51与41 之间？（）（A ）0.26 （B ）0.15 （C ）0.21 （D ）0.19 （E ）0.36. 小皮第一次看时针的时刻是 2：00 pm ，当天下午他再看它的时刻是4：00 pm 。

请问在这段期间内時钟的分针共旋转了多少度？（）（A ）90 （B ）180 （C ）360 （D ）270 （E ）7207. 小莉想将以下的蜂巢状的镶嵌六边形圆形之內部涂上顏色。

若任两个有共边的六边形所涂的顏色都不相同。

請問小莉至少要涂上几种顏色？（）（A）2 （B）3 （C）4 （D）5 （E）68.小雅花費半小時写完家庭作业的三分之一。

若她继续以相同的效率写作业请问她还要花費多少分钟才能写完家庭作业？（）（A）20 （B）30 （C）40 （D）60 （E）909.标记S 的哨兵守衛他所在方格上的同一行与同一列上的所有方格；标记T 的哨兵則守衛他所在方格上的45°斜線上的所有方格。

（）請問在上圖中，共有多少個小方格沒有被守衛？（A）1 （B）3 （C）5 （D）7 （E）810.一块矩形地毯的长度是宽度的 3 倍。

若將它的长度減少 3 m 而寬度增加 3 則会变成一个正方形。

澳大利亚数学竞赛小学中年级（3—4）（2013年）1.请问公元 2013 年之后经过十年是公元多少年？（）（A）2003 （B）2013 （C）2014 （D）2023 （E）21132.请问一个正立方体共有多少条边？（）（A）4 （B）6 （C）8 （D）9 （E）123.小兰学校的操场跑道一圈的长度是 400 m，而小兰一共跑了三圈。

请问她一共跑了多长的距离？（）（A）300 m （B）600 m （C）800 m （D）1200 m （E）3000 m4.请问下图中矩形的几分之几被涂上阴影？（）（A）五分之一（B）五分之二（C）三分之二（D）三分之一（E）五分之三5.请问 9 和 3 之差的三倍等于多少？（）（A）6 （B）9 （C）18 （D）36 （E）816.小珍所戴的帽子上有「COTTON CLUB」的字样。

当小珍向镜子里看去，请问她所看到这顶帽子上的字样是什么？（）7.直线棋盘上的格子从左至右的编号为 1, 2, 3, …。

小莎的棋子向右移动 6 格，向左移动 4 格，然后向右移动 3 格。

假如棋子停留在编号为 7 的方格，请问开始时小莎的棋子所在格子上的编号是什么？（）（A）1 （B）2 （C）3 （D）4 （E）58.小伊位于一个边长为 10 m 正方形的迷宫之中心。

他知道只要沿着如下图所示螺旋状的路径便可走出这个迷宫。

已知这个迷宫共有A、B、C、D、E 五个出口，请问小伊将会从哪一个出口走出这个迷宫？（A）A （B）B （C）C （D）D （E）E9.用下面 3 张数码卡片拼成三位数，请问在所能拼出的数中，最大的数与最小的数相差多少？（）（A）198 （B）200 （C）202 （D）298 （E）30210.小柏在心中想着一个数，他将这个数乘以 2 之后再加 2，所得到的值是 14。

请问他心中原来想的这个数是什么？（）（A）6 （B）7 （C）8 （D）12 （E）3011.小艾有两枚 50 元硬币、三枚 20 元硬币与八枚 5 元硬币，小德有四枚 20 元硬币与六枚 10 元硬币。