IGCSE math 数学试卷0580_s17_qp_43

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IGCSE 0511_w12_qp_43 试卷真题听力

w w w e tr .X m ap ePUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Educations er om .c*3336017255*ENGLISH AS A SECOND LANGUAGE Paper 4 Listening (Extended)0511/43October/November 2012 Approx. 45 minutesCandidates answer on the Question Paper. Additional Materials: As listed in Instructions to Supervisors.READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. Dictionaries are not permitted. 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.For Examiner's Use Questions 1-6 Question 7 Question 8 Question 9 Question 10 TotalThis document consists of 6 printed pages and 2 blank pages.IB12 11_0511_43/FP © UCLES 2012[Turn over2 Questions 1-6 For Questions 1-6 you will hear a series of short sentences. Answer each question on the line provided. Your answer should be as brief as possible. You will hear each item twice. 1 How do the friends decide to save time? [1]For Examiner's Use2What are the two disadvantages of catching a direct train? [1]3What should the guests do after visiting the lighthouse, and why is Tuesday best for the trip?[2]4What is the emergency contact number? [1]5Which subject does Mark choose for his book review, and where will he find the book? [1]6Which solution does the customer choose, and why?[2] [Total: 8]© UCLES 20120511/43/O/N/123 Question 7 Listen to the following interview with a table tennis trainer, and then complete the details below. You will hear the interview twice.For Examiner's UseSelin Kaya: table tennis coachSelin Kaya: trainer for ‘Ping’, a .................................... table tennis project. 2010: ‘Ping’ project set up table tennis tables in .................................... and at .................................... in Australia and UK. Aim: to bring table tennis to .................................... , shoppers and .................................... . Provided: bats and balls labelled ‘please .................................... after .................................... ’. Selin’s role: trains young players; much work and travel involved. Rewards of role: seeing players make .................................... . Selin’s advice for people wanting to play: Visit ............................................... to find local .................................... . Play table tennis anywhere: in the park, on your ................................. or even on your .................................... table. [1] [1] [1] [1] [1] [1] [1][Total: 7]© UCLES 20120511/43/O/N/12[Turn over4 Question 8 Listen to the following interview with an explorer, and then complete the details below. You will hear the interview twice.For Examiner's UseRecord-breaking walk: Amazon RiverTime taken: .................................... days. Dates of walk: 2nd .................................... 2008 until ................................. .................................... 2010. Amazon River: is world’s second .................................... river. Length: .................................... kilometres. Extra distance walked: .................................. kilometres added to the journey because of .................................... . Real purpose of walk: to provide funds for .................................... and to raise .................................... of the plight of Amazonian rainforests. Website: Survival tactics: Food: spider .................................... , snakes, fish, eels, scorpions and .................................... . Health: advice sought via .................................... . Cho: local forestry worker, acted as helper and .................................... , made great coffee. Summary of dangers survived: ...................................... by hostile tribes, mosquito bites and tropical .................................... . [1] [1] [1] [1] [1] [1] [1] [1] [1][Total: 9]© UCLES 2012 0511/43/O/N/125 Question 9 Listen to the following interview about a huge crab, and then answer the questions below. You will hear the interview twice. (a) Give one thing that a visitor can do at a Sea Life Centre. [1]For Examiner's Use(b) Give two physical details about the centre’s newest creature.[1](c) Give a reason for the nickname given to the crab. [1](d) Where exactly do these crabs usually live? [1](e) What is the creature’s diet? Give two details.[1](f) How does the huge crab disguise itself? [1] [Total: 6]© UCLES 20120511/43/O/N/12[Turn over6 Question 10 Listen to the following talk by a writer, and then answer the questions below. You will hear the talk twice. (a) How do we know that the speaker was already a successful writer before she received the invitation? [1]For Examiner's Use(b) How was the Bond book tradition continued after the original author died? [1](c) Why was the speaker able to read Bond novels at an early age? [1](d) What does the speaker tell us about her own first mini novel? Give two details. [1](e) What is the advice of the speaker to aspiring writers? Give two details. [1](f) How does the speaker try to keep her readers interested? Give two details. [1] [Total: 6]© UCLES 20120511/43/O/N/127 BLANK PAGE© UCLES 20120511/43/O/N/128 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. 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 20120511/43/O/N/12。

IGCSE试卷Part6

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSInternational General Certificate of Secondary Education *89547628*ENGLISH AS A SECOND LANGUAGE 0511/12Paper 1 Reading and Writing (Core) October/November 2013 1 hour 30 minutesCandidates answer on the Question Paper.No Additional Materials are required.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.Do not use staples, paper clips, highlighters, glue or correction fluid.DO NOT WRITE IN ANY BARCODES.Answer all questions.Dictionaries are not allowed.The number of marks is given in brackets [ ] at the end of each question or part question.ww w.Xtr em ePa p er s.comExercise 1Read the following article about places to visit in France, and then answer the questions on the opposite page.VISITING FRANCEFrance offers great opportunities for visitors and a wide variety of different types of holiday.Countryside and villagesThere is plenty to see in the French countryside, including beautiful wooded valleys, rivers and gorges. In most areas of France you can find pretty villages, especially in central Alsace, in the countryside of Normandy and along the river in the Dordogne.CastlesFrance is famous for its wonderful architecture, and two areas in France are particularly visited for their attractive castles. The Loire valley to the south-west of Paris is best known for its large houses or castles called ‘chateaux’, which were built by rich noblemen and kings from Paris. Towards the south of France the Dordogne is famous for its medieval castles.MountainsThe impressive mountains of the French Alps are popular in both summer and winter for skiing.The area attracts skiers of all abilities, from beginners to experts. Less visited by overseas visitors, the Pyrenees offer an attractive alternative to the French Alps for people interested in skiing or a holiday in the mountains.BeachesFrance has thousands of beaches to meet every requirement. Some of the most popular beaches with sun-seekers are those along the French Riviera, where high temperatures are almost guaranteed during the summer months. The long sandy beaches of the Atlantic Coast north of Biarritz are also well worth visiting, as is the very picturesque coast of Brittany.Family funAmong the most popular regions for people visiting France with children are the beaches of the western coast such as those found in the Vendee department, which also has several large attractions and events for families. Another favourite destination here is Ile de Ré, well known for having lots of cycle paths which make it a pleasure for families to travel around. In addition, amusement parks such as Disneyland and Asterix in the north of France offer great fun for both children and adults.ParisEveryone loves Paris, as much for its café life and general romantic atmosphere as for the more famous sights such as the Eiffel Tower, Notre Dame Cathedral and the Louvre museum. The Metro makes it easy to travel around the city and everywhere you go there is something new and exciting to discover.Eating outWherever you choose to visit, remember that good food is appreciated and widely known about throughout France. Eating out is generally inexpensive, outside the large cities. A decent two course lunch will cost about 12 euros. It is not necessary to leave a tip for the waiter or waitress because the service charge is now included in the bill. However, most people still leave a small tip, especially for good service.© UCLES 20130511/12/O/N/130511/12/O/N/13© UCLES 2013[Turn overFor Examiner’s Use (a) What three natural features can you see in the countryside in France? (1)(b) Why might tourists want to visit the Loire valley? (1)(c) What is particularly attractive about the beaches on the French Riviera? (1)(d) What makes Ile de Ré a good place for families to visit? (1)(e) Apart from the famous sights, what makes Paris so popular for visitors? Give two details....................................................................................................................................... (2)(f) Where is it especially good value for money to eat out? (1)[Total: 7]Exercise 2Read the following article about spices, and then answer the questions on the opposite page.© UCLES 20130511/12/O/N/130511/12/O/N/13© UCLES 2013[Turn overFor Examiner’s Use (a) How were Arabian traders able to make fortunes by the year 1000? (1)(b) How does the price of spices nowadays compare with the cost in the 15th century? (1)(c) How far in total did Vasco da Gama travel on his journey, and how long did the voyagelast? (1)(d) How do we know that Vasco da Gama’s journey was a financial success? (1)(e) How did the relationships between European countries change after da Gama returned?Give two details....................................................................................................................................... (2)(f) What modern industry has been as successful as the spice trade of the past? (1)(g) Why were spices used to hide the flavour of foods? (1)(h) What quality do cloves and mustard share that made them particularly important in thepast? (1)(i) According to the chart, which country spends the most on importing spices and howmuch does it spend? (1)(j) How have people learnt the skills needed to produce spices? (1)[Total: 11]Exercise 3Rachael Thomas is a 17-year-old girl who lives at 28 North Lane, Hillhead, RO14 7XY, which is in England. Recently she went to Spain to visit a friend in Madrid. It was the first time that she had travelled alone, and her father was very keen to make sure that the trip went well. He bought the tickets for her and made sure that the flights were at convenient times. Rachael flew from Southampton on Blue Sky Airways flight number 235, which departed at 2:00 pm. She returned on the same airline, flight number 437, which departed from Madrid at 10:00 am and arrived back in England at midday. Rachael’s father had booked a taxi to meet her when she arrived so that she could travel quickly and safely to her friend’s home at Mimbreras 2, 28027 Madrid, Spain. He also made sure that his daughter’s friend had Rachael’s mobile phone number, 079350642.Rachael had bought a new suitcase for the trip; it was bright pink, with wheels that made it very easy to manage. Rachael particularly liked the leather luggage tag that matched the case. She had chosen a suitcase with a hard case because she wanted to be sure that everything inside it would be well protected during the journey. Her mother had given her a personalised luggage strap, which she tied around the case to make it easier to identify.The mother of Rachael’s friend had asked Rachael to bring out a special jewellery set which she had seen advertised in a magazine and which was only available in England. The necklace and earrings were of an unusual design. The set had cost £80 and Rachael thought that it was very pretty. Of course her friend’s mother would pay her back as soon as she arrived. Rachael was also taking quite a lot of clothes as she wanted to be able to dress well during her stay.Although it seemed that everything had been planned very carefully, the trip was not completely successful because when Rachael arrived in Madrid, she discovered that her suitcase had been lost. Rachael then had to complete a lost luggage form so that the authorities could start trying to find her suitcase.Imagine you are Rachael. Fill in the form on the opposite page using the information above.© UCLES 20130511/12/O/N/13ForLOST LUGGAGE FORMExaminer’sUse Section A: Passenger detailsName: .........................................................................................................................................Home address: ........................................................................................................................... Telephone number: ..................................................................................................................... Destination address: ...................................................................................................................Section B: Flight detailsAirline and flight number: ............................................................................................................ Departure airport: .......................................................................................................................Arrival airport: .............................................................................................................................Section C: Luggage detailsType of suitcase (please circle as required):soft case hard case with wheels without wheelsWas there a luggage tag attached to your suitcase? (please delete) YES / NOColour of suitcase: (please circle)black brown red blue other (please give colour) ...........................Section D: Further detailsIn the space below, write one sentence giving other details which may help us to identify the luggage, and one sentence describing anything of value in the luggage.[Total: 14]© UCLES 2013[Turn over0511/12/O/N/13Exercise 4Read the following article about mobile phones, and then complete the notes on the opposite page.© UCLES 20130511/12/O/N/130511/12/O/N/13© UCLES 2013[Turn overFor Examiner’s UseY ou have been asked to give a talk to your technology club about mobile phones. Prepare some notes to use as the basis of your talk.Make your notes under each heading.[Total: 7]Exercise 5Imagine that you have given your talk to your technology club. Now your teacher wants you to follow up these notes with a short article for the school magazine.Look at your notes in Exercise 4. Using the ideas in your notes, write a summary about the disadvantages of the mobile phone.Your summary should be about 70 words long (and no more than 80 words long). You should use your own words as far as possible................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................[Total: 5]0511/12/O/N/13© UCLES 2013Exercise 6Recently, you were disappointed because you didn’t get something you had worked hard for.Write a letter to your friend about this experience.In your letter you should:• describe what you had worked hard for• explain why you didn’t get it • say what you have learnt from this experience.The pictures above may give you some ideas, and you should try to use some ideas of your own.Your letter should be between 100 and 150 words long. Do not write an address.Y ou will receive up to 7 marks for the content of your letter, and up to 6 marks for the style and accuracy of your language.ForExaminer’sUse ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... 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......................................................................................................................................................... ......................................................................................................................................................... .........................................................................................................................................................[Total: 13]Exercise 7A big international supermarket chain is planning to build a new store not far from where you live.Here are some comments already made by local people:A supermarket will give us a much greaterchoice of products to buy.People will stopusing our small local shops,which will have toclose down.There will be new jobs on offer for the people who live nearby.The crowds and traffic congestion will make the area very noisy.Write an article for the local newspaper giving your opinion of the plan.The comments above may give you some ideas, and you should try to use some ideas of your own.Your article should be between 100 and 150 words long.Y ou will receive up to 7 marks for the content of your article, and up to 6 marks for the style and accuracy of your language.ForExaminer’sUse ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... 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......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... .........................................................................................................................................................[Total: 13]Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been 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.。

IGCSE Maths past paper数学考试题

Q8
(Total 4 marks)
N20710RA
7
Turn over
9. The grouped frequency table gives information about the distance each of 150 people travel to work.
6
Ruler graduated in centimetres and
Nil
millimetres, protractor, compasses,
7
pen, HB pencil, eraser, calculator.
Tracing paper may be used.
8
9
Instructions to Candidates
Number
1
2
3
4
Probability
0.35
0.16
0.27
Magda is going to spin the pointer once. (a) Work out the probability that the pointer will stop on 4.
(b) Work out the probability that the pointer will stop on 1 or 3.
h b
The Quadratic Equation The solutions of ax2 + bx + c = 0 where a ≠ 0, are given by
x = −b ± b2 − 4ac 2a
N20710RA
2
Answer ALL TWENTY questions. Write your answers in the spaces provided. You must write down all stages in your working. 1. In July 2002, the population of Egypt was 69 million. By July 2003, the population of Egypt had increased by 2%. Work out the population of Egypt in July 2003.

igcse0580数学考纲

igcse0580数学考纲【最新版】目录1.IGCSE 0580 数学考试概述2.考试结构和题型3.考试涵盖的知识点4.备考建议正文【IGCSE 0580 数学考试概述】IGCSE 0580 数学考试是国际普通中等教育证书（IGCSE）的一门重要科目。

该考试旨在测试学生在数学领域的基本知识和技能，为学生进一步学习高级数学课程打下坚实基础。

IGCSE 0580 数学考试适用于全球各地的中学生，无论他们将来选择哪种教育路径，都可以通过该考试证明自己的数学能力。

【考试结构和题型】IGCSE 0580 数学考试分为两部分，共计 100 道题目，考试时间为 2 小时。

两部分分别为：1.选择题（共 40 题，每题 2 分，满分 80 分）2.填空题（共 60 题，每题 3 分，满分 180 分）选择题部分要求学生从四个选项中选出正确答案，填空题部分则要求学生在空白处填写正确答案。

考试涵盖了广泛的数学知识点，包括算术、代数、几何、统计和概率等内容。

【考试涵盖的知识点】IGCSE 0580 数学考试涵盖了以下知识点：1.算术：四则运算、乘方、开方、百分数、比例和比例问题等。

2.代数：代数表达式、方程与不等式、函数、图形和数据表示等。

3.几何：直线与角、三角形、四边形、圆、平面图形的性质和应用等。

4.统计：数据的收集、整理和分析、频数分布、概率等。

5.概率：事件的概率、条件概率、独立事件、概率树等。

【备考建议】1.熟悉考试结构和题型，了解评分标准。

2.系统学习数学知识点，加强基本概念的理解。

3.多做练习题，提高解题速度和准确率。

4.分析错题，找出自己的薄弱环节，针对性地进行复习。

5.参加模拟考试，了解自己在真实考试环境下的应对情况，调整心态。

吉林省长春市东北师范大学西湖实验学校2024-2025学年九年级上学期11月核心素养调研数学试卷

吉林省长春市东北师范大学西湖实验学校2024-2025学年九年级上学期11月核心素养调研数学试卷一、单选题1．若有理数a、b互为相反数，则a b+的值为（）A．0B．1C．1-D．无法确定2．联合国经济和社会事务部曾发布《世界人口展望报告》称，全球人口到2100年将达到112亿（即11200000000人），11200000000这个数据用科学记数法表示为（）A．9⨯B．1011.210⨯D．110.112101.1210⨯C．11⨯1.12103．如图，由5块完全相同的小正方体所搭成的几何体的俯视图，小正方形中的数字表示在该位置小正方体的个数，其主视图是（）A．B．C．D．4．如图，木工师傅用图中的角尺画平行线的依据是（）A．同位角相等，两直线平行B．平行于同一条直线的两条直线平行C．经过直线外一点，有且只有一条直线与这条直线平行两直线平行，同位角相等D．两直线平行，同位角相等5．如图，在A岛周围20海里水域有暗礁，一艘轮船由西向东航行到O处时，发现岛在北偏东64°的方向且与轮船相距52海里．若该轮船不改变航向，为航行安全，需要计算A到OB 的距离AC．下列算法正确的是（）A ．52cos64AC =︒B ．52cos 64AC =︒C ．52sin 64AC =︒D ．52tan 64AC =︒6．如图，AD 是O 的直径， AB CD=，若40AOB ∠=︒，则圆周角BPC ∠的度数是（）A ．40︒B ．50︒C ．60︒D ．70︒7．如图，在平面直角坐标系中，抛物线y ＝﹣x 2+4x +m 的顶点为A ，它与x 轴分别交于B ，C 两点，与y 轴的交点为D ，过点D 作DE 平行于x 轴交于抛物线于点E ，BF ∥CE 交DE 于点F ，若3S △ABC ＝4S △FEC ，则m 的值为（）A ．﹣127B ．﹣712C ．﹣12D ．128．如图，点A 在反比例函数(0)k y x x =<的图象上，连结OA ，分别以点O 和点A 为圆心，大于12AO 的长为半径作弧，两弧相交于B 、C 两点，过B 、C 两点作直线交x 轴于点D ，连结A ，若30AOD ∠=︒，AOD △的面积为3，则k 的值为（）A ．6-B ．6C ．9-D ．9二、填空题9．分解因式：2218m -=．10．关于x 的不等式11123x -<的非负整数解为．11．若关于x 的一元二次方程2420x x k -+-=有两个相等的实数根，则k 的值为．12．如图，A 是O 的直径，弦A 垂直于A 垂足为E ，若72ADC ∠=︒，则OCD ∠的大小为度．13．如图，在ABC V 中，35AC AB ==，，点D 在边BC 上，A 平分BAC ∠，点E 在线段A 上．若ACE B ∠=∠，则AE ED 的值为．14．如图是用无刻度的直尺和圆规完成的作图，则下列作法正确的是．①EF 是ABC V 的中位线；②180BAC EOF ∠+∠=︒；③O 是ABC V 的内心；④AEF △的面积等于ABC V 的面积的14．三、解答题15．（1）解方程：2650x x +-=（2）计算：112sin 30π3-⎛⎫︒- ⎪⎝⎭16．不透明的袋子中装有2个红球、1个白球，这些球除颜色外均相同．(1)从袋子中随机摸出1个球，放回并摇匀，再随机摸出1个球．请用画树状图（或列表）的方法，求两次摸出的球都是红球的概率．(2)从袋子中随机摸出1个球，如果是红球，不放回再随机摸出1个球如果是白球，放回并摇匀，再随机摸出1个球．两次摸出的球都是红球的概率是__________．17．《先生向北》这本书由鲍盛华所著，详细记述了20世纪五六十年代，一大批文艺界、科学界、教育界和思想界的精英奔赴东北，使东北文脉遽然隆起的故事．长春市某书店分别用1200元和1500元两次购进该小说，第二次购进的数量比第一次多10套，且两次购书时，每套书的进价相同．问书店第一次购进小说多少套？18．如图，在44⨯的正方形网格中，每个小正方形的边长均为1，每个小正方形的顶点称为格点，点A 、B 、C 均为格点，只用无刻度的直尺，分别在给定的网格中找一格点满足下列要求：(1)在图①中，作格点M ，并连结MA 、MB 、MC ，使MA MB MC ==．(2)在图②中，作格点N ，并连结NA 、NC 使o 108ANC ABC ∠+∠=．(3)在图③中，作格点P ，并连结PA 、PC ，使12APC ABC ∠=∠．19．如图，AB 为⊙O 的直径，C 为BA 延长线上一点，CD 是⊙O 的切线，D 为切点，OF AD ⊥于点E ，交CD 于点F ．（1）求证：ADC AOF ∠=∠；（2）若1sin ,123C BD ==，求EF 的长．20．“一粥一饭，当思来之不易”，为了解落实“光盘行动”的情况，某校数学兴趣小组的同学调研了七、八年级部分班级某一天的餐食垃圾质量．从七、八年级中各随机抽取10个班的餐食垃圾质量的数据（单位：kg ），进行整理和分析（餐食垃圾质量用x 表示，共分为四个等级：A ．1x <，B ．1 1.5x ≤<，C ．1.52x ≤<，D ．2x ≥），下面给出了部分信息．七年级10个班的餐食垃圾质量：0.8，0.8，0.8，0.9，1.1，1.1，1.6，1.7，1.9，2.3．八年级10个班的餐食垃圾质量中B 等级包含的所有数据为：1.0，1.0，1.0，1.0，1.2．七、八年级抽取的班级餐食垃圾质量统计表年级平均数中位数众数方差A 等级所占百分比七年级1.3 1.1a 0.2640%八年级 1.3b 1.00.23%m 八年级抽取的班级餐食垃圾质量扇形统计图根据以上信息，解答下列问题：(1)直接写出上述表中a ，b ，m 的值；(2)该校八年级共20个班，估计八年级这一天餐食垃圾质量符合A 等级的班级数；(3)根据以上数据，你认为该校七、八年级的“光盘行动”，哪个年级落实得更好？请说明理由（写出一条理由即可）．21．电子体重科读数直观又便于携带，为人们带来了方便．某综合实践活动小组设计了简易电子体重秤：制作一个装有踏板（踏板质量忽略不计）的可变电阻R 1，R 1与踏板上人的质量m 之间的函数关系式为R 1＝km ＋b （其中k ，b 为常数，0≤m ≤120），其图象如图1所示；图2的电路中，电源电压恒为8伏，定值电阻R 0的阻值为30欧，接通开关，人站上踏板，电压表显示的读数为U 0，该读数可以换算为人的质量m ，温馨提示：①导体两端的电压U ，导体的电阻R ，通过导体的电流I ，满足关系式I ＝U R；②串联电路中电流处处相等，各电阻两端的电压之和等于总电压．（1）求k ，b 的值；（2）求R 1关于U 0的函数解析式；（3）用含U 0的代数式表示m ；（4）若电压表量程为0~6伏，为保护电压表，请确定该电子体重秤可称的最大质量．22．综合与实践图①图②【基本模型】如图①，O 的半径为1，P 是O 外一点，3OP =，点A 是O 上一个动点，连结AP ，则AP 长度最小值为__________．【模型应用】如图②，矩形ABCD 中，43AB BC ==，，点P 、Q 分别是边AB BC 、上的动点，连结PQ ，2PQ =，M 是PQ 的中点，连结MD ．（1）当MD 最短时，求MD 的长．（2）连结AC ．当M 到AC 的距离最小时，AP 的长度为__________．23．如图，在Rt ABC △中，9086C AC BC ∠=︒==，，，动点P 从点A 向终点B 运动，速度为5个单位/秒，作PQ PA =交射线AC 于点Q ，设点P 的运动时间为t 秒（0t >）．(1)直接写出线段CQ 的长（（用含t 的代数式表示）．(2)设APQ △与ABC V 重叠部分周长为L ，当AP CQ =时，求L 的值．(3)连接BQ ，当PBQ 是轴对称图形时，直接写出t 的值．(4)作点C 关于直线PQ 的对称点为C '．当点C '到直线AC 的距离为4时，直接写出t 的值．24．在平面直角坐标系中，函数(2)()y x x m =-+-（m 为常数）的图象与x 轴交于定点P ．(1)直接写出点P 的坐标．(2)当函数图象经过点(1,3)时，求函数的表达式，并写出该抛物线的顶点坐标．(3)当2x ≤-时，若函数(2)()y x x m =-+-（m 为常数）的图象最高点到直线3y m =+的距离为1，求m 的值．(4)矩形ABCD 的四个顶点的坐标分别为(1,1)(1,1)(1,3)(1,3)A B m C m D ----、、、．当函数(2)()y x x m =-+-（m 为常数）的图象与矩形的边有两个交点时，直接写出m 的取值范围．。

吉林省长春市朝阳区长春外国语学校2024～2025学年八年级上学期9月月考数学试题[含答案]

长春外国语学校2024-2025学年第一学期第一次月考初二年级数学试卷本试卷包括三道大题，共24道小题，共6页．全卷满分120分，考试时间为90分钟．考试结束后，将答题卡交回．注意事项：1．答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区．2．选择题必须使用2B 铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚．3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效．4．作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑．5．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀．一、单选题（本大题共8小题，每题3分，共24分）1．11的算术平方根是（）A ．11B C ．D ．2．计算（－2a 2）3的结果是（）A ．66a -B ．68a -C ．56a D ．58a -3．下列说法正确的是（）A ．9-的平方根是3±B ．9-的算术平方根是3-C 4±D ．0的平方根与算术平方根都是04．如图，数轴上点P 表示的数可能是（）A B C D 5．下列命题中，是真命题的是（）A ．对顶角相等B ．内错角相等C ．若22m n =，则m n=D ．若a b >，则55a b->-6．()()284x x x mx n +-=++，则m ，n 的值为（）.A ．4，32B ．4，32-C ．4-，32D ．4-，32-7．已知，552a =，443b =，334c =，则a 、b 、c 的大小关系是（）A ．b c a>>B ．a b c>>C ．c a b>>D ．c b a>>8．如图，圆的直径为1个单位长度，该圆上的点A 与数轴上表示1-的点重合，将该圆沿数轴正方向滚动1周，点A 到达点A ¢处，则点A ¢表示的数为（）A ．1p -+B ．1 3.14-+C ．1-pD ．1p -+或1-p二、填空题（本大题共6小题，每题3分，共18分）9．已知a ＋b ＝5，ab ＝6，则a 2＋b 2＝．10．一个等腰三角形的一个底角为40°，则它的顶角的度数是度．11．计算：()22877a a a -¸=．12．计算：()202420240.254-´=．13=．14．已知2(1)16x m x --+是一个完全平方式，则m 的值等于．三、解答题（本大题共10小题，共78分）15．计算：(1)()32325x x x x -+；(2)()3224x x x ×¸；(3)()()3223x x +-；(4)()2-．16．分解因式：(1)325x x -；(2)228168a ab b -+．17．先化简，再求值：()()()2133423x x x x -+-+，其中13x -=．18．已知实数9a +的一个平方根是5-，2b a -的立方根是2-，求2a b +的算术平方根．19．如果关于x 的多项式2x -与25x mx ++的乘积中不含x 的一次项，求m 的值．20．某学生化简2(1)(3)a a a +--出现了错误，解答过程如下：解：原式22(69)a a a a =+--+（第一步）2269a a a a =+--+（第二步）59a =-+（第三步）(1)该学生解答过程是从第______步开始出错，其错误原因是______；(2)请你帮助他写出正确的简化过程．21．某同学在计算一个多项式乘23x -时，算成了加上23x -，得到的结果是2112x x -+，那么正确的计算结果是多少？22．如图，AC 、DB 相交于点O ，AB ＝DC ，∠ABO ＝∠DCO ．求证：（1）AO ＝DO ；（2）∠OBC ＝∠OCB ．23．而无理数是无限不循环小数，出来，而23<<2的小数部分为_________，2______；(2)若m 的整数部分，n m n +24．数学活动课上，老师准备了若干个如图1的三种纸片，A 种纸片是边长为a 的正方形，B 种纸片是边长为b 的正方形，C 种纸片是长为a 、宽为b 的长方形，并用A 种纸片一张，B 种纸片一张，C 种纸片两张拼成如图2的大正方形．(1)若要拼出一个面积为()()25a b a b ++的长方形，则需要A 号卡片_____张，B 号卡片____张，C 号卡片_______张．(2)观察图2的面积关系，写出正确的等式_________________．(3)两个正方形ABCD 、AEFG 如图3摆放，边长分别为x ，y ，若22x y 34+=，2BE =，求图中阴影部分面积的和．1．B【分析】本题主要考查算术平方根的定义，注意一个正数的平方根有两个，它们为相反数，其中正的平方根，就是这个数的算术平方根．0的算术平方根是0；负数没有平方根．根据算术平方根的定义即可解答．【详解】解：11 故选：B ．2．B【分析】由题意直接根据积的乘方的运算性质：每一个因式分别乘方，再把所得的幂相乘．即（ab ）n =anbn （n 是正整数），进行计算求解即可．【详解】解：323623((2)()82)a a a =--=-g ．故选：B ．【点睛】本题主要考查了积的乘方的运算性质，注意：①因式是三个或三个以上的积的乘方，法则仍适用；②运用时数字因数的乘方应根据乘方的意义计算出最后的结果．能根据积的乘方的性质准确计算是做出本题的关键．3．D【分析】本题考查了平方根与算术平方根，熟练掌握平方根和算术平方根的性质是解题关键．根据平方根和算术平方根的性质逐项判断即可得．【详解】解：A 、9的平方根是3±，9-没有平方根，则此项错误，不符合题意；B 、9-没有算术平方根，则此项错误，不符合题意；C 4=，4的平方根是2±，则此项错误，不符合题意；D 、0的平方根与算术平方根都是0，则此项正确，符合题意；故选：D ．4．C【分析】根据实数的比较大小，找出符合范围的实数即可．【详解】解：12<<，故A 选项不符合题意；12<<，故B 选项不符合题意；23<<，故C 选项符合题意；34<<，故D 选项不符合题意；故选：C ．【点睛】本题考查的是实数与数轴，掌握实数的比较大小是解决此题的关键．5．A【分析】依据内错角、对顶角的定义以及平方根的运算法则、不等式性质逐项分析判断即可．【详解】解：A ．“对顶角相等”，这个命题是真命题，故符合题意；B ．“内错角相等”，这个命题是假命题，两直线平行，内错角相等才是真命题，故不合题意；C ．“若22m n =，则m n =”，这个命题是假命题，“若22m n =，则m n =±”是真命题，故不符合题意：D ．“若a b >，则55a b ->-”，这个命题是假命题，“若a b >，则55a b -<-”才是真命题，故不合题意．故选：A ．【点睛】本题主要考查了真假命题的判断、内错角、对顶角、平方根以及不等式性质等知识，熟练掌握相关知识是解题关键．6．B【分析】根据多项式乘以多项式进行计算，即可求解．【详解】解：∵()()284432x x x x +-=+-∴4,32m n ==-,故选：B ．【点睛】本题考查了多项式乘以多项式，熟练掌握多项式乘以多项式的运算法则是解题的关键．7．A【分析】首先根据幂的乘方运算的逆用可得，1132a =，1181b =，1164c =，再根据指数相等时，底数越大，幂就越大，据此即可解答．【详解】解：55511112=2=32a =（），44411113=3=81b =（），33311114=4=64c =（），816432>>Q ，111111816432\>>，b c a \>>，故选：A ．【点睛】本题考查了幂的乘方运算的逆用，有理数大小的比较，熟练掌握和运用幂的乘方运算的逆用是解决本题的关键．8．A【分析】根据圆的直径为1个单位长度,其周长为d p p =,设点A ¢表示的数为t ，则()1t p --=,解答即可．本题考查了有理数的加法，数轴上表示数，熟练掌握运算是解题的关键．【详解】解：根据题意，得圆的直径为1个单位长度,其周长为d p p =,设点A ¢表示的数为t ，则()1t p --=,解得1t p =-+．故选：A ．9．13【分析】由题意利用完全平方和公式可得222()2a b a b ab +=+-，进而整体代入a ＋b ＝5，ab ＝6即可得出答案.【详解】解：2222()252613a b a b ab +=+-=-´=.故答案为：13.【点睛】本题考查代数式求值，熟练掌握和利用完全平方和公式进行变形是解题的关键，注意整体思维的运用.10．100【分析】本题考查了等腰三角形的性质和三角形内角和，解答时根据等腰三角形两底角相等，求出顶角度数即可．【详解】解：因为其底角为40°，所以其顶角180402100=°-°´=°．故答案为：100．11．41a -【分析】本题考查的是多项式除以单项式，掌握多项式除以单项式的运算法则是解本题的关键．根据多项式除以单项式的运算法则计算即可．【详解】解：()22877a a a -¸，228777a a a a =¸-¸，41a =-，故答案为：41a -．12．1【分析】本题考查积的乘方的逆运算，熟记积的乘方的逆运算是解决问题的关键．由()nn n a b ab =g 恒等变形计算即可得到答案．【详解】解：()20242024202420242024110.25444144æöæö-´=-´=-´=ç÷ç÷èøèø，故答案为：1．13．1-【分析】本题考查了算术平方根的非负性、立方根，熟练掌握算术平方根和立方根的性质是解题关键．先根据算术平方根和绝对值的非负性可求出,a b 的值，再代入计算立方根即可得．【详解】解：50+=0,50b ³+³，∴40,50a b -=+=，∴4,5a b ==-，1==-，故答案为：1-．14．9或-7##-7或9【分析】利用完全平方公式的结构特征判断即可得到m 的值即可．【详解】解：根据题意得21162m -æö=ç÷èø，142m -=±，9m =或7m =-，故答案为：9或-7【点睛】此题考查了完全平方式，熟练掌握完全平方公式是解本题的关键．15．(1)4326315x x x -+(2)4x (3)2656x x --(4)11-【分析】本题考查了整式的混合运算即实数的混合运算，熟练掌握运算顺序是解答本题的关键．（1）根据单项式乘以多项式运算法则计算即可；（2）先计算幂的乘方，再计算同底数幂的乘法和除法即可；（3）根据多项式乘以多项式运算法则计算即可；（4）先计算立方根和算式平方根，再计算乘法，最后计算减法即可．【详解】（1）解：原式3232335x x x x x x =×-×+×4326315x x x =-+；（2）解：原式462x x x =×¸48x x =¸4x =；（3）解：原式26946x x x =-+-2656x x =--；（4）解：原式()243=-´-83=--11=-．16．(1)(5)(5)x x x +-；(2)28()a b -．【分析】此题考查了分解因式．（1）先提取公因式，再用平方差公式分解因式；（2）先提取公因式，再用完全平方公式分解因式．【详解】（1）解：325x x -()225x x =-(5)(5)x x x =+-；（2）解：228168a ab b -+()2282a ab b =-+()28a b =-．17．312,13x --【分析】本题考查的是整式的混合运算，化简求值，先计算整式的乘法运算，再合并同类项，最后把13x -=代入计算即可．【详解】解：()()()2133423x x x x -+-+222669812x x x x x =-++--312x =-；当13x -=时，原式1312112133=-´-=--=-．18．6【分析】根据已知条件列出关于,a b 的方程组，然后解方程组，求出,a b 的值，最后代入2a b +计算，最后再求算术平方根．【详解】解：由题可知()()239522a b a ì+=-ïí-=-ïî解方程组得164a b =ìí=î将164a b =ìí=î代入2a b +得216436´+=6=∴2a b +的算术平方根为6【点睛】本题考查了二元一次方程组、平方根、立方根、算术平方根、掌握相关知识并正确计算是解题关键．19．52【分析】本题考查了多项式乘多项式，多项式不含某项的问题，先列式求出多项式的乘积，再根据乘积中不含x 的一次项，得到一次项的系数为0，据此即可求解，掌握多项式乘多项式的运算法则是解题的关键．【详解】解：()()()()2322525210x x mx x m x m x -++=+-+--，∵乘积中不含x 的一次项，∴52m 0-=，∴52m =．20．(1)二；去括号未变号；(2)见解析．【分析】本题考查了整式的运算，涉及到了完全平方公式的展开，熟悉掌握运算的法则是解题的关键．（1）根据运算法则逐步判断即可；（2）根据运算法则运算即可．【详解】（1）解：由题意可得：该学生解答过程是从第二步开始出错，其错误原因是去括号未变号；故答案为：二；去括号未变号；（2）解：正确过程为：2(1)(3)a a a +--原式22(69)a a a a =+--+2269a a a a =+-+-79a =-21．43231232x x x -+-【分析】先用错误的结果减去23x -求得原多项式，再乘以23x -即可解答．【详解】这个多项式是()22222111131341222x x x x x x x x -+--=-++=-+正确的计算结果是：242231341123223x x x x x x æö-×-+=-+-ç÷èø．【点睛】本题考查了单项式与多项式相乘，整式的加减，熟练掌握单项式与多项式相乘运算法则是解答本题的关键．22．（1）见解析；（2）见解析【分析】（1）由已知条件，结合对顶角相等可以利用AAS 判定ABO DCO D @D ，由全等三角形的性质可得；（2）由全等三角形的性质和等边对等角得结论．【详解】证明：（1）在ABO D 和DCO D 中，AOB COD ABO DCO AB DC Ð=ÐìïÐ=Ðíï=î，()ABO DCO AAS \D @D ，AO DO \=；（2）由（1）知，ABO DCO D @D ，OB OC\=OBC OCB \Ð=Ð．【点睛】本题考查了全等三角形的判定，等边对等角，解题的关键是熟练掌握常见的判定三角形全等的方法．23．32；(2)3．【分析】本题主要考查了无理数的估算，二次根式的化简求值等知识点，（1）根据无理数的估算方法，确定出整数部分，进而求解即可；（2）先求出,m n 的值，代入代数式，求值即可；熟练掌握“夹逼法”进行无理数的估算是解题的关键．【详解】（1）∵34<<，3；∵23<<，∴425<<，∴2242=；32-；（2）∵56<<，m的整数部分，∴5m =，∵23<<，n 的小数部分，∴2n ，∴523m n +==．24．(1)2，5，11；(2)()2222a b a ab b +=++；(3)8．【分析】（1）根据题意，得()()22252115a b a b a ab b ++=++，结合A 种卡片的面积为2a ，B种卡片的面积为2b ，C 种卡片的面积为ab ，解答即可．（2）根据图形整体面积等于各部分面积之和即可解答．（3）根据题意，得2x y -=，结合22x y 34+=，()()224x y x y xy +=-+，表示阴影的面积解答即可．【详解】（1）解：根据题意，得()()22252115a b a b a ab b ++=++，∵A 种卡片的面积为2a ，B 种卡片的面积为2b ，C 种卡片的面积为ab ，∴需要A 号卡片2张，B 号卡片5张，C 号卡片11张．故答案为：2，5，11．（2）解：根据题意，得()2222a b a ab b +=++，故答案为：()2222a b a ab b +=++．（3）解：根据题意，得2x y -=，∴()22224x y x xy y -=-+=，∵22x y 34+=，∴15xy =，∴()2441564x y +=+´=，∴8,8x y x y +=+=-(舍去)，∴8x y +=，∴()11·22S BE y x x y =+-阴影1122822y x x y =´+´=+=．【点睛】本题考查了完全平方公式的计算，多项式乘以多项式，完全平方公式变形计算，正方形的性质，熟练掌握公式是解题的关键．。

吉林省长春市东北师范大学西湖实验学校2024-2025学年八年级上学期九月份月考数学试题

吉林省长春市东北师范大学西湖实验学校2024-2025学年八年级上学期九月份月考数学试题一、单选题1．下列各数0.5，227，）A ．0.5B ．227C ．D 2．下列计算正确的是（）A ．326a a a ⋅=B ．623a a a ÷=C ．()326a a -=D ．()2326ab a b = 3．通过如下尺规作图，能确定点D 是BC 边中点的是（）A ．B ．C ．D ．4．如图，ABC CDE △△≌，若35D ∠=︒，45ACB ∠=︒，则DCE ∠的度数为（）A ．90︒B ．100︒C ．110︒D ．120︒5．计算：23213a b c ab -÷=（）A ．27ab -B ．27ab c -C ．27ab cD ．7abc - 6．如图，为了让电线杆垂直于地面，工程人员的操作方法是：从电线杆DE 上一点A 往地面拉两条长度相等的固定绳AB 和AC ，点B 、E 、C 在同一直线上时，电线杆DE 就垂直于BC ，工程人员这种操作方法的依据是（）A ．等边对等角B ．垂线段最短C ．等腰三角形的三线合一D ．DE 是BC 的垂直平分线 7．如图，是利用割补法求图形面积的示意图，下列公式中与之相对应的是（）A ．222()2a b a ab b +=++B ．222()2a b a ab b -=-+C ．22()()a b a b a b +-=-D ．222()ab a b =8．如图，在Rt ABC △中，90BAC ∠=︒，AB AC =，分别过点B ，C 作过点A 的直线的垂线BD CE ，．若4cm BD =，3cm CE =，则DE 的长为（）cmA ．7B ．8C ．9D ．10二、填空题9．计算：()2332x y xy ⋅-=．10．命题“三角形的三个内角中至少有两个锐角”是（填“真命题”或“假命题”）．11．在ABC V 中，AD 为ABC V 的中线，13AE AD =，18ABC S =V ，则ACE S =V ．12．计算：()()()()()24816231313131311⨯++++++=．13．已知a m =10，a n =5，则2m n a -=14．如图，根据下列条件，能说明ACD ABD △△≌的是（填写正确的序号）①BD DC =，AB AC =；②ADB ADC ∠=∠，BAD CAD ∠=∠③C B ∠=∠，BAD CAD ∠=∠；④ADB ADC ∠=∠，AB AC =三、解答题15．先化简，再求值：()()()23a b a b a b ab +-+-+，其中35a =，2b =-． 16．图1、图2、均是66⨯的正方形网格，每个小正方形的边长均为1，每个小正方形的顶点称为格点，ABC V 的顶点均在格点上，只用无刻度的直尺，在给定的网格中，分别按下列要求画图，保留适当的作图痕迹．(1)在图1中的线段AB 上找一点D ，连接CD ，使BCD BDC ∠=∠；(2)在图2中的线段AC 上找一点E ，连接BE ，使ABE BAE ∠=∠．17．学校要举行校庆活动，现计划搭建舞台．有一座边长为b 的正方形场地，学生团队联合会献计献策提出两个方案：方案一：如图1，绕花坛搭建外围是正方形的“回”字形舞台（阴影部分），面积为1S ；方案二：如图2，在花坛的三面搭建“凹”字形舞台（阴影部分），面积为2S ；(1)请分别计算出1S 与2S 的面积．(2)比较1S 与2S 的大小18．如图，已知AC 平分BAD ∠，CE AB ⊥于E ，CF AF ⊥于F ，且BC DC =．求证：CFD CEB ≌△△．19．小聪学习多项式时研究了多项式值为0的问题，发现当0mx n +=或0px q +=时，多项式()()()2A mx n px q mpx mq np x nq =++=+++的值为0，把此时x 的值称为多项式A 的零点．(1)已知多项式()()213x x ++，则此多项式的零点为_______．(2)已知多项式()()()2212a B x bx c ax a x =-+=---有一个零点为2，求多项式B 的另一个零点．20．我国著名数学家曾说：数无形时少直觉，形少数时难入微，数形结合思想是解决问题的有效途径．请阅读材料完成：(1)算法赏析：若x 满足()()152x x --=，求()()2215x x -+-的值．解：设(1),(5),x a x b -=-=则()()152,x x ab --==(1)(5)4a b x x +=-+-=- ∴()()222215......x x a b -+-=+请继续完成计算．(2)算法体验：若x 满足()()3020580x x --=-，求()()223020x x -+-的值；(3)算法应用：如图，已知数轴上A 、B 、C 表示的数分别是m 、10、13．以AB 为边作正方形ABDE ，以AC 为边作正方形ACFG ，延长ED 交FC 于P ．若正方形ACFG 与正方形ABDE 面积的和为117，求长方形AEPC 的面积21．教材呈现：以下是华师版八年级上册数学教材第94页的部分内容．线段垂直平分线我们已经知道线段是轴对称图形，线段的垂直平分线是线段的对称轴，如图1，直线MN 是线段AB 的垂直平分线，P 是MN 上任一点，连结PA PB ，．将线段AB 沿直线MN 对折，我们发现PA 与PB 完全重合．由此即有：线段垂直平分线的性质定理线段垂直平分线上的点到线段两端的距离相等．已知：如图1，MN AB ⊥，垂足为点C 、AC BC =，点P 是直线MN 上的任意一点．求证：PA PB =．图中有两个直角三角形APC 和BPC ，只要证明这两个三角形全等，便可证得PA PB =．请根据所给教材内容，结合图①，写出“线段垂直平分线的性质定理”完整的证明过程．定理应用：（1）如图②，在ABC V 中，AB AC 、的垂直平分线分别交BC 于点D 、E ，垂足分别为M ，N ，30BC =，直接写出ADE V 的周长为__________．（2）如图③，在ABC V 中，AB AC =，AD BC ⊥，E 、P 分别是AB AD 、上任意一点，若5AB =，ABC V 的面积为30，直接写出BP EP +的最小值是__________．22．如图，在等腰直角ABC V 中，90B ??，AB BC =，16AC =，点D 从点A 出发以每秒2个单位长度的速度向终点C 运动，过点D 作DE AC ⊥交折线AB BC -于点E ，以DE 为边向右作长方形DEGF ，使2DF DE =，设点D 的运动时间为t 秒()08t <<．(1)用含t的代数式表示线段DE的长；(2)当点G落在BC边上时，求t的值；(3)求长方形DEGF与ABCV重叠部分图形的面积S与t之间的关系式；(4)点M为AC的中点，连接MG，当MG所在的直线垂直ABCV的一边时，直接写出t的值．。

Igcse-数学-历年真题-2

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。

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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.。