IGCSE数学试卷pastpaper

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a level数学备考经验分享容易拿a的数学,应该怎么备考 testdaily厚朴优学

a level数学备考经验分享容易拿a的数学,应该怎么备考testdaily厚朴优学a level数学介绍ciea level数学(9709)分为4张paper: p1、s1、m1、p3。

其中m1是力学(mechanics)，s1是统计学（statistics)，而p1和p3就是纯数(pure math)。

p1通常在a level的第一年学习，p3是在第二年学习。

p1包括一元二次方程、二次函数、三角函数、平面几何、圆的计算、数列、微分、积分这几大知识点，考试是考10道或者11道题，1小时45分钟做完。

p1考纲p3包括代数多项式、指数函数、三角函数、微分、积分、解高次方程、微分方程、向量、复数等，考试也是1小时45分钟10道题。

p3考纲p1作为igcse数学到a level数学的一个过渡，难度并不高，其中的一些知识点比如说基础的三角函数、二次函数及方程等都是体制内初中就已经学过的东西。

而微积分这些听起来“高大上”，其实很基础很容易“上手”。

但是对于p1千万不能掉以轻心，因为p3算是p1的进阶版，在p1学过的知识点上进行了深入扩展和拔高，比如说p1学的三角函数还是sin/cos/tan，p3就加入了cosec/cot/sec，如果基础没打好，p3是很难学懂的。

a level数学，务实基础才是关键。

a level数学备考工具“工欲善其事，必先利其器”，要想在a level纯数部分“顺利摘星”，首先要像做一桌满汉全席那样备好“食材”。

1. 计算器a level数学大考允许使用计算器，不仅可以用于加减乘除运算，还需要用计算器解方程、做微积分和三角函数。

大多数同学用的都是这款卡西欧fx-991科学计算器。

能画图的计算器是不允许的。

2. cie官方公式表大考时，剑桥官方会提供公式表，里面含盖了a level数学和高数所有的重要公式，但是要注意的是，不是每一个你需要的公式都会包括，所以不要过度依赖公式表，该好好背还是要背的。

2011 June igcse 英文数学试卷

This document consists of 19 printed pages and 1 blank page.IB11 06_0580_43/4RP© UCLES 2011[Turn over*8044643715*UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary EducationMATHEMATICS 0580/43Paper 4 (Extended) May/June 20112 hours 30 minutesCandidates answer on the Question Paper.Additional Materials: Electronic calculatorGeometrical instrumentsMathematical tables (optional)Tracing paper (optional)READ THESE INSTRUCTIONS FIRSTWrite your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.Answer all questions.If working is needed for any question it must be shown below that question. Electronic calculators should be used.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π use either your calculator value or 3.142.At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 130.© UCLES 20110580/43/M/J/11For Examiner's Use1 Lucy works in a clothes shop.(a) In one week she earned $277.20.(i) She spent 81of this on food.Calculate how much she spent on food. Answer(a)(i) $ [1](ii) She paid 15% of the $277.20 in taxes. Calculate how much she paid in taxes. Answer(a)(ii) $ [2](iii) The $277.20 was 5% more than Lucy earned in the previous week. Calculate how much Lucy earned in the previous week. Answer(a)(iii) $ [3](b) The shop sells clothes for men, women and children.(i) In one day Lucy sold clothes with a total value of $2200 in the ratio men : women : children = 2 : 5 : 4. Calculate the value of the women’s clothes she sold. Answer(b)(i) $ [2](ii) The $2200 was 7344of the total value of the clothes sold in the shop on this day. Calculate the total value of the clothes sold in the shop on this day. Answer(b)(ii) $ [2]© UCLES 2011 0580/43/M/J/11[Turn overUsex(a) (i) Draw the reflection of shape X in the x -axis. Label the image Y . [2](ii) Draw the rotation of shape Y , 90° clockwise about (0, 0). Label the image Z . [2](iii) Describe fully the single transformation that maps shape Z onto shape X .Answer(a)(iii)[2](b) (i) Draw the enlargement of shape X , centre (0, 0), scale factor21. [2](ii) Find the matrix which represents an enlargement, centre (0, 0), scale factor 21.Answer(b)(ii)[2](c) (i) Draw the shear of shape X with the x -axis invariant and shear factor –1.[2](ii) Find the matrix which represents a shear with the x -axis invariant and shear factor –1.Answer(c)(ii)[2]© UCLES 20110580/43/M/J/11Use(x + 5) cm2x cmx cmNOT TO SCALEThe diagram shows a square of side (x + 5) cm and a rectangle which measures 2x cm by x cm. The area of the square is 1 cm 2 more than the area of the rectangle.(a) Show that x 2 – 10x – 24 = 0 . Answer(a) [3]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(b) Find the value of x . Answer(b) x = [3](c) Calculate the acute angle between the diagonals of the rectangle. Answer(c) [3]© UCLES 2011 0580/43/M/J/11For Examiner's Use4NOT TO SCALEThe circle, centre O , passes through the points A , B and C . In the triangle ABC , AB = 8 cm, BC = 9 cm and CA = 6 cm. (a) Calculate angle BAC and show that it rounds to 78.6°, correct to 1 decimal place. Answer(a) [4](b) M is the midpoint of BC .(i) Find angle BOM . Answer(b)(i) Angle BOM = [1]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(ii) Calculate the radius of the circle and show that it rounds to 4.59 cm, correct to 3 significantfigures.Answer(b)(ii) [3](c) Calculate the area of the triangle ABC as a percentage of the area of the circle. Answer(c) % [4]© UCLES 2011 0580/43/M/J/11ForExaminer's Use5 (a) Complete the table of values for the function f(x ), where f(x ) = x 2 + 21x , x ≠ 0 .xO 3 O 2.5 O 2 O 1.5 O 1 O 0.50.5 1 1.5 2 2.5 3 f(x ) 6.41 2.69 4.25 4.252.69 6.41[3](b) On the grid, draw the graph of y = f(x ) for O 3 Y x Y O 0.5 and 0.5 Y x Y 3 .[5]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(c) (i) Write down the equation of the line of symmetry of the graph.Answer(c)(i)[1](ii) Draw the tangent to the graph of y = f(x ) where x = O 1.5. Use the tangent to estimate the gradient of the graph of y = f(x ) where x = O 1.5. Answer(c)(ii) [3](iii) Use your graph to solve the equation x 2 + 21x= 3.Answer(c)(iii) x = or x = or x = or x = [2](iv) Draw a suitable line on the grid and use your graphs to solve the equation x 2 + 21x = 2x .Answer(c)(iv) x =or x =[3]© UCLES 2011 0580/43/M/J/11For Examiner's Use6CumulativefrequencyMass (kilograms)mThe masses of 200 parcels are recorded. The results are shown in the cumulative frequency diagram above.(a) Find(i) the median, Answer(a)(i) kg [1](ii) the lower quartile, Answer(a)(ii) kg [1](iii) the inter-quartile range, Answer(a)(iii) kg [1](iv) the number of parcels with a mass greater than 3.5 kg. Answer(a)(iv) [2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(b) (i) Use the information from the cumulative frequency diagram to complete the groupedfrequency table.Mass (m ) kg0 I m Y 44 I m Y 66 I m Y 77 I m Y 10Frequency 36 50[2](ii) Use the grouped frequency table to calculate an estimate of the mean. Answer(b)(ii) kg [4](iii) Complete the frequency density table and use it to complete the histogram.Mass (m ) kg 0 I m Y 4 4 I m Y 6 6 I m Y 7 7 I m Y 10Frequency density916.7FrequencydensityMass (kilograms)m[4]© UCLES 20110580/43/M/J/11ForExaminer's Use7 Katrina puts some plants in her garden.The probability that a plant will produce a flower is107. If there is a flower, it can only be red, yellow or orange.When there is a flower, the probability it is red is 32 and the probability it is yellow is 41.(a) Draw a tree diagram to show all this information. Label the diagram and write the probabilities on each branch. Answer(a) [5](b) A plant is chosen at random. Find the probability that it will not produce a yellow flower. Answer(b) [3](c) If Katrina puts 120 plants in her garden, how many orange flowers would she expect? Answer(c) [2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use8A(a) Draw accurately the locus of points, inside the quadrilateral ABCD , which are 6 cm from thepoint D . [1](b) Using a straight edge and compasses only, construct(i) the perpendicular bisector of AB , [2](ii) the locus of points, inside the quadrilateral, which are equidistant from AB and from BC . [2](c) The point Q is equidistant from A and from B and equidistant from AB and from BC .(i) Label the point Q on the diagram. [1](ii) Measure the distance of Q from the line AB . Answer(c)(ii) cm [1](d) On the diagram, shade the region inside the quadrilateral which is• less than 6 cm from Dand• nearer to A than to Band• nearer to AB than to BC . [1]© UCLES 2011 0580/43/M/J/11For Examiner's Use9 f(x ) = 3x + 1 g(x ) = (x + 2)2(a) Find the values of(i) gf(2), Answer(a)(i)[2](ii) ff(0.5). Answer(a)(ii)[2](b) Find f –1(x ), the inverse of f(x ). Answer(b)[2](c) Find fg(x ). Give your answer in its simplest form. Answer(c)[2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(d) Solve the equation x 2 + f(x ) = 0. Show all your working and give your answers correct to 2 decimal places. Answer(d) x = or x =[4]UseBABCD is a parallelogram.DC, M is the midpoint of BC and N is the midpoint of LM.pq.(i)Find the following in terms ofp and q, in their simplest form.(a)Answer(a)[1](b)Answer(a)[2](c)Answer(a)[2] (ii) N lies on the line AC.Answer(a)(ii) [1]© UCLES 2011 0580/43/M/J/11© UCLES 2011 0580/43/M/J/11[Turn overUseEH J2x°75°(x + 15)°NOT TO SCALEEFG is a triangle. HJ is parallel to FG . Angle FEG = 75°. Angle EFG = 2x ° and angle FGE = (x + 15)°.(i) Find the value of x . Answer(b)(i) x = [2](ii) Find angle HJG . Answer(b)(ii) Angle HJG = [1]© UCLES 2011 0580/43/M/J/11For Examiner's Use11 (a) (i) The first three positive integers 1, 2 and 3 have a sum of 6. Write down the sum of the first 4 positive integers. Answer(a)(i) [1](ii) The formula for the sum of the first n integers is21)(+n n . Show the formula is correct when n = 3. Answer(a)(ii) [1](iii) Find the sum of the first 120 positive integers. Answer(a)(iii) [1](iv) Find the sum of the integers121 + 122 + 123 + 124 + …………………………… + 199 + 200.Answer(a)(iv)[2](v) Find the sum of the even numbers 2 + 4 + 6 + …………………………+ 800.Answer(a)(v)[2]© UCLES 20110580/43/M/J/11For Examiner's Use(b) (i) Complete the following statements about the sums of cubes and the sums of integers.13 = 1 1 = 113 + 23 = 9 1 + 2 = 3 13 + 23 + 33 =1 +2 +3 =13 + 23 + 33 + 43 =1 +2 +3 +4 =[2](ii) The sum of the first 14 integers is 105. Find the sum of the first 14 cubes. Answer(b)(ii) [1](iii) Use the formula in part(a)(ii) to write down a formula for the sum of the first n cubes. Answer(b)(iii) [1](iv) Find the sum of the first 60 cubes. Answer(b)(iv) [1](v) Find n when the sum of the first n cubes is 278 784. Answer(b)(v) n = [2]BLANK PAGEPer mission to r epr oduce items wher e thir d-par ty owned mater ial pr otected by copyr ight is included has been sought and clear ed wher e possible. Ever y reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.© UCLES 2011 0580/43/M/J/11。

0606_m19_qp_12(IGCSE 数学考试2019年3月真题

Identities Formulae for ∆ABC
2. TRIGONOMETRY
sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A
a sin A
=
b sin B
=
c sin C
a2 = b2 + c2 – 2bc cos A
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 number of marks for this paper is 80.
∆
=
1 2
bc
sin
A
© UCLES 2019
0606/12/F/M/19
3
1 (a) Given that
பைடு நூலகம்
= { x : 1 1 x 1 20},
A = {multiples of 3},
B = {multiples of 4},
find
(i)
n (A),
[1]
(ii)
n (A + B) .
[1]
*6715046212*
Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education

Igcse-数学-历年真题

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。

Igcse 数学历年真题

4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010 – AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: . (2).There are 22 questions in this question paper. The total mark for this paperis 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.This publication may be reproduced only in accordance with Edexcel Limited copyright policy.©2010 Edexcel Limited.Printer’s Log. No. N36905AIGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write down all stages in your working.1. Solve 6 y – 9 = 3 y + 7y = ................................(Total 3 marks) 2. The diagram shows two towns, A and B, on a map.(a) By measurement, find the bearing of B from A.....................................(2)C is another town.The bearing of C from A is 050.(b) Find the bearing of A from C.....................................(2)(Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will land on red isThe probability that it will land on blue isImad spins the spinner once.(a) Work out the probability that it will land on yellow......................................(2)Janet spins the spinner 30 times.(b)Work out an estimate for the number of times the spinner will land on blue......................................(2)(Total 4 marks)4. Rosetta drives 85 kilometres in 1 hour 15 minutes.(a) Work out her average speed in kilometres per hour...................................... km/h(2)Rosetta drives a total distance of 136 kilometres.(b) Work out 85 as a percentage of 136................................. %(2)Sometimes Rosetta travels by train to save money.The cost of her journey by car is £12The cost of her journey by train is 15% less than the cost of her journey by car.(c)Work out the cost of Rosetta’s journ ey by train.£ ...................................(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant figures.x = ................................(Total 3 marks)6. A = {2, 3, 4, 5}B = {4, 5, 6, 7}(a)(i) List the members of A B......................................(ii) How many members are in A B?.....................................(2)ℰ = {3, 4, 5, 6, 7}P = {3, 4, 5}Two other sets, Q and R, each contain exactly three members.P Q = {3, 4}P R = {3, 4}Set Q is not the same as set R.(b)(i) Write down the members of a possible set Q......................................(ii) Write down the members of a possible set R......................................(2)(Total 4 marks)7. Rectangular tiles have width (x + 1) cm and height (5x – 2) cm.Some of these tiles are used to form a large rectangle.The large rectangle is 7 tiles wide and 3 tiles high.The perimeter of the large rectangle is 68 cm.(a) Write down an equation in x...............................................................................................................(3)(b) Solve this equation to find the value of x.x = ................................(3)(Total 6 marks)8. Show that 121 141 = 1519. The depth of water in a reservoir increases from 14 m to m.Work out the percentage increase.................................. %(Total 3 marks)10. Quadrilaterals ABCD and PQRS are similar.AB corresponds to PQ.BC corresponds to QR.CD corresponds to RS.Find the value of(a) xx = ...............................(2)(b) yy = ...............................(1)(Total 3 marks)11. Simplify fully6x + 43x.....................................(Total 3 marks)12.(a)Find the equation of the line L......................................(3)(b) Find the three inequalites that define the unshaded region shown in the diagram below................................................................................................................(3)(Total 6 marks)13. (a) Solve x 2– 8x + 12 = 0.....................................(3)(b) Solve the simultaneous equationsy = 2x4x – 5y = 9x = ................................y = ................................(3)(Total 6 marks)14.The area of the triangle is cm2.The angle x° is acute.Find the value of x.Give your answer correct to 1 decimal place.x = ................................(Total 3 marks)15. The unfinished histogram shows information about the heights, h metres, ofsome trees.(a) Calculate an estimate for the number of trees with heights in theinterval < h ≤ 10.....................................(3)(b) There are 75 trees with heights in the interval 10 < h ≤ 13Use this information to complete the histogram.(2)(Total 5 marks)16. A bag contains 3 white discs and 1 black disc.John takes at random 2 discs from the bag without replacement.(a) Complete the probability tree diagram.First disc Second disc(3)(b)Find the probability that both discs are white......................................(2)All the discs are now replaced in the bag.Pradeep takes at random 3 discs from the bag without replacement.(c)Find the probability that the disc left in the bag is white......................................(3)(Total 8 marks)17. The diagram shows a sector of a circle, radius 45 cm, with angle 84°.Calculate the area of the sector.Give your answer correct to 3 significant figures.............................. cm2(Total 3 marks) 18.Calculate the length of AC.Give your answer correct to 3 significant figures................................ cm(Total 3 marks)19. A cone has slant height 4 cm and base radius r cm.The total surface area of the cone is 433π cm 2.Calculate the value of r .r = ................................(Total 4 marks)20. f(x) = (x – 1)2(a) Find f(8).....................................(1)The domain of f is all values of x where x ≥ 7(a)Find the range of f......................................(2)xg(x) =x1(c) Solve the equation g(x) =.....................................(2)(d) (i) Express the inverse function g –1 in the form g –1(x) = .......g –1(x) = ...................................(ii) Hence write down gg(x) in terms of x.gg(x) = ....................................(6)(Total 11 marks)21.In the diagram OA= a and OC= c.(a) Find CA in terms of a and c......................................(1)The point B is such that AB=1c.2(b) Give the mathematical name for the quadrilateral OABC......................................(1)The point P is such that OP= a + k c, where k ≥ 0(c) State the two conditions relating to a + k c that must be true for OAPCto be a rhombus.(2)(Total 4 marks)22. (a) Work out × 102+ × 104Give your answer in standard form......................................(2)a × 102 +b × 104 =c × 104(b) Express c in terms of a and b.c = ................................(2)(Total 4 marks)TOTAL FOR PAPER = 100 MARKSEND。

2018年深圳国际交流学院G1入学考试数学数学模拟试卷1

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则称抛物线 C1，C2 互为“友好抛物线”．关于“友好抛物线”有以下说法：（1） C1，C2 开口方向、开口大小相同; (2) C1，C2 的对称轴相同；(3) 如果 y2 的最值为 m，则 y1 的最值为 km； (4 ) 如果 C2 与 x 轴的两交点间距离为 d，则 C1 与 x 轴的两交点间距离也为 d．其中正确的结论是
3，4 对应密文 5，7，18，16．当接收方收到密文 14，9，23，28 时，则解密得到的明文为（
）
A． 7，6，1，4
B． 6，4，1，7
C． 4，6，1，7
D． 1，6，4，7
4．若一元二次方程式 ax（x+1）+（x+1）（x+2）+bx（x+2）=2 的两根为 0、2，则|3a+4b|的值
（把所有正确结论的序号都填在横线上）．
2
12．如图是我省某地一座抛物线形拱桥，桥拱在竖直平面内，与水平桥面相交于 A、B 两点，拱
桥最高点 C 到 AB 的距离为 9m，AB=36m，D、E 为拱桥底部的两点，且 DE ⊥AB，点 E 到直线

G10 Final Test Paper(国际学校数学)

1、Which of the following equations is true?( ).A.7×(2+3)=3+(7×2)B.7×(2+3)=7+(2×3)C.7×(2+3)=3×(2+7)D.7×(2+3)=7×(3+2)2、Which of the following is closest to the value of the expression below?( ).A.4B. 5C. 9D. 113、A container of soup is in the shape of a right circular cylinder. The container and its dimensions are shown below.What is the volume, in cubic centimeters, of the container?( ).A.200πB. 160πC. 80πD. 40π4、Which of the following is equivalent to the expression below? ( ).A.P2-2p-8B.p2-4p-2C. p2-8D. p2-25、Which of the following values of x is a solution of the equation below? ( ).A.4B. 16C. 128D. 5126、A waiter received a 15% tip for a restaurant bill of $59.14. Which of the following estimates is closest to the tip the waiter received? ( ).A.$5.00B. $7.50C. $9.00D. $12.007、The weights, in pounds, of 7 packages are listed below.The weight of an 8th package is added to the list. The mean weight of the 8 packages is 12 pounds. What is the weight, in pounds, of the 8th package?( ).A.19B. 16C. 11D. 108、Point S is the midpoint of RT. The coordinates of point R and point T are listed below.What are the coordinates of point S ?( ).R(-11, -12) T(-7, -4)A.(-2, -4)B. (-8, -10)C. (-9, -8)D. (-18, -16)9、Which of the following is equivalent to the expression below?( ).A.(x-1)(x-144)B. (x-1)(x+144)C. (x-12)(x-12)D. (x-12)(x+12)10、A rug in the shape of a square has an area of 33 square feet. Which of the following estimates is closest to the length of each side of the rug?( ).A.415feetB. 435feetC.436feetD. 418feet11、A set of data is shown in the scatterplot below,Which of the following equations best represents the line of best fit for the data in the scatterplot?( ).A.221--=x yB. 121+-=x yC.221-=x yD. 121+=x y12、A parallelogram and some of its dimensions are shown below.The area of the parallelogram is 90 square inches. What is h, the height in inches of the parallelogram?( ).A. 6B. 8C. 10D. 12 13、Which of the following expressions is equivalent to 17?( ). A.3173⋅ B.31731⋅ C.3317 D. 3317 14、Two groups are going on a trip to a theater. The first group has 30 students and 4 adult chaperones. The second group has 25 students and 4 adult chaperones. The cost, in dollars, for each student ticket, s, and each adult ticket, a, can be determined using the system of equations below. ( ).What is the cost for each student ticket?A. $5B. $20C. $25D. $30Questions 15 and 16 are short -answer questionsWhat is the value of the expression below?16、The line plot below shows the number of red items of clothing owned by each student in a class.What is the median number of red items of clothing owned by the students in the class?17、Rectangle ABCD is similar to rectangle EFGH. The rectangles and some of their dimensions are shown in the diagram below.Based on the dimensions in the diagram, what is the value of x?18、The equation below has two solutions.One solution of the equation is 3. What is the other solution of the equation?19、A company packages fruit baskets of different weights and ships them to customers. The company charges a flat fee for packaging the baskets. The total packaging and shipping cost in dollars, y, of a fruit basket weighing x pounds is represented by the line on the graph below.a.What is the y-intercept of the line on the graph?b. What does the y-intercept of the line represent in this situation?c. What is the slope of the line on the graph? Show or explain how you got your answer.d. What does the slope of the line represent in this situation?e. Write an equation that represents the line on the graph.f. Use the equation you wrote in part (e) to determine the weight, in pounds, of the heaviest fruit basket that could be packaged and shipped for $50. Show or explain how you got your answer.。

IGCSE Maths past paper数学考试题

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
10
In the boxes above, write your centre number and candidate number, your surname, initial(s) and
signature.
11
The paper reference is shown at the top of this page. Check that you have the correct question paper.
Surface area of sphere = 4πr2
r
l
h
r
hyp
θ adj
adj = hyp × cos θ opp = hyp × sin θ opp opp = adj × tan θ
or sinθ = opp hyp
In any triangle ABC C
b
a
cosθ = adj hyp
Mathematics
Paper 3H
Higher Tier
Monday 10 May 2004 – Morning Time: 2 hours
Page Leave Numbers Blank
3
4
5
Materials required for examination Items included with question papers

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。

九天国际教育GCSE真题November 2016 (v3) QP - Paper 5 CIE Chemistry IGCSE

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.Electronic calculators may be used.You may lose marks if you do not show your working or if you do not use appropriate units.Practical notes are provided on pages 11 and 12.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.CHEMISTRY0620/53Paper 5 Practical TestOctober/November 20161 hour 15 minutesCandidates answer on the Question Paper.Additional Materials:As listed in the Confidential InstructionsCambridge International ExaminationsCambridge International General Certificate of Secondary EducationThis document consists of 9 printed pages and 3 blank pages.[Turn overIB16 11_0620_53/2RP © UCLES 2016The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.For Examiner’s Use Total1Y ou are going to investigate what happens when two different metals, iron and magnesium, react with aqueous copper(II) sulfate.R ead all the instructions carefully before starting the experiments.I nstructionsY ou are going to carry out two experiments.(a)Experiment 1U se a measuring cylinder to pour 25 cm3 of aqueous copper(II) sulfate into the polystyrenecup provided. Put the polystyrene cup into a 250 cm3 beaker for support. Measure the initialtemperature of the solution and then the temperature after 30 seconds and 60 seconds. Recordyour results in the table.A t 60 seconds add all of the iron to the aqueous copper(II) sulfate and stir the mixturecontinuously with the thermometer.M easure the temperature of the mixture every 30 seconds for 300 seconds (5 minutes). Recordyour results in the table.time / s0306090120150180210240270300 temperature/ °C[2](b)Experiment 2E mpty the polystyrene cup and rinse it with water.U se a measuring cylinder to pour 25 cm3 of aqueous copper(II) sulfate into the polystyrenecup. Put the polystyrene cup into a 250 cm3 beaker for support. Measure the initial temperatureof the solution and then the temperature after 30 seconds and 60 seconds. Record your resultsin the table.A t 60 seconds add all of the magnesium to the aqueous copper(II) sulfate and stir the mixturecontinuously with the thermometer.M easure the temperature of the mixture every 30 seconds for 300 seconds (5 minutes). Recordyour results in the table.time / s0306090120150180210240270300 temperature/ °C[2](c) P lot the results for Experiments 1 and 2 on the grid and draw two smooth line graphs.C learly label the graphs.908070605040302010060120180time / stemperature / °C240300360[4](d) (i) F rom your graph , deduce the temperature of the mixture in Experiment 1 after135 seconds.S how clearly on the grid how you worked out your answer............................................ °C [2](ii) F rom your graph , deduce the time taken for the temperature of the mixture in Experiment 2 to change by 30 °C after the magnesium was added .S how clearly on the grid how you worked out your answer.............................................. s [2](e)P redict the temperature of the mixture in Experiment 2 after one hour. Explain your answer..................................................................................................................................................... (2)(f)S uggest an advantage of taking the temperature readings every 15 seconds..................................................................................................................................................... (2)(g)E xplain why a polystyrene cup is used in the experiments and not a copper can..................................................................................................................................................... (2)[Total: 18]2Y ou are provided with two solutions, solution Q and solution R.C arry out the following tests on solution Q and solution R, recording all of your observations at eachstage.tests on solution Q(a)D ivide solution Q into four equal portions in four test-tubes. Carry out the following tests.(i)U se pH indicator paper to measure the pH of the first portion of solution Q.pH (1)(ii)A dd a 2 cm strip of magnesium ribbon to the second portion of solution Q. Test the gas given off.R ecord your observations.............................................................................................................................................. (2)(iii) A dd a spatula measure of sodium carbonate to the third portion of solution Q. Test the gas given off.R ecord your observations.............................................................................................................................................. (2)(iv)A dd a few drops of dilute nitric acid and about 1 cm3 of aqueous barium nitrate to the fourth portion of solution Q.R ecord your observations. (1)tests on solution R(b)Divide solution R into four equal portions in four test-tubes. Carry out the following tests.(i)M easure the pH of the first portion of solution R.pH (1)(ii)A dd several drops of aqueous sodium hydroxide to the second portion of solution R and shake the test-tube.T hen add excess aqueous sodium hydroxide to the test-tube.R ecord your observations.............................................................................................................................................. (2)(iii)A dd aqueous silver nitrate to the third portion of solution R and leave to stand for about5 minutes.R ecord your observations.............................................................................................................................................. (2)(iv)A dd a spatula measure of iron(II) sulfate crystals to the fourth portion of solution R and shake the mixture.R ecord your observations. (1)(c)I dentify solution Q. (2)(d)I dentify solution R. (2)[Total: 16]3A liquid cleaner is a mixture of three substances. These substances are shown in the table.name of substance properties of substancewater liquid, boiling point 100 °Csodium carbonate solid, soluble in watersilica solid, insoluble in waterP lan experiments to obtain separate pure samples of each substance from the mixture in the liquid cleaner. You are provided with common laboratory apparatus.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... (6)[Total: 6]NOTES FOR USE IN QUALITATIVE ANALYSIS Test for anions aniontesttest resultcarbonate (CO 32–)add dilute acideffervescence, carbon dioxide produced chloride (C l –)[in solution]acidify with dilute nitric acid, then add aqueous silver nitratewhite ppt.bromide (Br –)[in solution]acidify with dilute nitric acid, then add aqueous silver nitratecream ppt.iodide (I –)[in solution]acidify with dilute nitric acid, then add aqueous silver nitrateyellow ppt.nitrate (NO 3–)[in solution]add aqueous sodium hydroxide then aluminium foil; warm carefully ammonia produced sulfate (SO 42–)[in solution]acidify, then add aqueous barium nitratewhite ppt.sulfite (SO 32–)add dilute hydrochloric acid, warm gently and test for the presence of sulfur dioxidesulfur dioxide produced will turn acidified aqueous potassium manganate(VII ) from purple to colourlessTest for aqueous cations cationeffect of aqueous sodium hydroxide effect of aqueous ammonia aluminium (A l 3+)white ppt., soluble in excess giving a colourless solutionwhite ppt., insoluble in excessammonium (NH 4+)ammonia produced on warming –calcium (Ca 2+)white ppt., insoluble in excessno ppt. or very slight white ppt.chromium(III ) (Cr 3+)green ppt., soluble in excess grey-green ppt., insoluble in excess copper (Cu 2+)light blue ppt., insoluble in excess light blue ppt., soluble in excess giving a dark blue solution iron(II ) (Fe 2+)green ppt., insoluble in excess green ppt., insoluble in excess iron(III ) (Fe 3+)red-brown ppt., insoluble in excess red-brown ppt., insoluble in excess zinc (Zn 2+)white ppt., soluble in excess giving a colourless solutionwhite ppt., soluble in excess, giving a colourless solutionPermission 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.Test for gases Flame tests for metal ions gastest and test resultsmetal ion flame colour ammonia (NH 3)turns damp, red litmus paper bluelithium (Li +)red carbon dioxide (CO 2)turns limewater milky sodium (Na +)yellow chlorine (C l 2)bleaches damp litmus paper potassium (K +)lilac hydrogen (H 2)‘pops’ with a lighted splint copper(II ) (Cu 2+)blue-greenoxygen (O 2)relights a glowing splintsulfur dioxide (SO 2)turns acidified aqueouspotassium manganate(VII ) from purple to colourless。

ALEVEL IGCSE 数学试卷-1汇编

• Note:
B2 or A2 means that the candidate can earn 2 or 0. B2/1/0 means that the candidate can earn anything from 0 to 2.
The marks indicated in the scheme may not be subdivided. If there is genuine doubt whether a candidate has earned a mark, allow the candidate the benefit of the doubt. Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored.
A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. Accuracy marks cannot be given unless the associated method mark is earned (or implied).
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Subsidiary and Advanced Level
MARK SCHEME for the May/June 2015 series

accurate)

IGCSE数学试卷 past paper汇编

*0835058084*ADDITIONAL MATHEMATICS 0606/11Paper 1October/November 20122 hoursCandidates answer on the Question Paper.Additional Materials:Electronic calculator.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.Y ou may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid.Answer all the questions.Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.The use of an electronic calculator is expected, where appropriate.Y ou are reminded of the need for clear presentation in your answers.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 number of marks for this paper is 80.For Examiner’s Use 1 2 3 4 5 6 7 8 9101112TotalUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary EducationForExaminer’s UseMathematical Formulae1. ALGEBRA Quadratic EquationFor the equation ax 2 + bx + c = 0,x=Binomial Theorem(a + b )n = a n + (n 1)a n –1 b + (n 2)a n –2 b 2 + … + (nr )a n–rb r + … + b n ,where n is a positive integer and (n r )=n !(n – r )!r !2. TRIGONOMETRY Identitiessin 2 A + cos 2 A = 1sec 2 A = 1 + tan 2 A cosec 2 A = 1 + cot 2 AFormulae for ∆ABCa sin A =b sin B =csin C a 2 = b 2 + c 2 – 2bc cos A∆ = 1 2bc sin AForExaminer’s Use1 (i) Sketch the graph of y = |3 + 5x |, showing the coordinates of the points where your graphmeets the coordinate axes. [2](ii) Solve the equation |3 + 5x | = 2. [2]2 Find the values of k for which the line y = k – 6x is a tangent to the curve y = x (2x + k ). [4]For Examiner’s Use3Given that p = log q 32, express, in terms of p ,(i) log q 4,[2](ii) log q 16q . [2]4 Using the substitution u = 5x , or otherwise, solve52x +1 = 7(5x ) – 2.[5]For Examiner’s Use5Given that y =x 2cos 4x, find (i) d yd x,[3](ii) the approximate change in y when x increases from π4 to π4+ p , where p is small.[2]For 6 (i) Find the first 3 terms, in descending powers of x, in the expansion of ΂x + 2x2΃6. [3]Examiner’sUse (ii) Hence find the term independent of x in the expansion of ΂2 – 4x3΃΂x + 2x2΃6. [2]For Examiner’s Use7Do not use a calculator in any part of this question.(a) (i) Show that 3 5 – 2 2 is a square root of 53 – 1210. [1](ii) State the other square root of 53 – 1210. [1](b)a +b 6, where a and b are integers to be found.[4]For Examiner’s Use8The points A (–3, 6), B (5, 2) and C lie on a straight line such that B is the mid-point of AC .(i) Find the coordinates of C .[2]The point D lies on the y -axis and the line CD is perpendicular to AC .(ii) Find the area of the triangle ACD . [5]ForExaminer’s Use9A function g is such that g(x ) = 12x – 1 for 1р x р 3. (i) Find the range of g.[1](ii) Find g –1(x ). [2](iii) Write down the domain of g –1(x ). [1](iv) Solve g 2(x ) = 3.[3]For Examiner’s Use10 The table shows values of the variables x and y .x 10°30°45°60°80°y11.21619.522.424.7(i) Using the graph paper below, plot a suitable straight line graph to show that, for10° р x р 80°,y = A sin x + B , where A and B are positive constants.[4](ii) Use your graph to find the value of A and of B. [3]ForExaminer’sUse (iii) Estimate the value of y when x = 50. [2](iv) Estimate the value of x when y = 12. [2]For 11 (a) Solve cosec ΂2x – π3΃ = 2 for 0 < x < π radians. [4]Examiner’sUse(i) Given that 5(cos y + sin y)(2 cos y – sin y) = 7, show that 12 tan2y – 5 tan y – 3 = 0. [4](b)(ii) Hence solve 5(cos y + sin y)(2 cos y – sin y) = 7 for 0° < x < 180°. [3]ForExaminer’sUseForExaminer’sUse 12 Answer only one of the following two alternatives.EITHERThe diagram shows part of the graph of y = (12 – 6x)(1 + x)2, which meets the x-axis at thepoints A and B. The point C is the maximum point of the curve.(i) Find the coordinates of each of A, B and C. [6](ii) Find the area of the shaded region. [5]ORThe diagram shows part of a curve such that d yd x = 3x2 – 6x – 9. Points A and B are stationarypoints of the curve and lines from A and B are drawn perpendicular to the x-axis. Given that the curve passes through the point (0, 30), find(i) the equation of the curve, [4](ii) the x-coordinate of A and of B, [3](iii) the area of the shaded region. [4]For Examiner’s UseStart your answer to Question 12 here.Indicate which question you are answering. EITHEROR .....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................Continue your answer here if necessary.ForExaminer’sUse ................................................................................................................................................................... ................................................................................................................................................................... ................................................................................................................................................................... ................................................................................................................................................................... ................................................................................................................................................................... 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...................................................................................................................................................................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.。

剑桥IGCSE课程数学科目试卷四

UCLES 2007
Answer(c)
0607/04/SP/10
minutes [3] [Turn over
4 2 f(x) = 5 .
1− x (a) Find f(–9).
For Examiner's
Use
(b) Solve f(x) = 2.
Answer(a)
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. You may use a pencil for any diagrams or graphs.
For Examiner's
Use
Answer(a)
km/h [2]
(b) One day, the train departed at 08 50 but, due to delays, the average speed was reduced by 10%. Calculate (i) the new arrival time,
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
CAMBRIDGE INTERNATIONAL MATHEMATICS Paper 4 (Extended) SPECIMEN PAPER

2013年CIE剑桥国际考试IGCSE数学真题(43)

READ THESE INSTRUCTIONS FIRSTWrite your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction ﬂ uid.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 speci ﬁ ed in the question, and if the answer is not exact, give the answer to three signi ﬁ cant ﬁ gures. 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.MATHEMATICS0580/43Paper 4 (Extended)May/June 20132 hours 30 minutesCandidates answer on the Question Paper.Additional Materials:Electronic calculator Geometrical instrumentsTracing paper (optional)UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certi ﬁ cate of Secondary EducationThis document consists of 19 printed pages and 1blank page.[Turn overIB13 06_0580_43/5RP © UCLES 2013*9687546924*0580/43/M/J/13© UCLES 2013ForExaminer ′s Use1 (a) A li and Ben receive a sum of money. T hey share it in the ratio 5 : 1. A li receives $2345.C alculate the total amount. Answer(a) $ (2)(b) A li uses 11% of his $2345 to buy a television.C alculate the cost of the television. Answer(b) $ (2)(c) A different television costs $330.(i) B en buys one in a sale when this cost is reduced by 15%.H ow much does Ben pay? Answer(c)(i) $ (2)(ii) $330 is 12% less than the cost last year.C alculate the cost last year. Answer(c)(ii) $ (3)0580/43/M/J/13© UCLES 2013[Turn overFor Examiner ′s Use(d) Ali invests $1500 of his share in a bank account.The account pays compound interest at a rate of 2.3% per year.Calculate the total amount in the account at the end of 3 years.Answer(d) $ (3)(e) Ali also buys a computer for $325.He later sells this computer for $250.Calculate Ali’s percentage loss.Answer(e) ........................................... % [3]_____________________________________________________________________________________0580/43/M/J/13© UCLES 2013For Examiner ′s Use2(a) I n this question show all your construction arcs and use only a ruler and compasses to drawthe boundaries of your region.T his scale drawing shows the positions of four towns, P , Q , R and S , on a map where 1 cm represents 10 km.SScale: 1 cm to 10 kmA nature reserve lies in the quadrilateral PQRS . The boundaries of the nature reserve are:● equidistant from Q and from R ● equidistant from PS and from PQ ● 60 km from R ● along QR .(i) S hade the region which represents the nature reserve. [7](ii) M easure the bearing of S from P .Answer(a)(ii) (1)0580/43/M/J/13© UCLES 2013[Turn overFor Examiner ′s Use(b) A circular lake in the nature reserve has a radius of 45 m.(i) Calculate the area of the lake.Answer(b)(i) .......................................... m 2 [2](ii)NOT TO SCALEA fence is placed along part of the circumference of the lake. This arc subtends an angle of 210° at the centre of the circle.Calculate the length of the fence.Answer(b)(ii) ........................................... m [2] _____________________________________________________________________________________For3 (a)Luk wants to buy x goats and y sheep.Examiner′sUse(i)H e wants to buy at least 5 goats.Write down an inequality in x to represent this condition.Answer(a)(i) (1)(ii)H e wants to buy at least 11 sheep.Write down an inequality in y to represent this condition.Answer(a)(ii) (1)(iii)H e wants to buy at least 20 animals.W rite down an inequality in x and y to represent this condition.Answer(a)(iii) (1)(b)G oats cost $4 and sheep cost $8.The maximum Luk can spend is $160.Write down an inequality in x and y and show that it simpliﬁ es to x + 2y Y 40 .Answer(b)[1]© UCLES 20130580/43/M/J/130580/43/M/J/13© UCLES 2013[Turn overFor Examiner ′s Use(c) (i) O n the grid below, draw four lines to show the four inequalities and shade the unwanted regions.[7](ii) Work out the maximum number of animals that Luk can buy.Answer(c)(ii) ............................................... [2]_____________________________________________________________________________________0580/43/M/J/13© UCLES 2013For Examiner ′s Use4IGEFJH40 cm22 cm7 cmNOT TO SCALEEFGHIJ is a solid metal prism of length 40 cm. The cross section EFG is a right-angled triangle. EF = 7 cm and EG = 22 cm.(a) Calculate the volume of the prism.Answer(a) ........................................ cm 3 [2](b) Calculate the length FJ .Answer(b) FJ = ......................................... cm [4]For (c)Calculate the angle between FJ and the base EGJH of the prism.Examiner′sUseAnswer(c) (3)(d)The prism is melted and made into spheres.Each sphere has a radius 1.5cm.Work out the greatest number of spheres that can be made.4πr3.]V, of a sphere with radius r is V =[Thevolume,3Answer(d) (3)(e) (i) A right-angled triangle is the cross section of another prism.This triangle has height 4.5cm and base 11.0cm.Both measurements are correct to 1 decimal place.Calculate the upper bound for the area of this triangle.Answer(e)(i) ........................................ cm2 [2] (ii)Write your answer to part (e)(i) correct to 4 signiﬁ cant ﬁ gures.Answer(e)(ii) ........................................ cm2 [1]_____________________________________________________________________________________© UCLES 2013[Turn over0580/43/M/J/130580/43/M/J/13© UCLES 2013ForExaminer ′s Use5 (a) Complete this table of values for the function f(x ) = x 1 – x 2, x ¸0.[3](b) Draw the graph of f(x ) = x 1 – x 2for –3 Y x Y –0.2 and 0.2 Y x Y3.y [5]For(c)Use your graph to solve f(x) = –3.Examiner′sUseAnswer(c) x = ................ or x = ................ or x = . (3)(d)By drawing a suitable line on your graph, solve the equation f(x) = 2x – 2.Answer(d) x = ................ or x = ................ or x = . (3)(e)B y drawing a suitable tangent, work out an estimate of the gradient of the curve at the point wherex = –2.You must show your working.Answer(e) (3)_____________________________________________________________________________________For Examiner ′s Use6 In a box there are7 red cards and 3 blue cards.A card is drawn at random from the box and is not replaced. A second card is then drawn at random from the box.(a) Complete this tree diagram.RedBlueRedBlue BlueRed........................................First cardSecond card710[3](b) Work out the probability that the two cards are of different colours.Give your answer as a fraction.Answer(b) ............................................... [3]_____________________________________________________________________________________For Examiner ′s Use7y(a) (i) Draw the image of shape A after a stretch, factor 3, x -axis invariant.[2](ii) Write down the matrix representing a stretch, factor 3, x -axis invariant.Answer(a)(ii) eo [2](b) (i) Describe fully the single transformation which maps shape A onto shape B .Answer(b)(i) (3)(ii) Write down the matrix representing the transformation which maps shape A onto shape B .Answer(b)(ii) eo [2]_____________________________________________________________________________________ForExaminer′sUse8 (a)27°BCOAED NOT TO SCALEA, B, C, D and E are points on the circle centre O.AngleABD = 27°.Find(i) angle ACD,Answer(a)(i) Angle ACD = (1)(ii) angle AOD,Answer(a)(ii) Angle AOD = (1)(iii) angle AED.Answer(a)(iii) Angle AED = (1)(b)LKN M67°100°45cm32cm NOT TO SCALEThe diagram shows quadrilateral KLMN.KL = 45cm, LN = 32cm, angle KLN = 100° and angle NLM = 67°.ForExaminer′sUse (i)Calculate the length KN.Answer(b)(i) KN = ......................................... cm [4](ii)The area of triangle LMN is 324cm2.Calculate the length LM.Answer(b)(ii) LM = ......................................... cm [3](iii) Another triangle XYZ is mathematically similar to triangle LMN.LN MXZYNOT TOSCALEXZ = 16cm and the area of triangle LMN is 324cm2.Calculate the area of triangle XYZ.Answer(b)(iii) ........................................ cm2 [2] _____________________________________________________________________________________For Examiner ′s Use9 Sam asked 80 people how many minutes their journey to work took on one day.The cumulative frequency diagram shows the times taken (m minutes).CumulativefrequencyTime (minutes)(a) Find(i) the median,Answer(a)(i) ........................................ min [1](ii) the lower quartile,Answer(a)(ii) ........................................ min [1](iii) the inter-quartile range.Answer(a)(iii) ........................................ min [1]For(b)One of the 80 people is chosen at random.Examiner′sUse Find the probability that their journey to work took more than 35 minutes.Give your answer as a fraction.Answer(b) (2)(c)Use the cumulative frequency diagram to complete this frequency table.Time (m minutes)0 < m Y 1010 < m Y 1515 < m Y 3030 < m Y 4040 < m Y 50Frequency301218[2](d)Using mid-interval values, calculate an estimate of the mean journey time for the 80 people.Answer(d) ........................................ min [3](e)U se the table in part (c) to complete the histogram to show the times taken by the 80 people.O ne column has already been completed for you. Array FrequencydensitymTime (minutes)[5]_____________________________________________________________________________________For Examiner ′s Use10 (a) (i) Solve 2(3x – 7) = 13.Answer(a)(i) x = (3)(ii) Solve by factorising x 2 – 7x + 6 = 0.Answer(a)(ii) x = ................. or x = .. (3)(iii) Solve5x 32- + 102x + = 4. Answer(a)(iii) x = (4)ForExaminer ′s Use(b) 12 = 112 + 22 = 5 12 + 22 + 32 = 1412 + 22 + 32 + 42 = 3012 + 22 + 32 + 42 + ..................... + n 2 = an 3 + bn 2 + 6nWork out the values of a and b .Answer(b) a = ...............................................b = ............................................... [6]_____________________________________________________________________________________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.。

igcse考试_整理20182019学年第2学期期末考试试题A卷

201820JUNE 2021 19学年第2学期期末考试试整理人尼克知识改变命运2018-2019学年第2学期期末考试试题（A）卷课程名称任课教师签名出题教师签名审题教师签名考试方式（）卷适用专业考试时间（）分钟1.填空题(每空x分，共x分)（四号，黑体，1.5倍行距）1、当一零件受脉动循环变应力时，则其平均应力是其最大应力的________。

正文（小四号字宋体 1.2倍行距；所有英文采用Times New Roman字体）2.选择题(每题x分，共x分)1、螺栓的材料性能等级标成6.8，其数字6.8代表（）。

（A）对螺栓材料的强度要求（B）对螺栓的制造精度要求（C）对螺栓材料的刚度要求（D）对螺栓材料的耐腐蚀性要求3.判断题(每题x分，共x分)1、变应力中，循环特征r=-1时，称为对称循环变应力。

（）4.简答题(每题x分，共x分)1、简述带传动中弹性滑动和打滑的概念，并说明两者的区别。

（x分）5.分析题(每题x分，共x分)1.试说出下图中各是哪一种键连接，在图中标出工作面的位置？（x分）（图居中）6.计算题(每题x分，共x分)暨南大学考试试卷（试卷正文）一、****题（共**小题，每小题**分，共**分）注：1. 按《暨南大学全日制本科学生考试管理办法》（暨教[2006]94号）规定，试卷不额外配备答题纸，请命题教师在每道试题后留适当位置供考生作答。

2. 试卷正文为“小四号”宋体二、****题（共**小题，每小题**分，共**分）三、****题（共**小题，每小题**分，共**分）四、****题（共**小题，每小题**分，共**分）五、****题（共**小题，每小题**分，共**分）高等教育自学考试公关与策划专业（本科）考试计划主考学校：吉林大学一、指导思想高等教育自学考试是我国高等教育基本制度之一,是对自学者进行以学历考试为主的高等教育国家考试,是个人自学、社会助学、国家考试相结合的高等教育形式，是我国高等教育的重要组成部分。

0455_s07_qp_1IGCSE真题

This document consists of 11 printed pages and 1 blank page.IB07 06_0455_01/4RP© UCLES 2007[Turn over*020********UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary EducationECONOMICS0455/01Paper 1 Multiple Choice (Core) May/June 20071 hourAdditional 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 n ame, Cen tre n umber an d can didate n umber on the An swer 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 possible 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.w w w .X t r e m e P a pe r s .c o m21What is an example of the factor of production ‘capital’?A a truckB a truck driverC a truck driver’s savingsD a truck driver’s wage2What makes specialisation easier?A the imposition of taxationB the protection of tradeC the system of barterD the use of money3In a market economy, who determines the allocation of resources?A central authorities onlyB firms onlyC consumers and firms onlyD central authorities and firms only4 A government is faced with the choice of raising taxation or cutting public spending.Of what is this an example?A conservation of resourcesB monetary policyC opportunity costD substitution of factors5Each country of Southern Africa has a mixed economy.Which statement about a mixed economy is correct?A The government employs most primary sector workers.B The government owns all major secondary sector industries.C The government owns the transport network.D The government provides public and merit goods.© UCLES 2007 0455/01/M/J/073© UCLES 2007 0455/01/M/J/07[Turn over6When will a trade union be most effective in pursuing its members' interests? A The economy is in recession with rising unemployment. B The employers have few orders for the product.C The government passes a law to increase competition in the labour market.D The members' wages make up a small part of total costs.7What is the main advantage that a public limited company has over a private limited company? A It operates in the public sector.B Its shares can be sold on the stock exchange.C It is managed by a director.D Its shareholders have limited liability. 8What is the function of a stock exchange? A It enables shareholders to sell their shares. B It fixes fair prices for shares. C It promises to buy unsold shares.D It sets the number of shares.9 A French company employs French people, is located only in France, sells shares on the stock exchange but uses other firms to transport its products to other countries.What type of company is this? A a co-operative B a private company C a public companyD a multi-national10 A demand curve for a product shows the relationship between its price andA cost of production.B population changes.C the income of the consumer.D the quantity of the product consumed.4© UCLES 2007 0455/01/M/J/0711 The following was printed in a magazine.More soft drinks are being consumed than ever before by the 16 – 34 age group. Schweppes, the drink manufacturers, claim that over 45 per cent of their soft drinks are now being consumed without alcohol as people switch away from alcoholic spirits.How would this change be represented on a demand and supply diagram for soft drinks?A decrease in demandB decrease in supplyC increase in demandD increase in supply12 In many countries, the price of personal computers has fallen while the quantity sold has risen.What is the most likely reason for these changes?A Advertising campaigns for computers increased.B Computer production technology improved.C Computer software became cheaper.D Real incomes rose.13 Australian mines are among the world’s largest suppliers of uranium but the mines arecontaminating Australia’s natural environment. It is recommended that the mining companies install new equipment which causes less pollution.If this is done, how would it be represented on a demand and supply diagram for uranium?demand curve supply curve A shift to left no change B shift to right shift to left C no change shift to left D shift to leftshift to right5© UCLES 2007 0455/01/M/J/07[Turn over14 The diagram shows the demand and supply of places in independent (private) schools whichcharge fees. The equilibrium position is X.The costs of independent (private) schools rise. Also a report is issued which states that Government schools achieve very good examination results.What is likely to be the new equilibrium position?pricequantity15 Which group is likely to save the largest proportion of its income?A employed workersB retired peopleC school studentsD unemployed workers16 What is not included in a person’s stock of wealth?A a gold watchB annual incomeC an oil paintingD company shares17 Which asset is the most illiquid?A cashB money orderC government bondsD a house6© UCLES 2007 0455/01/M/J/0718 The graph shows women’s wages as a percentage of men’s wages in year 1 and year 2.percent85807570656055273035404550556062ageyear 2year 1Which statement is shown by the graph to be true? A Younger women earn more than older women.B Women’s wages remain roughly the same between the ages of 40–50.C In year 2, all women were earning more than men.D In year 2, women were earning a higher percentage of men’s wages than in year 1.19 Which service is most likely to be supplied by a small business?A bankingB dental treatmentC heart surgeryD rail travel20 A British firm, Dyson, moved production of its vacuum cleaners from the UK to Malaysia.Why might it have made this change?A average costs would fallB average revenue would riseC market share would fallD transport costs would rise721What is a fixed cost of production?A the commission paid to sales staffB the cost of using the telephoneC the interest paid on a bank loanD the money spent on repairs22 What is not equal to the average revenue?A the price of each unitB the profit from each unitC the revenue from each unitD the total revenue divided by output23The information below refers to an economy for a financial year.Government expenditure = $2 866 millionGovernment revenue = $1 940 millionWhat was the budget balance of the Government in that year?A$926 million in deficitB$4 806 million in deficitC$926 million in surplusD$4 806 million in surplus24 A local tax will usually beA raised by a central government.B used to provide a national road network.C different from region to region.D raised by using import tariffs.25 A government establishes a body to control monopolies and mergers.Who is this intended to protect?A consumersB foreign investorsC multi-nationalsD the government© UCLES 2007 0455/01/M/J/07[Turn over826Frictional unemployment occurs whenA workers are temporarily between jobs.B there is a general fall in total demand.C certain major industries go into economic decline.D new technology reduces the need for labour.27What is a reason for collecting national income statistics?A to calculate population changesB to compare standards of livingC to fix exchange ratesD to keep inflation low28The table shows the proportion of the working population in different sectors in three countries.country agriculture % manufacturing % services %Iran 38 33 29Nepal 93 2 5UK 2 42 56 What can be concluded from the table?A Iran has fewer people working in manufacturing than the UK.B Nepal is a developed economy.C Services are more developed in Iran than Nepal.D The UK is dependent on agriculture.29In rural areas in developing countries women often do unpaid work on traditional activities.Why might this mean that the GDP is not a good measure of the standard of living in those countries?A The GDP does not include international trade.B The GDP only refers to companies in urban areas.C The work is not counted in GDP statistics.D The work is not economically important.© UCLES 2007 0455/01/M/J/079© UCLES 2007 0455/01/M/J/07[Turn over30 The table shows the annual percentage changes in GDP and consumer prices in selectedcountries during a year.Which country has shown the biggest rise in real GDP over this period?country% change in GDP% change in consumer pricesA Argentina 5.1 7.3B India 4.9 4.4C Malaysia 4.0 1.0 DPhilippines 4.53.331 Two industries in Namibia are fishing and tourism. The value of the currency of Namibia fell in2001.If there were no other changes, what resulted from the fall?A Imported goods in Namibian shops became cheaper.B The price of Namibia’s fish sold in foreign markets became cheaper.C The volume of Namibia’s exports decreased.D Tourists were discouraged by higher prices in Namibia.32 The diagram shows the percentage of the population of Germany aged under 20 and over 60between 1950 and 2000.1950607080902000343026221814under 20over 60%What may be concluded from the diagram? A The average age was similar in 1950 and 2000. B The dependency ratio was similar in 1950 and 2000. C The growth in total population ceased by 2000. D The standard of living fell continuously from 1950.10© UCLES 2007 0455/01/M/J/0733 Which country is likely to have the lowest standard of living?birth ratedeath ratelife expectancyinfant mortalityA 25 10 57 24B 43 31 40 42C 25 5 72 22 D36 14 48 5634 In 2005, world population had grown to 6.5 billion with an increase of more than 4 billion since1950.What is most likely to have been the cause of this?A an increase in the death rate in developed countriesB an increase in the birth rate in developing countriesC an increase in migration from developing to developed countriesD an increase in the death rate in developing countries35 At the G8 Economic Summit in 2005, it was decided to cancel much of the debt which Africancountries owed to European and North American countries.This will have the same effect as a transfer of resources fromA developed countries to developing countries.B developing countries to developed countries.C market economies to planned economies.D planned economies to market economies.36 A government decides to reduce the size of the quota on a good.What is likely to happen?A The balance of trade will worsen.B The good will become cheaper.C The government’s revenue will decline.D There will be less of the good imported.11 © UCLES 2007 0455/01/M/J/0737 Which combination would offer increased trade protection for an economy?domestic subsidies tariffs Abigger higher Bbigger lower Csmaller higher D smaller lower38 Why may it be better to increase public expenditure while reducing private expenditure?A Goods and services which the market ignores can be provided.B Government officials are likely to be more careful spending money than private individuals.C The profit motive makes government departments more efficient than private firms.D The government is the best judge of the satisfaction gained from goods and services.39 Zambia is the fifth largest producer and the second largest exporter of copper in the world. Copper brings Zambia 85 % of all the money Zambia earns in trade.What can be concluded from this?A Copper prices are high because Zambia is a large producer.B Manufacturing production in Zambia is very diversified.C Zambia can influence the world price of copper.D Zambia produces copper more cheaply than all other countries.40 What will result if Europe reduces trade barriers to increase imports of clothing and food from Asia and Africa?A greater choice for European consumersB increased income for European producersC lower unemployment in the European clothing industryD slower economic growth in Asia and Africa12BLANK PAGEPer mission to r epr oduce items wher e thir d-par ty owned mater ial pr otected by copyr ight is included has been sought and clear ed wher e possible. Ever y reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.0455/01/M/J/07。

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSInternational General Certificate of Secondary Education*8006817548*ADDITIONAL MATHEMATICS 0606/12Paper 1 October/November 20122 hoursCandidates answer on the Question Paper.Additional Materials:Electronic calculator.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.Y ou may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid.Answer all the questions.Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.The use of an electronic calculator is expected, where appropriate.Y ou are reminded of the need for clear presentation in your answers.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 number of marks for this paper is 80.For Examiner’s Use 1 2 3 4 5 6 7 8 91011TotalMathematical Formulae1. ALGEBRA Quadratic EquationFor the equation ax2 + bx + c = 0,xba =−2Binomial Theorem(a + b)n = a n + (n1)a n–1b + (n2)a n–2b2 + … + (n r)a n–r b r + … + b n, wheren is a positive integer and (n r)= n!(n – r)!r!2. TRIGONOMETRYIdentitiessin2A + cos2A = 1sec2A = 1 + tan2Acosec2A = 1 + cot2AFormulae for ∆ABCasin A =bsin B =csin Ca2 = b2 + c2 – 2bc cos A∆ = 12bc sin A0606/12/O/N/12© UCLES 20120606/12/O/N/12© UCLES 2012[Turn overFor Examiner’s Use1It is given that a = 43 , b = –12 and c = 212 .(i) Find |a + b + c |. [2](ii)Find λ and μ such that λ a + μ b = c . [3]0606/12/O/N/12© UCLES 2012For Examiner’s Use2 (i) Find the inverse of the matrix2 –1–1 1.5 . [2](ii) Hence find the matrix A such that 2 –1–1 1.5 A = 1 6–0.5 4 . [3]3 (i) Show that cot θ +sin θcos θ= cosec θ. [5](ii)Ex plain why the equation cot θ + sin θ1 + cos θ = 12has no solution.[1]0606/12/O/N/12© UCLES 2012[Turn overForExaminer’s Use4Given that log a pq = 9 and log a p 2q = 15, find the value of(i) log a p and of log a q , [4](ii) log p a + log q a . [2]0606/12/O/N/12© UCLES 2012For Examiner’s Use5 The line x – 2y =6 intersects the curve x 2 + xy + 10y + 4y 2 = 156 at the points A and B .Find the length of AB . [7]0606/12/O/N/12© UCLES 2012[Turn overFor Examiner’s Use6( 3 – 1) and without using a calculator, find the value of sin θ in the forma +b 2, where a and b are integers.[5]0606/12/O/N/12© UCLES 2012For Examiner’s Use7Solutions to this question by accurate drawing will not be accepted.The vertices of the trapezium ABCD are the points A (–5, 4), B (8, 4), C (6, 8) and D . The line AB is parallel to the line DC . The lines AD and BC are extended to meet at E and angle AEB = 90°.(i) Find the coordinates of D and of E . [6](ii) Find the area of the trapezium ABCD. [2]ForExaminer’sUse© UCLES 2012[Turn over0606/12/O/N/120606/12/O/N/12© UCLES 2012For Examiner’s Use8BThe diagram shows an isosceles triangle OBD in which OB = OD = 18 cm and angleBOD = 1.5 radians. An arc of the circle, centre O and radius 10 cm, meets OB at A and OD at C .(i) Find the area of the shaded region.[3](ii) Find the perimeter of the shaded region. [4]For Examiner’s Use 9 (a) (i) Using the axes below, sketch for 0 р x р π, the graphs ofy = sin 2x and y = 1 + cos 2x . [4]y––– (ii) Write down the solutions of the equation sin 2x – cos 2x = 1, for 0 р x р π. [2] (b) (i) Write down the amplitude and period of 5 cos 4x – 3. [2] (ii) Write down the period of 4 tan 3x. [1]For Examiner’s Use 10 A function f is such that f(x ) = 4x 3 + 4x 2 + ax + b . It is given that 2x – 1 is a factor of both f(x )and f ʹ(x ).(i) Show that b = 2 and find the value of a . [5] Using the values of a and b from part (i),(ii) find the remainder when f(x ) is divided by x + 3,[2]ForExaminer’s Use(iii) express f(x ) in the form f(x ) = (2x – 1)(px 2 + qx + r ), where p , q and r are integers to befound, [2] (iv) find the values of x for which f(x ) = 0. [2]For Examiner’s Use11 Answer only one of the following two alternatives.EITHERA curve is such that y = 5x 21 + x 2 . (i) Show that d y d x = kx (1 + x 2)2 , where k is an integer to be found. [4] (ii) Find the coordinates of the stationary point on the curve and determine the nature of thisstationary point. [3](iii) By using your result from part (i), find ͵x (1 + x 2)2 d x and hence evaluate ͵2–1x (1 + x 2)2 d x .[4] ORA curve is such that y = Ax 2 +B x 2 – 2 , where A and B are constants. (i) Show thatd y d x = – 2x (2A + B )(x 2 – 2)2 . [4] It is given that y = –3 andd y d x = –10 when x = 1. (ii) Find the value of A and of B . [3] (iii) Using your values of A and B , find the coordinates of the stationary point on the curve, anddetermine the nature of this stationary point. [4]Start your answer to Question 11 here.Indicate which question you are answering. 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