HONG KONG EXAMINATIONS AUTHORITY HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 2001 MATHEMATICS PAPER 2

Transcription

1 00-CE MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 00 MATHEMATICS PAPER 5 am 45 pm (½ hours) Subject Code 80 Read carefull the instructions on the Answer Sheet and insert the information required (including the Subject Code) in the spaces provided When told to open this book, ou should check that all the questions are there Look for the words END OF PAPER after the last question All questions carr equal marks 4 ANSWER ALL QUESTIONS You should mark all our answers on the Answer Sheet 5 You should mark onl ONE answer for each question If ou mark more than one answer, ou will receive NO MARKS for that question 6 No marks will be deducted for wrong answers 香港考試局保留版權 Hong Kong Eaminations Authorit All Rights Reserved CE-MATH

2 FORMULAS FOR REFERENCE SPHERE Surface area = 4π r Volume = 4 π r CYLINDER Area of curved surface = π rh Volume = π r h CONE Area of curved surface = π rl Volume = π r h PRISM Volume = base area height PYRAMID Volume = base area height 00-CE-MATH

3 There are 6 questions in Section A and 8 questions in Section B The diagrams in this paper are not necessaril drawn to scale Section A If a =, then b = + b A a a B C a a a + a D a a E a a ( + ) ( ) = A B 6 9 C D E CE-MATH Go on to the net page

4 Let f ( ) = ( ) ( + ) + + Find the remainder when f ( ) is divided b + A B C 0 D E 4 The figure shows a right-angled triangle where AB : BC = : 4 Find sin θ A 5 C B 4 C 5 4 D 5 A θ B E CE-MATH 4

5 5 The bar chart below shows the distribution of scores in a test Find the percentage of scores which are less than A 5% B 40% C 50% D 65% E 70% Frequenc Score 6 If the straight lines + = 0 and 5 + k = 0 are perpendicular to each other, find k A B C D E CE-MATH 5 4 Go on to the net page

6 7 In the figure, find correct to significant figures A 65 B 79 C 6 cm cm D 400 E cm 8 In the figure, the solid consists of a clinder and a hemisphere with a common base of radius 6 cm Find the total surface area of the solid A π cm 6 cm B 68π cm C 04π cm 5 cm D 40π cm E 4π cm 00-CE-MATH 6 5

7 9 The figure shows a regular pentagon Find its area correct to the nearest 00 cm A 6 cm B 588 cm C 68 cm D 688 cm E 85 cm cm 0 a n n + a n a A = n a B a n ( + a) C D + n a + a E + a 00-CE-MATH 7 6 Go on to the net page

8 Which of the following is an identit / are identities? I + + = 0 II III + > = ( + ) A I onl B II onl C III onl D I and III onl E II and III onl = 4 44 If = + 4, then = A or 5 B or 6 C or 96 D 8 or 0 E or 4 00-CE-MATH 8 7

9 A piece of wire of length 6 cm is cut into two parts One part, cm long, is bent into a square and the other part is bent into a circle If the length of a side of the square is equal to the radius of the circle, which of the following equations can be used to find? A 6 4 = π B = 6 π C D E 6 4 = 4 π = 6 4 π = 6 4 π 4 The sum of the first n terms of an arithmetic sequence is term of the sequence n Find the 0th A 9 B C 8 D E CE-MATH 9 8 Go on to the net page

10 5 The n th term of a geometric sequence is common ratio Find the first term and the n first term A common ratio B C D E 6 A bank offers loans at an interest rate of 8% per annum, compounded monthl A man took a loan of $ and repas the bank in monthl instalments of $ Find the outstanding balance after his first instalment A $6 000 B $6 40 C $6 00 D $8 880 E $ CE-MATH 0 9

11 7 If 0 < < < 90, which of the following must be true? I sin < sin II cos < cos III sin < cos A I onl B II onl C I and II onl D I and III onl E II and III onl 8 In the figure, AEC is a diameter and DEB is a straight line Find A 54 D B 70 C 74 6 E C D 9 E 94 A 47 B 00-CE-MATH 0 Go on to the net page

12 9 Which of the following pairs of triangles is/are similar? I II III A II onl B III onl C I and II onl D I and III onl E I, II and III 00-CE-MATH

13 0 In the figure, = A 50 B C 60 D E If the mean of the ten numbers 8, 6, 6, 6, 7, 4, 0, 9, 9, is 7, find the median of the ten numbers A 55 B 6 C 65 D 7 E CE-MATH Go on to the net page

14 Which of the following is a factor of ( a b) a + b? A a b B a b C a + b D a + b E a b In the figure, the graph of = cuts the -ais at A and B, and the -ais at C Find the area of ABC A 4 B 6 C 7 C = D 8 E 4 O A B 00-CE-MATH 4

15 4 In the figure, a solid right circular cone of height cm is put into a clinder which has the same internal radius as the base radius of the cone Water is then poured into the clinder until the water level just reaches the tip of the cone If the cone is removed, what is the height of the water in the clinder? A cm B 4 cm C 6 cm D 8 cm E 9 cm cm 5 In the figure, OABC is a sector Find the length of the arc ABC A π cm C B 4 π cm C 5 π cm 6 cm B D 6 π cm E π cm O 6 cm A 00-CE-MATH 5 4 Go on to the net page

16 6 In the figure, A, B and C are the centres of three equal circles, each of radius cm Find the area of the shaded region A π cm B π 4 cm A C C π + 4 cm B D π cm E π 4 cm 7 40% of the students in a class failed in a test The had to sit for another test in which 70% of them failed again Find the percentage of students who failed in both tests A 0% B % C 8% D 8% E 0% 00-CE-MATH 6 5

17 8 If + =, then = + A 5 6 B 5 C 5 D 4 E Suppose is partl constant and partl varies inversel as When =, = 7 and when =, = Find when = A 5 B 5 C 4 D 5 E CE-MATH 7 6 Go on to the net page

18 0 In the figure, find correct to significant figures A cm B 94 C 948 D 07 E cm cm Ship A is 8 km due north of a light house L and ship B is 6 km due east of L Find the bearing of B from A A N5 W (correct to the nearest 0 ) B N69 W (correct to the nearest 0 ) C N69 E (correct to the nearest 0 ) D S5 E (correct to the nearest 0 ) E S69 E (correct to the nearest 0 ) In the figure, ABCD is a semicircle, AB : BD = 4 : Find AB correct to the nearest 0 cm A 57 cm B 76 cm C 07 cm D 5 cm C D 0 cm E 4 cm A B 00-CE-MATH 8 7

19 If the straight lines + 5 = 0 and a + = 0 intersect at (, b), find a and b A a = 4, b = B a =, b = 0 C a =, b = D a =, b = E a =, b = 4 In the figure, A, B and C are points on a rectangular coordinate plane AC and BC are parallel to the -ais and -ais respectivel If the coordinates of C are (, ) and the equation of the straight line AB is = +, find the distance between A and B A 5 B 5 B = + C 7 D 5 E 65 A C (, ) 00-CE-MATH 9 8 Go on to the net page

20 5 Two cards are drawn randoml from five cards numbered,,, 4 and 4 respectivel Find the probabilit that the sum of the two numbers drawn is even A B C D E A bag contains black balls and white balls A bo randoml draws balls from the bag one at a time (without replacement) until a white ball appears Find the probabilit that he will make at least draws A B C D E CE-MATH 0 9

21 Section B 7 If log = (log ), then = A B 0 C 00 D or 0 E or 00 8 If a > b, which of the following must be true? I a < b II a + b > b III a > b A I onl B II onl C III onl D I and II onl E I, II and III 00-CE-MATH 0 Go on to the net page

22 a 9 If a, b are distinct real numbers and b + 4a + = 0 + 4b + = 0, find a + b A B 9 C 4 D 6 E 8 40 Suppose the graph of = is given In order to solve the quadratic equation 6 = 0, which of the following straight lines should be added to the given graph? A = 4 B C = = + D = E = + 00-CE-MATH

23 4 Find the mean deviation of the five numbers 0,, 4, 6 and 7 A 0 B C 0 D E 6 4 For 0 60, how man roots does the equation cos = cos have? A B C 4 D 5 E 6 00-CE-MATH Go on to the net page

24 4 If tan (90 θ ) =, then sin θ + sinθ cos θ = cosθ A B C 5 D E 44 The figure shows the graph of the function A = sin B = sin C = + sin D = + cos E = cos O π π 00-CE-MATH 4

25 45 In the figure, O is the centre of the circle, AOB is a straight line and BCD is the tangent to the circle at C Find A 50 B 5 C 56 A O D 59 E 6 D C 8 B 46 In the figure, AB = BC = CD Find ABC A 00 B 05 D C 5 D 0 A E 50 B C 75 E 00-CE-MATH 5 4 Go on to the net page

26 = A + 6 ( + ) ( + 5) B C D E ( + ) ( + 5) ( + 4) ( ) ( + ) ( + 5) ( ) ( 4) ( + ) ( 5) ( ) ( 6) ( + ) ( 5) 48 Let f() = + + a + b If f() is divisible b + and, f() can be factorized as A ( )( + )( ) B ( + ) ( ) C ( )( + )( ) D ( + )( + )( ) E ( + )( ) 00-CE-MATH 6 5

27 00-CE-MATH 7 6 Go on to the net page 49 The shaded region in the figure represents the solution of one of the following sstems of inequalities Which is it? A B C D E O = 0 = 6 +

28 50 In the figure, ADB, BEC and CFA are straight lines If the area of ABC is 5 cm, find the area of the parallelogram DECF A 8 cm A B 08 cm C 6 cm D 5 cm D F E 6 cm B 0 cm E 0 cm C 5 In the figure, PC is a vertical pole standing on the horizontal ground ABC D is a point on line AB If BCA = CDB = 90, AC = m, BC = 4 m and PC = 5 m, find tan θ P A 5 B C D A θ m 5 m C E 5 9 D 4 m B 00-CE-MATH 8 7

29 5 In the figure, ABCD and AGFE are straight lines Find CF A 4 cm A B cm cm C 7 cm B cm G D 5 cm C F 4 cm E 7 cm D 5 cm E 5 Consider the circle = 0 Find the equation of the chord whose mid-point is (5, ) A = 0 B + 4 = 0 C + 7 = 0 D + = 0 E = 0 00-CE-MATH 9 8 Go on to the net page

30 54 In the figure, the inscribed circle of OPQ touches PQ at R Find the coordinates of R A, 6 B, 5 5 Q(0, 4) 9 8 C, 5 5 R 9 6 D, 7 7 O P(, 0) E, 7 7 END OF PAPER 00-CE-MATH 0 9

31 00 Mathematics (Paper ) Question No Ke Question No Ke A E C B A E 4 E 4 D 5 B 5 B 6 D 6 A 7 A 7 E 8 B 8 A 9 D 9 C 0 E 40 B B 4 D B 4 D E 4 B 4 A 44 E 5 C 45 D 6 C 46 D 7 A 47 A 8 C 48 D 9 E 49 A 0 C 50 B C 5 D A 5 E C 5 E 4 D 54 C 5 B 6 A 7 D 8 E 9 C 0 B