MATHEMATICS Compulsory Part

Transcription

1 07/8-ME MATH CP PAPER HK YAU CLUB HNG KNG MCK EXAMINATIN 07/8 MATHEMATICS Compulsor Part PAPER 00 nn - 5 pm (¼ hours) INSTRUCTINS Read carefull the instructions on the Answer Sheet After the announcement of the start of the eamination, ou should first stick a barcode label and insert the information required in the spaces provided No etra time will be given for sticking on the barcode label after the Time is up announcement When told to open this book, ou should check that all the questions are there Look for the words END F PAPER after the last question 3 All questions carr equal marks 4 ANSWER ALL QUESTINS You are advised to use an HB pencil to mark all the answers on the Answer Sheet, so that wrong marks can be completel erased with a clean rubber You must mark the answers clearl; otherwise ou will lose marks if the answers cannot be captured 5 You should mark onl NE answer for each question If ou mark more than one answer, ou will receive N MARKS for that question 6 No marks will be deducted for wrong answers 學友社保留版權 Hok Yau Club All Rights Reserved 07 Not to be taken awa before the end of the eamination session 07/8-ME-MATH-CP

2 There are 30 questions in Section A and 5 questions in Section B The diagrams in this paper are not necessaril drawn to scale Choose the best answer for each question Section A A B C D a 3ab b a b A ( a b)( a b ) B ( a b)( a b ) C ( a b)( a b ) D ( a b)( a b ) 3 If a 3b a b 4a, then b A a 7 B 6a 7 C 7a 6 D 3a 07/8-ME-MATH-CP

3 4 A 0 43 (correct to 4 significant figures) B (correct to 5 significant figures) C (correct to 6 decimal places) D (correct to 7 decimal places) 5 The solution of 4 or 7 3 is A 3 B C 3 D 3 or 6 Let k be a constant If f ( ) k, then f ( k ) f ( k) A 0 B 4k C k D 4k 4k 07 7 Let p( ) k 4, where k is a constant If p ( ) is divisible b, find the remainder when p( ) is divided b A 8 B 5 C 0 D 5 07/8-ME-MATH-CP 3 3 Go on to the net page

4 8 If a, b and c are constants such that 3 5 a( ) b( ) c, then c A 8 B 3 C 5 D 0 9 The figure shows the graph of ( a ) b, where a and b are constants Which of the following is true? A a 0 and b 0 B a 0 and b 0 ( a ) b C a 0 and b 0 D a 0 and b 0 0 The cost of coffee of brand A is $40 / kg If 3 kg of coffee of brand A and kg of coffee of brand B are mied so that the cost of the miture is $64 / kg, find the cost of coffee of brand B A $80 / kg B $88 / kg C $300 / kg D $30 / kg The scale of a map is : k If the area of a park on the map and the actual area of the park are 0 cm and 6 5 m respectivel, then k 5 0 A 500 B 5000 C 0000 D /8-ME-MATH-CP 4 4

5 If r varies directl as the square root of p and inversel as q, which of the following must be constant? A q r p q r B p C q r p p D q r 3 In the figure, the st pattern consists of dots For an positive integer n, the ( n ) th pattern is formed b adding ( 3n ) dots to the n th pattern Find the number of dots in the 7th pattern A 57 B 70 C 77 D 00 4 In the figure, AED and BDC are straight lines such that AD BC It is given that AB 6cm, AC 0cm and EC 3cm, then EB A 5 cm A B 6 cm C 7 cm E D 9 cm B D C 07/8-ME-MATH-CP 5 5 Go on to the net page

6 5 The figure shown a right circular cone Find the curved surface area of the circular cone A 8 cm B 7 cm 30 6 cm C 9 3 cm D 8 3 cm 6 In the figure, ABCD is a rectangle E is a point ling on AB such that AE : EB : 3 6 F is a point ling on DC such that DF : FC 4: BD and EF intersect at G If the area of the quadrilateral AEGD is 78 cm, then the area of BEG is A 4 cm A E B B 7 cm C 30 cm G D 3 cm D F C 7 In the figure, D is a point ling on AB and E is a point ling on AC BE and CD 6intersect at G It is given that ABE ACD, AD 6cm, AE 4cm, EC cm and BG 6cm Find GC A 3 5cm B 5 cm 6cm A 4cm E C 6 cm D G cm D 6 5cm B 6cm C 07/8-ME-MATH-CP 6 6

7 8 Find the sum of the five angles marked in the figure A 50 B 80 C 0 D 40 9 ABCD is a rhombus Let E and F are the mid-points of BC and DC respectivel, which of the following must be true? I ADF ABE II III AC EF EAF ECF 80 A I and II onl B I and III onl C II and III onl D I, II and III 0 In the figure, AD is the diameter of the semicircle E is a point ling on AD such that CE // BA If AB BC and BAD 63, then ECD A 7 B 54 B C C 58 5 A 63 E D D 63 07/8-ME-MATH-CP 7 7 Go on to the net page

8 cos 60 cos 40 cos(90 ) cos(70 ) A cos tan B cos C tan cos D cos tan In the figure, ABCD is a quadrilateral with AD CD It is given that AB 8cm, AD 4cm and CD cm Find BCD correct to the nearest degree A 47 C B 53 B 8cm cm C 56 D 59 A 53 4cm D 3 In the figure, the equations of the straight lines L and L are m n and p q respectivel Which of the following are true? I n q II m p III m n p q A I and II onl B I and III onl L L C II and III onl D I, II and III 07/8-ME-MATH-CP 8 8

9 4 It is given that the straight lines and m n 3 0 are perpendicular to each other and intersect at a point on the -ais Find the area of the triangle bounded b the two straight lines and the -ais A 6 B C 5 D 8 5 The polar coordinates of the point A are (, 0 ) If A is reflected with respect to the -ais, then the rectangular coordinates of its image are A ( 3, ) B ( 3,) C (, 3) D (, 3) 6 The equation of the circle C is Which of the following are true? I The coordinates of the centre of C are ( 4, 0) II The diameter of C is 4 III C and the -ais intersect at two distinct points A I and II onl B I and III onl C II and III onl D I, II and III 7 It is given that A and B are two distinct points ling on the circle 6 k 5 0, where k is a constant Let P be a moving point in the rectangular coordinate plane such that AP BP If the equation of the locus of P is 3 5 0, then k A 3 B 8 C 8 D 3 07/8-ME-MATH-CP 9 9 Go on to the net page

10 8 Two cards are randoml drawn from si cards numbered to 6 respectivel Find the probabilit that both the numbers drawn are prime number A 5 B C D The bo-and-whisker diagram below shows the distribution of the numbers of reading hours spent b a class of students in a certain week It is given that the inter-quartile range of the distribution is Find the upper quartile of the distribution 3 k 3k 5 Number of reading hours A 6 B C D 8 30 Consider the following integers : a b If the mean and the median of the above integers both are 6, which of the following must be true? I a b 35 II a 5 III b 9 A I and II onl B I and III onl C II and III onl D I, II and III 07/8-ME-MATH-CP 0 0

11 Section B The figure above shows the graph of f ( ) If g ( ) f (), which of the following ma represent the graph of g ( )? A B C D ED000AB A B C D /8-ME-MATH-CP Go on to the net page

12 33 The graph in the figure shows the linear relation between and Which of the following must be true? A B C D If log (log ) 3(log 3 ) 0 A or 9, then B or 9 C 9 or 7 D 7 or 9 35 Let then z ( a 3i ) i ( a 5i ) i, where a is a real number If z is a pure imaginar number, a A 5 B 3 C 3 D 5 36 Let a n be the n th term of a geometric sequence If a 0 and the sum to infinit of the sequence is 8, then a A 30 B C 30 D or 30 07/8-ME-MATH-CP

13 37 The figure shows a shaded region (including the boundar) If ( a, b) is a point ling in the shaded region, which of the following are true? I a 36 II a 36 b III a 36 3b 36 A I and II onl B I and III onl 36 C II and III onl D I, II and III 38 Let k be a constant and If the figure shows the graph of cos( k ), then A k and 30 cos( k ) B k and 30 C k and D k and In the figure, ABCD is a rectangle It is given that E is a point ling on AC such that EC 5cm and N is a point ling on DE such that AN DE Find AN A cm A B B cm 9cm E C cm D N cm C D 7 cm 07/8-ME-MATH-CP 3 3 Go on to the net page

14 40 In the figure, DB is a diameter of the circle ABCD PA and PC are tangents to the circle at A and C respectivel AB produced and DC produced meet at Q If APC 5, then AQD A 4 A 5 P B 6 B C 36 D 38 D C Q 4 Let be the origin The coordinates of the point P are ( 0,) and Q is a point ling on the -ais If the equation of the inscribed circle of PQ is ( ) ( ) 4, then the -coordinate of the circumcentre of A B 5 C 3 D 5 PQ is 4 6 couples are going to a banquet 3 people are selected from the 6 couples to form a team to sing a song in the banquet If there are no couples in the team, how man different teams can be formed? A 60 B 0 C 960 D 30 07/8-ME-MATH-CP 4 4

15 43 The probabilities for Kell to pass a Mathematics test and an English test are p and If the probabilit that she passes at least one subject is 9, then p respectivel A B C D The mean and the standard deviation of the scores of a Mathematics eamination are 56 marks and 8 marks respectivel while the mean and the standard deviation of the scores of an English eamination are marks and 6 marks respectivel It is given that the scores of Matthew in the Mathematics eamination and the English eamination are 7 marks and 68 marks respectivel, the standard score of Matthew in the Mathematics eamination is 0 5 higher than that in English eamination Find A 53 B 56 C 59 D Let m, r and s be the mean, the range and the variance of a group of numbers,,, 3, respectivel while m, r and s be the mean, the range and the variance of a group of numbers,, 3,, 0 respectivel If 0 m I m m II r r III s s A I and II onl B I and III onl C II and III onl D I, II and III, which of the following must be true? END F PAPER 9 07/8-ME-MATH-CP 5 5