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1 DSE 01 DSE 01 DSE 015 DSE 016 A B A B A B A B , 1, 5, 10, 11 9, 10 9, 10 10,, 8, 1, 5, , 8, 7 5, , 8 8, 9 1, 1 1, 1 11, 1 11, 1, ,, 1,, , , 1 16, 17, 15, 16, , 1 1 0, , 17, , 16, 17 18, 19, 0 1,,, 5,, 5 5, , , 19 8, 9 1 7, 8 0, , 8 8, 9 7, 8, 9, 0 5 8, 9, 0, 5 9, 0 5 0, 5 V

2 DSE Assorted Eercises on Junior Secondary Topics Chapter 1. In the figure, cos + tan A. B. C. D In the figure, ABC is an equilateral triangle and BCDE is a square. F is a point on DE such that AC // BF. Find DCF correct to the nearest degree. A. 15 B. C. 0 D In DXYZ, XY : YZ : ZX 7 : : 5. Find sin X : cos Z. A. 1 : 1 B. 7 : C. : 7 D. : 5 7. In the figure, if D is a point lying on AC such that BD is an altitude of DABC, then AB A. B. C. D. CD tan β cosα. CD tan β. sinα CD cosαtan β. CD sinαtan β. 8. If 5 < < 90, which of the following must be true? I. sin > cos II. tan > sin III. cos > tan A. I and II only B. I and III only C. II and III only D. I, II and III 6. In the figure, the bearings of A and B from O are 198 and S59 W respectively. If OB AB, then the bearing of A from B is A. N1 E. B. N59 E. C. S E. D. S1 E. 9. In DABC, C 90. Which of the following must be true? I. sin A cos B II. tan A tan C tan B III. cos C cos A + cos B A. I only B. III only C. I and III only D. I, II and III Hong Kong Educational Publishing Company 8

3 Integrated Test There are THREE sections in this test. Marks: / 100 Answer ALL questions. Time Allowed: 1 hours Section A: Short Questions (0 marks) 1. Simplify y - - ( ) and epress your answer with positive indices. 6 y ( marks) Integrated Test. Factorize (a) - 1, (b) ( marks) 5 Hong Kong Educational Publishing Company

4 Please stick the barcode label here. 1. Let f() a b, where a and b are constants. f() is divisible by + p + 1 and + + q, where p and q are constants. It is given that + p + 1 and + + q have no common factors. (a) Find p and q. (b) How many real roots does the equation f() 0 have? Eplain your answer. ( marks) ( marks) Answers written in the margins will not be marked. Answers written in the margins will not be marked. Answers written in the margins will not be marked. CP MOCK PAPER Go on to the net page Page total

5 A E 16. B E 16. C E 16. D E Let a and b be the negative roots of the quadratic equation + k + 5 0, where k is a constant. If a - b, then the equation of the ais of the symmetry of the graph of y + k + 5 is A. -6. B. -. C.. D Let p I. II. a + i and a i q, where a is a real number. Which of the following must be true? q p is a rational number. The real part of p is equal to the real part of 1. q III. The imaginary part of A. II only B. I and II only C. I and III only D. II and III only 1 is equal to the imaginary part of q. p 7. The figure shows a shaded region (including the boundary). If (h, k) is a point lying in the shaded region, which of the following is true? A. h - k 0 B. k 5 - h C. - h - k D. 5k - h attains its least value at the origin. Go on to the net page CP MOCK PAPER Hong Kong Educational Publishing Company

6 Mathematics: Mock Eam Papers (Compulsory Part) Fourth Edition Solution Guide 8. Reference: HKDSE 016 Paper Q15 C Consider the figure a (int. s, // lines) y c (alt. s, // lines) b + y b a + c a + b - c Reference: HKDSE 01 Paper Q A For I, sum of interior angles (n - ) 180 ( sum of polygon) 180 n - 60 sum of eterior angles 60 (sum of et. s of polygon) \ 180 n n 1 \ I is true. For II, 5 60 interior angle \ II is not true. For III, the number of ais of reflectional symmetry of a regular 1-sided polygon is 1. \ III is not true. 10. Reference: HKCEE 00 Paper Q A + > 6 (triangle inequality) > > (triangle inequality) > > (triangle inequality) < 6 \ 1. < < 6 \,, or 5 Hence, different triangles can be constructed. 11. Reference: HKCEE 007 Paper Q50 C Chapter 10 Mensuration If h : 6h : 16, then we have 1. Reference: HKCEE 010 Paper 1 Q1 16h 6h + 16 (a) Let E be a point lying on BC such that AE BC. 6h 6h + 16 AB AC and AE BC \ BE CE (property of isos. D) h or - 7 (rejected) 7 16 cm \ The ratio is 1 : 16 only when h 8 cm 7. The claim is disagreed. 8 Hong Kong Educational Publishing Company \ AE + BE AB AE cm (Pyth. theorem) cm \ Area of DABC 1 (16)(6) cm 8 cm (b) Let h cm be the height of ABCD. 1 (8)(h) 18 h 8 Note the ABCD is similar to XYZD. Let V cm be the volume of ABCZXY. 18 V 18 8 V 11.5 \ The volume of ABCZXY is 11.5 cm.. Reference: HKCEE 1999 Paper 1 Q9 (a) r (Pyth. theorem) r 1 or -1 (rejected) θ 1 tan 5 θ (cor. to sig. fig.) (b) Area of the shaded region π( 1) ( )( ) cm 19 cm (cor. to sig. fig.). Reference: HKDSE 01 Paper 1 Q1 (a) pr 16 p(1) R or - (rejected) 1 π() 1 h π( ) H 6h H \ h : H 1 : 6 (b) Curved surface area of a cylinder : Curved surface area of the cone π(1) h : π () H + h : 6h + 16

7 Mathematics: Mock Eam Papers (Compulsory Part) Fourth Edition Solution Guide Section B 15. (ii) Profit $[80M - ( M )] $(-M + 80M ) When profit hundred dollars, -M + 80M M - 80M (M - 60)(M - 0M - 100) 0 (By (a)) M 60, 6.1 or -6.1 (rejected) (cor. to sig. fig.) \ The cost of the materials is $6000 or $610. log8 y 0 log tan0 log8 y (log ) log8 y log 1 (7) (b) Alternative Solution: Required probability 1 - P(no girls) 6 9 CC C 5 65 () Required probability P( students from senior secondary 1 boy) P(1 boy) CC 1 + C1 ( C1C1 ) 15 C 9 6 CC C 11 7 () log y log log 8 log y log 8 log y log log 8 log log y log log y log y 8 8 () 17. (a) By the method of completing the square, f() 1 - -( - 1) -( ) -( - 7) + 9 \ The coordinates of the verte are (7, 9). (b) (i) A 56 () 8 - (ii) Note that A f(), where f() 1 - and 0 < < 1. By (a), the greatest value of A is 98. \ The claim is disagreed. () 18. (a) Sum of roots - p 1 Candidates may overlook the difference of the bases of the logarithms on both sides. 16. (a) Required probability CC 1 + CC 1 + CC 15 C p + qi + 1 p - qi -p (p - qi) + (p + qi) (p) - (qi) -p p p -p... (1) + q Candidates may wrongly eliminate p on both sides. 0 Hong Kong Educational Publishing Company

8 Mock Eam B Number of dots in the 1st pattern Number of dots in the nd pattern + (1 + ) 5 Number of dots in the rd pattern 5 + ( + ) 9 Number of dots in the th pattern 9 + ( + ) 1 Number of dots in the 5th pattern 1 + ( + ) 0 Number of dots in the 6th pattern 0 + (5 + ) 7 Number of dots in the 7th pattern 7 + (6 + ) 5 Number of dots in the 8th pattern 5 + (7 + ) 16. A 17. A Required distance (10 + 6) + ( + ) cm cm 5 cm (Pyth. theorem) 1. D Marked price $000 ( %) $5000 Selling price $5000 (1-5%) $750 $( ) Profit percentage 100% $ % 1. C Scale 1 : cm : cm 1 cm : 000 m 1 cm : km Let km be the actual area of the garden D \ The actual area of the garden is 5 km. k q Let p, where k is a non-zero constant. r pr pr q q k k Note that k is a non-zero constant. 15. B The verte of the graph is (-a, b). From the graph, we have -a > 0 and b > 0 \ a < 0 and b > 0 Candidates may redraw the figure in scale, then measure the distance between A and F directly. 18. C Let r and h be the original radius and height of the cone respectively. New radius (1 + 10%)r 1.1r Original volume 1 pr h New volume 1 p(1.1r) h 1.1 pr h Percentage increase in the volume πr h πr h 100% 1 πr h 1% Candidates may let the original values of r and h be some simple values, then find the percentage increase directly. 19. D Let be the area of DABC. AE EC \ AE : EC : 1 \ Area of DABE + 1 AD is a median of DABC. \ BD DC 1 1 \ Area of DACD 1+ 1 \ \ Area of DABE : Area of DACD 1 : : Hong Kong Educational Publishing Company

HKDSE Exam Question Distribution

HKDSE Exam Question Distribution HKDSE Eam Question Distribution Paper 1 Sample Paper Practice Paper DSE 01 DSE 013 Topics A(1) A() B A(1) A() B A(1) A() B A(1) A() B Number System and Estimation 17* 8(E) Percentages 4 4 4(E) Formulas