Page 1 of 48St Margaret’s Co-Educational English Secondary and Primary School S.4 MathematicsSummer Holiday Homework 2017 –2018 NAME: ___________________________________________ Class: ___________________________________________ Class No.:___________________________________________ Contents Set 1 –2003 HKCEE (Paper 1&2) ...........................................................2 Set 2 –2004 HKCEE (Paper 1&2) .........................................................14 Set 3 –2005 HKCEE (Paper 1&2) .........................................................24 Set 4 –2006 HKCEE (Paper 1&2) .........................................................35

Page 2 of 48Set 1 – 2003 HKCEE (Paper 1&2)Paper 11.Make mthe subject of the formula )(2cmmx.(3 marks)2.Factorize(a)22)(zyx,(b)cdbcadab.(3 marks)3.Solve the equation841x.(3 marks)4.A handbag costs $ 400. The marked price of the handbag is 20% above the cost. It is sold at a 25% discount on the marked price.(a)Find the selling price of the handbag.(b)Find the percentage profit or percentage loss.(4 marks)5.There are only two kinds of tickets for a cruise: first-class tickets and economy-class tickets. A total of 600 tickets are sold. The number of economy-class tickets sold is three times that of first-class tickets sold. If the price of a first-class ticket is $ 850 and that of an economy-class ticket is $500 , find the sum of money for the tickets sold.(4 marks)6.Figure 1 shows a parallelogram ABCD. The diagonals ACand BD cut at (a)Prove that the triangles ABCand CDAare congruent.(b)Write down all other pairs of congruent triangles.(4 marks)E.

Page 3 of 487.At 1:00 a.m., a ship Sis 100 km due east of a lighthouse L. Sis moving at a speed of 20 km/h in the direction N30°W as shown in Figure 2.(a)Find the shortest distance between the ship and the lighthouse, correct to the nearest km.(b)At what time will the ship be nearest to the lighthouse?(5 marks)8.Sector OCD is a thin metal sheet. The sheet ABCDis formed by cutting away sector OBAfrom sector OCDas shown in Figure 4(a).It is known that xCOD, AD= BC= 24 cm, OA= OB= 56 cm and CD= 30πcm.(a)(i)Find x(ii)Find, in term of π, the area of ABCD(4 marks)(b)Figure 4(b) shows another thin metal sheet EFGHwhich is similar to ABCD. It is known that FG=18 cm.(i)Find, in term of π, the area of EFGH(ii)By joining EHand FGtogether, EFGHis then folded to form a hollow frustum of base radius rcm as shown in Figure 4(c). Find r(5 marks)....

Page 4 of 489.Figure 5(a) shows a triangular metal plate OABstanding on the horizontal ground. The side OAlies along the north-south direction on the ground. OA= 3 m, OC= 4 m and AC= 6 m.(a)Find OAC.(2 marks)(b)In Figure 5(b), OADis the shadow of the plate cast on the horizontal ground when the sun shines from S θ Wwith an angle of elevation 30°. AOis produced to cut CDat E. AD(i)Find CD(ii)Find CAD(iii)Using CE+ ED= CD, or otherwise, find θ.(9 marks)= 8 m..

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