PHSS 2022 EYE 3NA Ans

1 NAME: ( ) CLASS: TEACHING GROUP: MARKS /100 PEI HWA SECONDARY SCHOOL END OF YEAR EXAMINATION 2022 Secondary Three Normal (Academic) MATHEMATICS 28 September 2022 2 hour 30 minutes Candidates answer on the question paper. No Additional Materials are required READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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. Answer all questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. 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 , use either your calculator value or 3.142, unless the question requires the answer in terms of . 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 100. This question paper consists of 21 printed pages, inclusive of this cover page. For Examiner’s Use Category Question No. Correction tape Pencil written Arrows Units Others

2 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos222 2 −+= Statistics Mean =   f fx Standard deviation = 22fx fx ff  −  

3 Answer all the questions 1  3.14 3.14 • 22 7− 3.142− Write these number in order of size, starting with the largest. Answer …….……., ……….…., ……….…., …….……., …….……. [2] largest 2 (a) Express 792 as the product of its prime factors. Answer …..………………………….. [1] (b) Hence find the smallest integer of p such that 792 p is a perfect square. Answer p= …..……………………... [1] 3 It is given that yx z= . (a) Find x when 125y= and 3z= . Answer x= ………………..……… [1] (b) Express z in terms of x and y . Answer z= ……………………….. [2] [Turn Over

4 4 Sam placed $25 000 in an account earning a compound interest of 3.6% per year for 5 years. Find the total interest he earned at the end of 5 years. Answer $ …..……………………….. [3] 5 (a) cos152 cos z=−  . Given that z is an acute angle, find z . Answer z= ………………………… [1] (b) The area of a triangle XYZ is 236.736 cm . 12.8 cmXY = and 8.2 cmYZ = . Find the two possible sizes of angle XYZ . Answer Angle XYZ= .……….… or …………… [3]

5 6 (a) A bag contains some balls, of which 13 are blue, 9 are red and the rest are green. A ball is drawn from random from the bag. If the probability of drawing the green ball from the bag is 2 13 , show that the total number of balls in the bag is 26. Answer [2] (b) Find the probability that the ball drawn is not red. Answer …...………………………….. [1] 7 The frequency, f hertz, of a microwave is 123 gigahertz . (a) Write 123 gigahertz in hertz using standard form. (1 gigahertz = 910 hertz) Answer …………………………hertz [1] (b) The wavelength,  m of the microwave is calculated using the formula 83 10 f = , where f is the frequency in hertz. Find the wavelength of the microwave in millimeters. Answer ………………………… mm [2] [Turn Over

6 8 The line l has equation 3 2 9yx−= . (a) (i) State the gradient of the line l . Answer gradient= …………………... [2] (ii) Write down the coordinates of the point where the line l cuts the y− axis. Answer (……….……, ……………..) [1] (b) Determine if the point ( )2, 1− lies on the line l . Answer [2] 9 (a) By using construction, (i) construct a line such that it cuts the side AB into half, [1] (ii) mark and label P such that P is the intersection of the angle bisector of angle BAC and the line drawn in part (ai). [2] (b) Measure the longest possible distance of P from a vertex. Answer …...………………...…… cm [1] A B C

7 10 The diagram shows three regular polygons, ,AB and C joined together. Polygon A is a square and polygon B is a pentagon. Find the number of sides in polygon C . Answer …....………………...………. [4] [Turn Over A B C

8 11 Xing Qin is standing 125 m away from the building. The distance of her eyes from her feet is 1.65 m. A flag is placed at the top of the building. The distance from the top of the flag to the ground is 115 m. She claims that by tilting her head up at an angle of 40 , she can see the top of the flag. Explain with working, state whether her claim is correct. Answer [4] F X G E D 125 m 115 m

9 12 The diagram shows a quadrilateral ABCD . (a) Show that the length of AC is 7 cm . Answer [2] (b) Calculate angle ACD . Answer …....………………...………. [2] C B A D 5 cm 4 cm 8 cm [Turn Over

10 13 Each of the sequence is found by subtracting the same number from the previous term. The first five terms of the sequence are 47 23a b c . (a) Find the values of ,ab and c . Answer …...………………...……….. [2] (b) Find an expression for the thn term of the sequence. Answer …...………………...……….. [1] (c) Determine if 123− is a term in this sequence. Answer [2]