Hua Yi Sec Sch P1 2020

,., ' ,t \) ;\I jf I Name:_ ' I I Index Number: I Class: .N' 'I . \A ' ' I @ HUA YI SECONDARY SCHOOL Preliminary Examination MATH:EM-ATICS I ' Paper1 . Candidates answer on the Question Paper. 4045/1 -· 4 August 2020 2h ,, -'· :, l--r=-------------------------------------, ,, ' READ T'f.lESE INSFRU :Cl110NS~FIRST W.riite your Name, Class and Index Number in the spaces provided at the top of this pag~. Write your answers in the spaces provided on the question paper. ·1,~rite in dark blue or black pen. , You may use a pencil for any diagrams or graphs. Answer all questions. If war-king is needed for any question it must be shown in the space below that question. The use of an approved scientific calculator is expected, where appropriate. If the degree 9f accuracy is not specified in the question, and if the answer is not exact, give the· answer to three significant figures. Give your answers in degrees to one decimal place. For n, use either your calculator value or 3.142, unless the question requires the answer in tentls of n. The number of marks is given in brackets [ ] at the end of each question or part question. The ,total number of marks for this paper is 80. For Examiners Use This doeunieAt consists of 1'5 printed pages including the cover page. ©HYSS2020 No part of this · document may be repmdUced In any fonn•or transmitted In any fonn or by any means with t th . pennlssion of Hua Yi Secondary School. . ou e pnor [Turn Over

Compound interest Mensuration Trigonometry · -".statistics 2 Mathematical Formulae Total amount= J l + _:.....)" , l 100 Curved surface area of a cone = ,rr/ Surface area of a sphere= 4,rr 2 1 Volume of a cone = - ,rr 2 h 3 4 Volume of a sphere = - ,rr 3 3 Area of triangle ABC .!. ab,sin.C 2 Ardength = r(J', where 0 is in radians 1 Sector area = - r 2 (} , where 0 is in radians 2 a b c --=--=--sinA sinB sine a 2 =b 2 +c 2 -2bccosA Mean= 'I.ft 'I.I Standanl devration = -( 'I. fx) 2 "f.J "f.J Sec 4NA Preliminary Examination 2020 Mathematics Paper 1

3 Answer all the questions. 1 (a) Express 0.013 as a percentage. Answer _____ 0_1/o_ [I] (b) Express 56.6% as a fraction. Answer ______ [I] 2 (a) Written as a product of:its prime factors, 18225= 36 x 52 . 3 Without using a calculat9r, find the square root of 18225, leaving your answer in index notation. --o- Answer _____ [1] (b) Explain why the product of 5 and 18225 is a perfect cube. (a) Answer __________________________ _ -------------------- [1] ~;. 5 , ,solve --= 3. (2x-6) Answer _____ [2] (b) E _ 1_ + _2 _ as a single fraction, in its simplest form, . xpress (x2-9) (x+3) Answer _____ [3] . . E amination 2020 Mathematics Paper 1 sec 4NA Prehmmary x

4 \ \ 4 John said that the following is part of a regular polygon. Is he correct? Support your explanation with workings. \ \ \ \ \ \ \ Answer 5 (a) A is inversely proportional to B2. When B = 4 , A =2. Find the value of A when B = 2. (b) 2 Given that 125i = 52m, find m. Sec 4NA Preliminary Examination 2020 Mathematics Paper 1 [2] Answer A = [2] ----- Answer _m_= ____ [3] \ \ \

5 6 The figure shows the speed time graph ot an object during a duration of 14 seconds. I I I I ! ' j ' ! i I I ' t l l I. l I I , . I I I I l, I I : I' I I 11 I I !nl I I', ' , I I ~• (a) Given that the total distance travelled by the object during the first 10 seconds is 270 metres, find the average speed of the object. Answer ------- [l] (b) Given that the area under the graph gives the distance travelled, find the distance travelled during the last 4 seconds. Answer [1] ---- (c) Find the acceleration from t = 2 to t = 10 s. Answer ---- [2] Sec 4NA Preliminary Examination 2020 Mathematics Paper 1

r 7 I I,, J ·,', ,, I, ' 8 I I ' f t I " ,, ' ,, 6 ,4 j ' The fo~.l~wing shows a rectangle of where the diagonals intersect to form an acute angle of 48°. ·· · A....-....,.....,....---------718 C (a) Firid the values of x andy. Answer x= [1] y= [1] (b) Write down one pair of congruent triangles. Answer [1] .(~) Given that siny = 0.25, find two possible values of y. Answer ..... Y'-------=o::.:.r __ [2] (b) BCD is a right angled triangle. A B 5cm C Find the value of (i) sinLCDB (ii) cos LAB D 12cm D Sec 4NA Preliminary Examination 2020 Mathematics Paper 1 Answer (i) (ii) [2] [l]

7 9 E is on the perpendicular bisector of BC and is 5 cm away from A. Using construction, (a) find.the point E, (b) draw the angle bisector of angle BCD. A B D C [3] Sec 4NA Preliminary Examination 2020 Mathematics Paper 1

r 8 10 Raymond and Sammi have each $4000 to invest for 4 years. (a) Raymond invest it at 5% per year simple interest at Bank A. Calculate the total interest Raymond will earn. Answer _____ [1] (b) Sammi invests the amount at an interest rate of 5.2% per year compounded half-yearly. Find the interest he would get at the end of 4 years. 11 The first 4 terms of a sequence is 5, 9, 13, 17, ..... Find (a) the next term, (b) the nth term. 12 Given that the equation of a line is 3x - 4y = 8, (a) state the gradient of the line, Answer _____ [2] . Answer(a) _____ [I] (b) ____ [I] Answer _____ [l] (b) write down the coordinates of the point A, where the line crosses the y-axis. Answer A = ( , ) [ 1] Sec 4NA Preliminary Examination 2020 Mathel'J'latics Paper 1

I I 9 {c) Given B = (3, 6), find the distance between A and B. Answer _____ [2] 13 Solve 3x - 4 < 10 and state the largest prime number that satisfy the inequality. 14 Solve the simultaneous equations. 2x +y = 3 2y = 11 +x 15 A map showing part of an island is drawn to scale of 1 :55000. Answer [2] ---- Answer x= -------"'y_= ____ [3] (a) The distance on the map between two destinations A and B is 5 cm. Find the actual distance, giving your answer in kilometres. Answer km [2] Sec 4NA Preliminary Examination 2020 Mathematics Paper 1

10 (b) . • 2 c 1 late the area on the map. The area of destination A 1s 24200 m · a cu Answer cm2 [2] 16 The stem-and-leaf diagram shows the marks obtained in a test by a group of students. Marks Girls Boys 2 4 6 9 6 6 4 5 0 0 2 3 5 8 3 3 3 2 0 6 2 2 3 7 8 6 6 4 0 7 8 8 9 4 3 1 8 1 1 1 4 4 3 9 3 4 8 Key: Girls 214 means 42 Boys 41 6 means 46 (a) State the modal score obtained by the boys. Answer [I] ----- (b) State the median score obtained by the girls. Answer [1] ----- (c) Compare the distribution of the marks obtained by the boys and girls. Which group performed better? Answer [2] ---- Sec 4NA Preliminary Examination 2020 Mathematics Paper 1 \ \