Hillgrove Sec 4NA 2022 Prelim

------- -- HILLGROVE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2022 SECONDARY FOUR (NORMAL ACADEMIC) CANDIDATE NAME CENTRE NUMBER Is I I I I I MATHEMATICS Paper1 Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST ( >I INDEX NUMBER CLASS □-□ I I I I I 4045/01 29 July 2022 2 hours 10.45 AM to 12.45 PM Write your class, index number and name on the work you hand in. You may use an HB pencil for any diagrams, graphs, tables or rough working. Write in dark blue or black pen. Do not use staples, paper clips, glue or correction fluid. Answer all questions. The number of marks is given in brackets [] at the end of each question or part question. 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 total marks for this paper is 80. 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 n, either use your calculator value or 3.142. Parent's/ Guardian's Signature: _______ _ Setter: Mrs Valerie Loh This document consists of 16 printed pages. Partnerlnleaming 288 For Examiner's Use Total 80

Compound interest Mensuration Trigonometry Statistics Mathematical Formulae Total amount= P (1 + ~)" 100 Curved surface area of a cone = ;rr/ Surface area of a sphere= 4n- r 2 1 Volume of a cone= - ;r r 2 h 3 4 Volume ofa sphere= -;r r 3 3 AI a oftriangle ABC= .!..absin C 2 Arc length = r0 , where 0 is in radians Sector area = .!._ r 2 0 , where 0 is in radians 2 a b C --=--=-- sin A sin B sin C a 2 = b 2 + c 2 - 2bc cos A 'I,fx Mean= -- Lf . . J:.,jx2 (J:.,fx)2 Standard deVIatlon = I, f - L f Partnerlnleaming 289

Answer all questions . 1 Workout ( a) 1/~6-78_4_.5_8_7_8_+_0_.0_0_3, 4.63 3 (b) 395+0.445 . 2 Solve 2(p + 7) - 3(p - 4) = 20. 3 Find the smallest integer y satisfying 14 ~ 25 - 3y. Partnerlnlearning 290 Answer .............................. [1] Answer .............................. [1] Answer p = ......................... [2] Answer .............................. [2] BP-295

4 S. l"fy 2a 3 b . Ba5 c rmpl ---3ac 2 • 9b 4 • Answer ............. ................. [2] 5 p is inversely proportional to the cube of r. Given that p = 5 for a certain value of r, find the value of p when r is doubled. Answer p = ........................ [2] 6 Draw a reduction of this pentagon using the scale factor of :. . 3 . , (i;~ c~ :~~ ~~- " ~ '"'1. ~ ~t a~: *·~..._.-+-+-~~,c-+-t---t--+--t--+-1--+---+--+--+---+-----, ~◄1-,,,.....-..---____ --+---4--+--I-·- '~-+--+---4--+--...--+-+----+--+--.f----+---! " PartnerlnLeaming 291 [2] BP-296

- ------ 7 Given that :0 + 27 = 3:m, find m . 8 The point E lies on the line D F. DE: EF = 3: 4. (a) Write EF as a fraction of DF. (b) EF is 48 cm. Calculate DE. Partnerlnleaming 292 Answer m = ....................... [2] Answer .............................. [1] Answer DE = ................... cm [2] BPN297

9 15% of the hand area is 26.25 cm2 . (a) Find the area of the whole hand? Answer ...................... cm2 [1] (b) It is estimated that on our hand, there are 1500 bacterial living on each square centimetre of our skin. Find the amount of bacterial on the whole hand leaving your answer in standard form. Answer ............................ [2] 10 (a) Find angle A such that cosA 0 = -0.35. Answer A = ....................... [1] (b) 690% 21[ ft 6.9 Write these numbers in order, starting with the largest. Answer ............. , ............. , ............. , ............. [2] Partnerlnleaming 293 BPN298

11 (a) Simplify and factorise 1Sxy - 20x - Syx + 12x. (b) Simplify 3q + S(q-l) . 5 3 12 Simplify- 3 - + -2 5 . X-2 X -4 PartnerlnLearning 294 BPN299 Answer ........ ......... .. ........ . [2] Answer ...... ...................... [2] Answer ...... ..... ... .............. [3]

13 Solve these simultaneous eq ations. 2x- 3y = 8, 3x = Sy- 3. Show your working. Answer x = ........................... . y = ......................... [3] 14 Sam needs to travel from Town A to Town B which is 190 km apart. From Town A, he drove at an average speed of 70 km/h for 45 minutes. He stopped at a rest station for half an hour and then continued his journey till he reached TownB . (a) If his average speed is 9 km/h, fmd the total time he took for his journey. (b) What is the distance of Town A to the rest station? Partner! nleaming 295 Answer ...... ................ h [2] Answer ................. .... . km [2]

15 (a) Write 600 as a product of its prime factors. Answer ............................ [2] (b) (i) Write down the lowest common multiple (LCM) of 21 and 600. Give your answer as a product of its prime factors. Answer ............................ [1] (ii) Is the lowest common multiple from (bi) a perfect square? Explain your answer. Answer .............................. ............. ................................... ............... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . ... [1] Tuitio r1 Answer ............................ [2] (b) A quadratic graph has the equation y = x 2 - 12x + 8. (i) Hence, write down the coordinate for the turning point of this graph. Answer ( ............. , ............ ) [1] (ii) Write down the equation of line of symmetry. Answer x = ............... ............. [1] Partnerlnleaming 296 gp .. 301

17 A set of heights in centimetr e of 6 students are given. 15 169 188 164 177 164 (a) State the modal height. (b) Find (i) the mean height , (ii) the median height. PartnerlnLeaming 297 Answer ...... ...... ... .... .... cm [1] Answer .. .............. ....... cm [2] Answer .. .. ........... ........ cm [1] BP-30: