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.