BMSS 4NA 2022 E Math Prelim with ANS

\ Class \ Index Number \ Name BUKIT MERAH SECONDARY SCHOOL PRELIMINARY EXAMINATION 2022 SECONDARY 4 NORMAL (ACADEMIC) MATHEMATICS SYLLABUS A Paper 1 Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your class, index number and name in the spaces at the top of this page. 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 the questions. 4045/01 18 August 2022 2 hours 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 of the 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 re, use either your calculator value or 3.142. Calculator Model: Setter: Mr Eric Yong This document consists of 20 printed pages. Partnerlnlearning 133 For Examiner's Use [Turn over

Compound Interest Mensuration Trigonometry Statistics Mathematical Formulae Total amount= P ( 1 + 1~0) n Curved surface area of a cone = rrrl Surface area of a sphere = 4nr 2 1 Volume ofa cone= 3nr 2 h 4 Volume of a sphere = 3 nr3 1 Area of triangle ABC = 2 ab sin C Arc length= r0, where 9 is in radians 1 Sector area= 2r 2 0, where 9 is in radians a b C --=--=--sin A sin B sin C a 2 = b2 + c2 - 2bccosA r.tx Mean=--L[ r.fx 2 r.tx Stand ard deviation = YT - ( L f Partnerlnlearning 134 ) 2

- - -- ~--- Answer all the questions. 1 (a) Evaluate ;.3 2 + (3.0s-1 i) 2 , giving your answer correct to 2 significant figures. 5.2 x0.08 7 Answer .. .. . . . . . . . . . .. .. .......... ... .. [1] (b) A number is rounded off to 3 significant figures as 0.0308. What is the smallest possible value of the number? Answer . . . .. . .. . . . . . ... .......... .. .... [1] 2 The numbers a, b, c and dare represented on the number line shown below. 11 1.8 ab The values of a, b, c and dare listed below. 1.843, Find a, b, c and d. • 1.8, Partnerlnleaming 135 11 cd 1.9 184% Answer a= ...... ... ......... ...... .. . b = ..... ....... ... ...... ..... . c= ...... .......... ....... ... . d= .. .... .. .. ......... .... .... [2]

BP-140 3 Factorise completely Answer . . . . . . .. ... . . . . . . ..... .. . . . .. . . . [1] Answer .. . . .. . . ... . . .. . . .... ...... ... . . [2] 4 (a) Given that x2 -4x-2=(x+p)2+q,findpandq. Answer p = .......... ... ..... .... .... . q = . ......... .. .. . . ...... ..... [2] (b) Hence, or otherwise, solve the equation x2 - 4x - 2 = 0 . Partnerlnleaming 136 Answer x = ....... ..... or ......... ... [2]

BP-141 5 (a) Calculate the sum of the interior angles of a polygon with 10 sides. Answer ............ .. .. .............. .. [2] (b) Calculate the number of sides of a regular polygon with an interior angle of 162°. Answer .............. ........ ... . sides [2] 6 Nathan is p years old. His brother, Matthew, is 3 years older than him. His sister, Joelle, is 7 years younger than Matthew. Express their average age in terms of p . PartnerlnLeaming 137 Answer ... ..... ... .... ...... years old [3]

7 2-x x-1 Express --- -- as a single fraction. 5 10 8 A road of actual length 8.25 km is 11 cm on a map. (a) Find the scale of the map in the form 1 : n. (b) On the map, a reservoir has an area of 10 cm2. Find the actual area, in km2, of the reservoir. PartnerlnLearning 138 BP-142 Answer .. .. .. .. . .. ...... .... ..... .. .. . . [2] Answer ................ .. .... ...... .... [I] Answer .. .. .... ........ ........ .. km.2 [2]

9 Triangle ABC is equilateral and BD is parallel to AC. Triangle DEC is isosceles and angle EDC is 35°. Giving reasons, find (a) angle BDE, (b) angle BAD. D Partnerlnlearning 139 BP-143 ·tion C Answer ................... ............. [2] Answer ............................... [2]

10 (a) Simplify XJ,,2 x 3;. X (b) Expand and simplify x + 2 ( 5 -3x) . 11 Given 2 = 3- p , write pas the s bject of the equation. p+q Partnerlnleaming 140 Answer .. . . . . . . . .. . ... . . . . .... .... .. . . . [1] Answer ................................ [2] Answer ........ ................... . .... [2]

12 Consider the pattern below. n=l n=2 n=3 The table below records the numbers of dots and lines in each pattern. (a) Complete the table. Answer n 1 2 3 4 No. of dots 3 4 5 6 No. of lines 3 5 7 9 (b) The sum of dots and lines in pattern 1 is 6. The sum of dots and lines in pattern 2 is 9. n Can the sum of dots and lines in any pattern be 503? Explain your answer with clear working. Answer ..... ...... ............ ..... .... .. ............. ... ............. ....................................... .. . . Partnerlnleaming 141 BP~14 [2] [2]

13 BP-146 A B 7.5 cm C D In the diagram above, MED is a right-angled triangle, where BC= 7.5 cm, LA.CB= 45° and LADB=23° . Find (a) the length of AB, (b) the length of CD. Partnerlnleaming 142 Answer AB= ... ... ......... ...... cm [I ] Answer CD = .................... cm [2]