Math - Sec 2 - SA 2 - 2021 - Punggol Sec

PUNGGOLSECONDARYSCHOOL SECONDARY 2 EXPRESS END-OF-YEAR EXAMINATION EXP ~-----~ QUESTION & ANSWER BOOKLET NAME CLASS Mathematics Paper1 READ THESE INSTRUCTIONS FIRST INDEX NUMBER Write your class, register number and name on all the work you hand in. Write in dark blue or black pen. You may use a 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. 4048 6 October 2021 1 hour 15 minutes 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, use either your calculator value or 3.142, unless the question requires the answer in terms of n. 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 50. For Examiner's use Parent's Signature /50 This paper consists of 11 printed pages and 1 blank page. Setter(s) : Vetter : Mdm Tng Say Ping Mdm Ho Wei Ling, Ms Jillian Khong PartnerlnLearning 331 BP-331

Compound Interest Mensuration Trigonometry Statistics 2 Mathematical Formulae r Total amount= P(l + -r 100 Curved surface area of a cone = ,rrl Surface area of a sphere= 4nr 2 1 Volume of a cone= -nr 2 h 3 4 Volwne of a sphere= -nr 3 3 Area of triangle ABC= _!_absinC 2 Arc length= r0, where 0 is in radians Sector area = _!_ r 2 0, ·where 0 is in radians 2 a b C -----=-- sinA sinB sinC a 2 = b2 + c2 -2bccosA I: +.x Mean= - 1-" I:J Standard Deviation = Partnerlnlearning 332 BP-332

3 1 If 3x = 2y, write down y2: x2• Answer .. .. .............. .... .. [2] 2 (a) 2 Solve 2-Sx :s;-(3x-9). 3 Answer .. .. ...... .. .... .. .. .. .. [2] (b) Represent the solution on a number line. [ 1] Partnerlnlearning 333 BP-333

4 3 n is a positive integer. Show that, for all values of n, ( 4n + 1)2 -( 4n-1) 2 is a multiple of 4. Answer ............... ............... ............ .... ........... .............. ...... . 4 The diagram shows the plan view (top view) of a box that contains ten spherical crystal balls with radius 2 cm. The box is in the shape of a cuboid and the crystal balls just fit into the box. Calculate the volume of empty space in the box. [3] Answer ............... cm 3 [3] Partnerlnlearning 334

5 5 T .. A regular polygon has n sides. The size of each interior anglhl l!e1 O n times the size of each exterior angle . Find the value of n.w it Answer n = .. . . . . . ... . . . . .. . . [3] 6 In the diagram, the line AC intersects the line BD at E. DE= 10 cm, BE= 5 cm and CD= 12 cm. MBE is congruent to WCE . A Find (a) LA.BE , (b) LEDC , (c) the length of AC. Partnerlnlearning 335 D Answer LA.BE= ............ • [1] Answer L..EDC = ........... 0 [1] Answer AC= ............ cm [1]

6 7 (a) Express 744 as a product of its prime factors . Answer . . . . . . . . . . . . . .. . . . . . . . . . [1] (b) Given that 720 = 24 x 32 x 5, find the highest common factor of both 744 and 720, leaving your answer as a product of prime factors. Answer . . . . . . . . . . . . . . . . . . . . . . . . [1] (c) Find the smallest whole number that is divisible by both 720 and 744, leaving your answer as a product of prime factors. Answer . . . . . . . . . . . . . . . . . . . . . . . . [1] 8 (a) Solve the following equation 16x2 -9 = 0. Answer x = ......... , . . . .... . . [3] (b) Explain why 16x2 + 9 = 0 has no real solutions. Answer....................................................... ............ ................... [1] PartnerlnLearning 336 BP-336

7 9 A distance of 1.6 km is represented by 4 cm on a map. (a) Find the map scale in the form of 1 : r. Answer 1 : . . .. . . . . . . . .. .. ... [1] (b) The distance between a park and a community club on the map is 3.8 cm. Find the actual distance in metres. Answer ............. ....... m [2] (c) The actual area of a park is 320000 m2 . Find the area on the map in cm2• Partnerlnlearning 337 Answer .. ... ..... ........ cm2 [2]

8 10 Express each of the following as a single fraction in its simplest form. (a) (b) 7 2-x ---+-- 2x+10 x+5 5x-2 6 -------- 10x2 +7x-12 3+2x Partnerlnlearning 338 Answer .... .. ........ ... ... .... [2] Answer ..... ................. .. [3] BP~338

11 9 In the diagram below , BD is parallel to LK. LK=BL = 5 cm, BC= 8 cm, JL = 6 cm, JK= 3 cm and CJ=4 cm. ~ ABC is similar to~ ALK and ~ CJD is similar to~ KJL . D Find (a) JD, (b) AC. B Tuition L Partnerlnlearning 339 wit A Answer .... ................ cm [2] Ans wer .............. ...... cm [3]

10 12 (a) y is inversely proportional to ✓x. It is known that y = 2.5 when x = 0.81 . (i) Write the equation connecting x and y . Answer [1] (ii) Find the value of x wheny = 4.5. A [2] nswer x = .......... ........ . (b) A moving object travels s metres int seconds. It is given thats is directly proportiona l to t 2 • If the object travels 75 metres when t = Q seconds, find the new value of s when t = 4Q seconds. Partnerlnlearning 340 Answer s = .. .. .. .. .. .. .. .. ... [2] BP~340