2023 CCSS Sec 2 EOY Math

2E /End of Year Examination Paper 1/ 2022 Candidate Name Class Register Number Calculator Model No CHANGKAT CHANGI SECONDARY SCHOOL End of Year Examination 2023 Subject : Mathematics Level : Sec 2 Express Paper : 4052/01 Date : 3 October 2023 Duration : 1 hour 15 minutes Setter : Ms Wong SY ___________________________________________________________________________ READ THESE INSTURCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use an HB for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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. 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 , use either your calculator value or 3.142, unless the question requires the answer in terms of . 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 Examiners’ Use Marks Marks / 50 Personal Target Actual Grade Parent’s / Guardian’s Signature This document consists of 11 printed pages, including the cover page. [Turn Over

2E /End of Year Examination Paper 1/ 2023 2 Mathematical Formulae Compound Interest Total Amount = nrP )1001( + Mensuration Curved Surface area of a cone = rl Curved surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector Area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == bccba 2222 −+= Acos Statistics Mean =   f fx Standard deviation = 2 2 )(     − f fx f fx

2E /End of Year Examination Paper 1/ 2023 3 Answer all the questions 11 (a) Simplify 3(2 1) 5x−+ . Answer …................................ [1] (b) Factorise 2 3x y x− . Answer …................................ [1] 2 (a) Express 441 as a product of its prime factors. Answer 441 = ……………….…..................... [2] (b) Using your answer to part (a), explain why 441 is a perfect square. Answer ….............................................................................................................. ……………………………………………………..……………………………………… …………………………………………………………………………………………….. [1] (c) The number 441k is a perfect cube. Find the smallest positive integer value of k. Answer …................................ [1] (d) Find two numbers, both smaller than 150, that have a lowest common multiple of 441 and a highest common factor of 21. Answer ….............. , …............ [2] [Turn Over

2E /End of Year Examination Paper 1/ 2023 4 3 The stem -and-leaf diagram shows the masses, in grams, of 15 packets of various brands of instant noodles. 7 2 2 5 5 8 8 8 8 4 5 5 9 8 10 0 11 0 5 12 5 For these masses, find (a) the range, Answer …...................... grams [1] (b) the mean, Answer …........................grams [2] (c) the median, Answer …........................grams [1] (d) the mode. Answer …........................grams [1] 2 2 2 4 Kate, Ting and Yen shared $450. The ratio of the amount that Kate receives to the to tal amount that Ting and Yen receive is 5 : 4. Ting receives $40 less than Yen. Calculate the difference between the largest and smallest share. Answer $….............................. [3] Key 7 2 represents 72 grams

2E /End of Year Examination Paper 1/ 2023 5 5 (a) Solve 5 1 27xx− − − + . Answer …................................ [2] (b) Represent the solution in (a) on the number line provided below. [1] (c) Write down the largest possible integer that satisfy the solution in (a). Answer ….…............................ [1] 6 n is a positive integer. Show that, for all n, (3𝑛 + 1)2 – (3𝑛 – 1)2 is a multiple of 12. Answer [2] - 11 - 10 - 9 - 8 - 7 - 6

2E /End of Year Examination Paper 1/ 2023 6 7 Factorise completely 6 3 2 1xy x y− + − . Answer …................................. [2] 8 Solve 15 124 yy+ −= . Answer y = ............................... [3] [Turn Over

2E /End of Year Examination Paper 1/ 2023 7 9 22 2 vus a −= (a) Calculate the value of s when 3v= , 2u=− and 1a= . Answer ….…............................ [1] (b) Make v the subject of the formula. Answer ….…........................... [2] 10 9 (a) Factorise completely 22 5 12xx+− . Answer …................................ [2] (b) Hence, factorise completely 22(3 1) 5(3 1) 12aa− + − − . Write your answer as simply as possible. Answer ….…........................... [2] [Turn Over

2E /End of Year Examination Paper 1/ 2023 8 11 In the quadrilateral ABCD, the diagonals AC and BD intersect at E. Triangles ABE and DCE are congruent, AD = 4 cm, CD = 7.9 cm, AE = 2.7 cm, CE = 7.7 cm, angle ABD = 20° and angle BDC = 75°. (a) Find the length of AB. Answer …............................ cm [1] (b) Calculate angle CED. Answer …............................... o [1] (c) State a triangle that is congruent to triangle ABD. Answer triangle ......................... [1] A B D C 4 cm 75° E 2.7 cm 7.9 cm 7.7 cm 20o

2E /End of Year Examination Paper 1/ 2023 9 12 The force, F, between two objects is inversely proportional to the square of the distance, r between them . When the force is 10 N, the distance between the two objects is 2 cm. Find the (a) Find the (i) formula for F in terms of r. Answer …................................ [2] (ii) F when r = 5 cm Answer …..............................N [1] (b) The distance between the two objects is reduced to 20%. Find the percentage increase of the force between the two objects. Answer …..............................% [2] [Turn Over

2E /End of Year Examination Paper 1/ 2023 10 13 A bag contains red counters, yellow counters and green counters. The probability that the counter is red is 1 3 . The probability that the counter is yellow is 7 15 . Red s (a) A counter is chosen at random from the bag. Find the probability that the counter is (i) white, Answer …................................ [1] (ii) green. Answer …................................ [1] (b) Another bag contains 7 blue counters and 11 pink counters. More pink counters are added to the bag. The probability of choosing a pink counter from this bag at random is now 2 3 . Find the total number of the pink counters in the bag. Answer …................................ [2] [Turn Over