Sec 2 Chung Cheng High School(Yishun) 2025 Math EOY

1119 2025 EYE Mathematics / Sec 2 G3 123[Turn_over 2025 End-Of-Year Examination Secondary Two General 3 CANDIDATE NAME FORM CLASS / SUBJECT GROUP / INDEX NUMBER MATHEMATICS 2 October 2025 2 hours 30 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number on the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all the 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. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. 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 π , use either your calculator value or 3.142. This document consists of 21 printed pages and 1 last page. Q1 Q2 Q3 Q4 Q5 Q6 Q7 4 4 5 3 3 2 4 Q8 Q9 Q10 Q11 Q12 Q13 Q14 3 3 3 4 3 5 6 Q15 Q16 Q17 Q18 Q19 Q20 Q21 5 5 4 8 8 9 9 Presentation Deduction –1 / –2 Total (100) CHUNG CHENG HIGH SCHOOL (YISHUN)

2219 2025 EYE Mathematics / Sec 2 G3 223[Turn_over Mathematical Formulae Compound interest Total amount 1 100 n rP=+  Mensuration Curved surface area of a cone πrl= 2Surface area of a sphere 4 πr= 21Volume of a cone 3 πr h= 34Volume of a sphere 3 πr= 1Area of triangle sin 2ABC ab C= , where is in radiansArc length r= 2 , where is in radians1Sector area 2 r = Trigonometry sin sin sin a b c A B C== 2 2 2 2 cos Aa c bcb += − Statistics Mean fx f=  22 Standard deviation fx fx ff  =−   

3319 2025 EYE Mathematics / Sec 2 G3 323[Turn_over 1 Simplify (a) 3(3 2) 1x−+ , Answer ................................................ [1] (b) 2 3 x x+ , Answer ................................................ [1] (c) 3 2( 5)xx−− . Answer ................................................ [2] 2 (a) Factorise 22 7 15xx+− . Answer ................................................ [2] (b) Hence factorise completely 22(2 1) 7(2 1) 15yy+ + + − .

4419 2025 EYE Mathematics / Sec 2 G3 423[Turn_over Answer ................................................ [2] 3 Simplify (a) 32 2 12 7 a b ac b , Answer ................................................ [2] (b) 2 2 91 3 16 5 a aa − ++ . Answer ................................................ [3] 4 Solve 2 3 xx − =− .

5519 2025 EYE Mathematics / Sec 2 G3 523[Turn_over Answer x= ................. or x= ................. [3] 5 Given 2 3 3 2 qrp qr −+= , (a) evaluate p when 2r =− and 3q= . Answer p= ........................................ [1] (b) express q in terms of p and r. Answer q= ........................................ [2] 6 There are 25 adults and 7 children in the theatre room. After another 2 y adults and y children entered the theatre room, the probability of selecting a child at random becomes 2 7 . Find the value of y.

6619 2025 EYE Mathematics / Sec 2 G3 623[Turn_over Answer y= ......................................... [2] 7 Mrs Chan has a map of Singapore drawn to a scale 1 : 120 000 . The distance on the map between Bird Paradise and her house is 15 cm. (a) Calculate the actual distance, in kilometres, between Bird Paradise and her house. Answer .......................................... km [2] (b) Bird Paradise covers an area of 20.17 km . Calculate the area, in square centimetres, covered by the Bird Paradise on the map. Answer .......................................... 2cm [2] 8 Express 2 2 6 4 2 3 4 12 9 x x x x −−− − + as a single fraction.

7719 2025 EYE Mathematics / Sec 2 G3 723[Turn_over Answer ................................................ [3] 9 In a physics experiment using Hooke’s Law, the force F in Newtons (N) required to stretch a spring is directly proportional to its extension ,x in metres. When the spring is stretched by 5 cm, a force of 2.5 N is needed. (a) Find the equation connecting F and .x Answer ................................................ [2] (b) Hence, calculate the force needed to stretch the same spring by 8 cm. Answer ............................................. N [1] 10 Given that 3( 1) 12 x x− + , find the greatest possible value of x if x is (a) a perfect square, Answer x= ......................................... [2] (b) a prime number.

8819 2025 EYE Mathematics / Sec 2 G3 823[Turn_over Answer x= ......................................... [1] 11 One solution of the equation 2 ( 2) 2 0kx k x+ + − = is 1 3x= . (a) Find the value of k. Answer k = ......................................... [2] (b) Hence, find the other solution of the equation. Answer x= ......................................... [2] 12 The dot diagram shows the distribution of marks that 15 students from Class A scored in a science quiz. The maximum score is 10 marks. (a) Describe the dot diagram shown above. .................................................................................................................................................... .................................................................................................................................................... 1 2 3 4 5 6 7 8 9 10 Number of marks

9919 2025 EYE Mathematics / Sec 2 G3 923[Turn_over .................................................................................................................................................... [2] (b) State the modal mark(s). Answer ................................... mark(s) [1] 13 A fraction is equivalent to 1 6 if 1 is subtracted from the numerator and 3 is added to its denominator. If 2 is added to the numerator and 5 is subtracted from the denominator of the original fraction, the resulting value is 3 5 . Find the original fraction.

101019 2025 EYE Mathematics / Sec 2 G3 1023[Turn_over Answer ................................................ [5] 14 The diagram shows a field PQRS on horizontal ground, crossed by a pathway PR. RS SP= , 60 mPQ= , 80 mQR= and angle 73.8PSR= . (a) Show that angle 106.2SPQ= , correct to one decimal place. Answer [2] (b) Find SR. Answer .......................................... m [2] (c) Find the shortest distance from Q to PR. P Q R S