NYGH 2025-S3EOY-IM2 with Ans

Class Register Number Name End-of-Year Examination 2025 Secondary 3 INTEGRATED MATHEMATICS 2 2 hours Thursday 9 October 2025 1145 – 1345 READ THESE INSTRUCTIONS FIRST 1. Write your name, register number and class on all the work you hand in. 2. Write in dark blue or black ink. 3. You may use an 2B pencil for any diagrams or graphs. 4. Do not use staples, paper clips, glue or correction tape/ fluid. 5. Write your answers and working on the separate writing paper provided, unless otherwise stated. 6. Answer all questions. 7. Omission of essential working will result in loss of marks. 8. The use of an approved scientific calculator is expected, where appropriate. 9. 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 degree to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. 10. At the end of the examination, fasten all your work securely together. 11. The number of marks is given in brackets [ ] at the end of each question or part question. 12. The total of the marks for this paper is 80. For Examiners’ Use Question Marks 1 / 4 2 / 4 3 / 3 4 / 5 5 / 3 6 / 6 7 / 6 8 / 6 9 / 9 10 / 10 11 / 6 12 / 9 13 / 9 Total This document consists of 21 printed pages and 1 blank page. NANYANG GIRLS' HIGH SCHOOL [Turn over 80

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0 , x = a acbb 2 42 −− .

3 1 (a) Express y = x2 + 6x + 8 in the form y = (x + a)2 + b, where a and b are constants. [2] (b) Hence state (i) the minimum value of y, [1] (ii) the value of x at which the minimum value occurs. [1]

4 2 Simplify 27 3 48 8 − + , leaving your answer in the form 3ab+ where a and b are rational numbers. [4]

5 3 Given that 7cos 4A=− and tan A is positive, without finding the value of A , find the exact value of 4cos 3tanAA− . [3]

6 4 Express 2 2 4 5 32 ( 2) ( 11) xx xx +− +− in partial fractions. [5]

7 5 If 11lg( ) lg lg lg 322x y x y− = + + , prove that 22 11x y xy+= . [3]

8 6 The function f is defined by f ( ) 3sin 2xx= for 02 πx . (a) State the amplitude and period of f. [2] (b) Sketch the graph of f ( )yx= for 02 πx . Indicate clearly the intercepts and the turning points. [4]

9 7 Given that sin 50 = p , express each of the following in terms of p. (a) cos50 [2] (b) sin 40 [2] (c) tan130 [2]

10 8 (a) Solve 32 16 8 32 x  = . [3]