NYGH 2022-S4EOY-IM2 with answer

Class Register Number Name End-of-Year Examination 2022 Secondary 4 INTEGRATED MATHEMATICS 2 2 hour 30 minutes Monday 3 October 0845 – 1115 Additional Materials: Nil READ THESE INSTRUCTIONS FIRST 1. Write your name, register number and class on all the work y ou hand in. 2. Write in dark blue or black ink. 3. You may use an HB pencil for any diagrams or graphs. 4. Do not use staples, paper clips, glue or correction tape/flu id. 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, wh ere 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 securel y together. 11. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 6 printed pages. Setter(s): NYGH/HCI NANYANG GIRLS' HIGH SCHOOL [Turn over

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, x = a acbb 2 42  Binomial expansion (a + b) n = a n +       1 n a n  1b +       2 n a n  2b2 + . . . +       r n a n  r br + . . . + b n , where n is a positive integer and ! ))......(( )!(! ! r rnnn rnr n r n 11 =        . 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A sin (A  B) = sin A cos B  cos A sin B cos (A  B) = cos A cos B ∓ sin A sin B tan (A  B) = BA BA tantan1 tantan   sin 2A = 2 sin A cos A cos 2A = cos 2A – sin 2A = 2 cos 2A – 1 = 1 – 2 sin 2A tan 2A = A A 2tan1 tan2  )(2 1sin)(2 1sin2coscos )(2 1cos)(2 1cos2coscos )(2 1sin)(2 1cos2sinsin )(2 1cos)(2 1sin2sinsin BABABA BABABA BABABA BABABA     Formulae for △ABC ௔ ୱ୧୬ ஺ൌ ௕ ୱ୧୬ ஻ൌ ௖ ୱ୧୬ ஼ 𝑎ଶ ൌ𝑏 ଶ ൅𝑐 ଶ െ2 𝑏 𝑐c o s𝐴 △ൌ 1 2 𝑏𝑐 sin 𝐴

3 [Turn Over 1 The equation of a curve is 225 7yx x  . (i) Express 225 7xx in the form 2()ax b c  , where a, b and c are constants. Hence sketch the curve, indicating clearly the turning point and the intercepts. [5] (ii) Find the range of values of m for which 225 7yx x  intersects the line 9ym x at two distinct points. [3] 2 (a) Solve 145 ( 2 ) 1 6 0xx   . [4] (b) The electric power, P watts, is given by 2P IR where I amperes is the current flowing through the circuit and R ohms is the resistance. Calculate the resistance of a 72 watts light bulb that draws  31 amperes of current. Leave your answer in the form 3ab , where a and b are integers. [