2019 CCHY MYE 4047 P1

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 1 of 17 1 Mid-Year Examination (2019) Secondary 4 Express / 5 Normal (Academic) Candidate Name Register No Class Additional Mathematics Paper 1 4047 / 1 Date : 13th May 2019 Duration : 2 hours READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all 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 staples, paper clips, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total marks for this paper is 80. Setter : Poh Eng Hua Terence This paper consists of 17 printed pages, INCLUDING the cover page. For examiner’s use / 80 [Turn over

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 2 of 17 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, x = a acbb 2 42 Binomial Expansion nba = na +    1 n 1na b +    2 n 2na 2b +    +    r n rna  rb +    + nb , where n is a positive integer and    r n =  !! ! rnr n  =  ! 11 r rnnn  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 ) = cosA cos B  sin A sin B tan ( A  B ) = BA BA tantan1 tantan   sin 2A = 2 sin A cos A cos 2A = cos2 A - sin2 A = 2 cos2 A – 1 = 1 – 2 sin2 A tan 2A = A A 2tan1 tan2  Formulae for ABC A a sin = B b sin = C c sin a2 = b2 + c2 – 2bc cos A area of ABC = 1 2 ab sin C

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 3 of 17 1. (i) Show that 4|4𝑥− 6|− 2|9 − 6𝑥| =𝑘|2𝑥− 3|, where k is a constant. [2] (ii) Hence, find x when 𝑘|2𝑥− 3| = 5. [2] 2. A curve has an equation of 𝑦= 2𝑥ଶ− 4𝑥+𝑐 where c is a constant. Find the range of values of c for which line 𝑦= 2𝑥+ 1 intersects the curve at 2 distinct points. [3]

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 4 of 17 3. Given that rectangle ABCD has side CD = 5 cm, AE =√18 cm and 3ADB radian, show that 15sin 212AED radian. [3] A B C D E గଷ radian 5cm √18 cm

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 5 of 17 4. ଻ √଻ି√ଶ− ଵ √଻ can be expressed as 𝑎√2+𝑏√7. Find the value of 𝑎 and 𝑏 where 𝑎 and 𝑏 are rational numbers. [3]

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 6 of 17 5. 2𝑥ଶ−𝑥− 1 is a factor of 2𝑥ସ− 7𝑥ଷ+𝑎𝑥ଶ+ 13𝑥+𝑏. Find the value of 𝑎 and of 𝑏. [6]

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 7 of 17 6. (i) Sketch the graph of 𝑦=|36 −𝑥ଶ|, showing clearly the x-intercepts, [3] y-intercept and the turning point. (ii) On the same axes, sketch the graph of 𝑦=|4𝑥+ 25|. [2] (iii) Write down the number of solution(s) for |25 + 4𝑥| =|36 −𝑥ଶ|. [1] x y o

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 8 of 17 7. A, B and C are vertices of a triangle and coordinates of A and B are (1, 5) and (4, 1) respectively. The perpendicular bisector of AB cut the x-axis at C. Find (i) the equation of the perpendicular bisector of AB, [4] (ii) the area of triangle ABC. [3]

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 9 of 17 8. f(𝑥)= 3 − sin2𝑥 is defined for 0 ≤𝑥≤ 2𝜋. (i) State the amplitude and period of f(𝑥). [2] (ii) Sketch graph of 𝑦= f(𝑥) for 0 ≤𝑥≤ 2𝜋, showing clearly the turning points and the intercepts with y = 3. [3] (iii) Solve 2.5 = 3 − sin2𝑥 for 0 ≤𝑥≤ 2𝜋. [4]

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 10 of 17 9. The cross-section of a trough ABCDEF is an isosceles triangle with height 2 m and base angle 45o. The length of the trough is 8 m. The trough ABCDEF is initially filled to the brim with water. Due to a leak, the height of the water level is dropping at a constant rate of 0.25 m/s. (i) Show that the volume (V) of water in the trough is given by 𝑉 = 8ℎଶ, where h is the height of water in the trough. [4] 45o 2 m h 45o 8m A B C D E F