JVSS 4E A Math Prelim 2021 Paper 02 QP

This document consists of 18 printed pages. [Turn over JURONGVILLE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2021 Secondary 4 Express STUDENT NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS 4049/02 Paper 2 31 AUGUST 2021 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. 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. DO NOT WRITE ON ANY BARCODES. Answer ALL 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 83. DO NOT OPEN THE BOOKLET UNTIL YOU ARE TOLD TO DO SO Setter: Mr Billy Chew For Examiner’s Use 83

2 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 1. ALGEBRA Quadratic Equation For the equation ,02 =++ cbxax a acbbx 2 42 −−= Binomial expansion ,......21)( 221 nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− where n is a positive integer and ! )1(...)1( )!(! ! r rnnn rnr n r n +−−=−=      2. TRIGONOMETRY Identities AAec AA AA 22 22 22 cot1cos tan1sec 1cossin += += =+ BA BABA BABABA BABABA tantan1 tantan)tan( sinsincoscos)cos( sincoscossin)sin(   = = = A AA AAAAA AAA 2 2222 tan1 tan22tan sin211cos2sincos2cos cossin22sin − = −=−=−= = Formulae for ABC Cab Abccba C c B b A a sin2 1 cos2 sinsinsin 222 = −+= ==

3 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 [Turn Over 1 Represent the solution set of (k + 2)2 > 13k − 16 on a number line. [4]

4 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 2 The equation of a curve is 5 6 3 4 xya =+ . The normal to the curve at 1 2x= is parallel to the line 5 4 2yx+= . (a) Show that 7 64a=− . [4] (b) Find the equation of the tangent to the curve at 1 2x= . [3]

5 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 [Turn Over 3 The binomial expansion of (1 3 ) nx− , where 0n , in ascending powers of x is 231 6 54 ....px x qx− + + + (a) Find the value of n, p and q. [5] (b) Find the coefficient of x3 in (1 – 3x)n (1 + 2x) [2]

6 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 4 In the diagram, DEFG is a cyclic quadrilateral in which DE = FE and DG is parallel to EF. The tangent to the circle at F meets DG produced at A. (a) Show that angle GFA = angle EDF. [3] (b) Show that triangle FGA is isosceles. [4] D E F G A

7 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 [Turn Over 5 The diagram shows two rods, AB and BC, of lengths 30 cm and 70 cm respectively. The rods are fixed at B such that angle ABC = 90° and hinged at C so as to rotate in a vertical plane. The rod BC makes an acute angle  with horizontal ground. The height of A above the ground is h cm. (a) Show that the height, h cm, can be expressed in the form 𝑝 sin 𝜃 − 𝑞 cos 𝜃 , where p and q are constants to be found. [3] (b) Express h in the form )sin( −R , where R > 0 and  is an acute angle. [3] (c) Find the value of θ for which h = 20 cm. [2]

8 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 6 The table below shows some values of x and y. x 2 4 6 8 y 5.3 12.3 27.3 61.5 (a) On the grid provided, plot ln y against x and draw a straight line graph [3] (b) Find the gradient of your straight line and hence express y in the form of abx, where a and b are constants. [4] (c) By drawing a suitable line on your graph, solve the equation abx = e0.7x [2]

9 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 [Turn Over

10 Jurongville Secondary School 4E PRELIM / 4049_02 / 2021 7 (a) Find the range of values of c for which the curve ( )5 12y x x=− does not intersect the line 𝑦 = 2𝑥 − 𝑐. [3] (b) By expressing 2 47xx−+ in the form of ( ) 2 x h k−+ , where h and k are constants, explain why 2 47xx−+ is always greater than or equal to 3. [3]