Regent 4E5N AM Prelim Examination Paper 1 QP

1 NAME: ________________________________ INDEX NUMBER: ________ CLASS: ________ SETTER: MS SU RY _________________________________________________________________________ ADDITIONAL MATHEMATICS 4047/01 Paper 1 14 September 2020 2 hours Candidates answer on the Question Paper. No Additional Materials are required. _________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. Give your answers on the separate Answer Paper provided. 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 of the marks for this paper is 80. _________________________________________________________________________ This document consists of 18 printed pages. TARGET PARENT’S SIGNATURE REGENT SECONDARY SCHOOL PRELIMINARY EXAMINATION 2020 SECONDARY FOUR EXPRESS 80

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , Binomial expansion where n is a positive integer and 2. TRIGONOMETRY Identities AA 22 tan1sec += 22cosec 1 cotAA=+ ( ) BABABA sinsincoscoscos = Formulae for 02 =++ cbxax a acbbx 2 42 −−= ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− ......21 221 ( ) ! )1)...(1( ! ! ! r rnnn rrn n r n +−−=−=      1cossin 22 =+ AA ( ) BABABA sincoscossinsin = ( ) BA BABA tantan1 tantantan  = AAA cossin22sin = AAAAA 2222 sin211cos2sincos2cos −=−=−= A AA 2tan1 tan22tan −= ABC C c B b A a sinsinsin == Abccba cos2222 −+= Abcsin2 1=

3 1 Given that 5tan 12A= , 4cos 5B=− and that A and B are in the same quadrant, calculate without the use of calculator, the value of (i) cos A , [2] (ii) sin( )AB+ . [2]

4 2 Express 32 52 2 −− − xx x in partial fractions. [5]

5 3 (i) On the same diagram sketch the curves 2 121yx= and 11y x= . [2] (ii) Find the coordinates of the point of intersection of the two curves [3]

6 4 The area of a rectangle is (8 7 2)+ cm2. Given that its breadth is (5 2 2)− cm, without using a calculator, show that its length can be expressed in the form ( 2)ab+ cm, where 𝑎 and 𝑏 are integers. [4]

7 5 (i) Solve ( ) 2log 5 7 8 1x xx+ − = [4] (ii) Given that 39log log 2ab−= , express b in terms of a. [3]

8 6 (i) Use the substitution 2xu= to express the equation 28 2 15xx +−= as a cubic equation in u. [3] (ii) Show that 3u= is the only real solution of this equation [4] (iii) Hence solve the equation 28 2 15xx +−= . [3]

9 7 A viscous liquid is poured onto a flat surface. It forms a circular patch which grows at a steady rate of 48 cm2/s (i) Show that the radius of the patch after pouring for 12 seconds is 24  cm/s. [3] (ii) Find in terms of 𝜋, the rate of the increase of the radius at this instant. [3]

10 r h 8 A manufacturer makes jellies using the jelly mould which is made of a hollow hemisphere of radius r cm attached to a hollow cylinder of radius r cm with height h cm as shown in the figure. The thickness of the mould is negligible. 3 2 4Volume of a sphere 3 Surface area of a sphere 4 r r    =  = (i) Given that the volume of the jelly mould is 3200 cm3, express h in terms of r. [2] (ii) Hence, show that the total external surface area of the jelly mould, A cm2, is given by 26400 2 3Ar r =+ . [2]