Greendale Sec 2024 Prelim P1 with Solutions

Name:_______________________________________ ( ) Write in BLOCK Letters Class: S____ TG:______ This document consists of 17 printed pages including this cover page. Greendale Secondary School 2024 GREENDALE SECONDARY SCHOOL Preliminary Examination 2024 Additional Mathematics 4049/01 Paper 1 22 August 2024 Secondary 4 Express / 5 Normal Academic 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your index number and name 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. 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. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. My Target BEFORE My Reflection: My Target AFTER Qn 1 2 3 4 5 6a 6b 7 8 9 10 11 12a 12b(i) 12b(ii)c Strand A1 A2 A6 A6 G1 C1 C2 G2 G1 C3 A5 G2 C2 C1 C2 Marks 4 6 6 6 6 3 3 8 8 8 9 11 5 3 4 90

Greendale Secondary School 2 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −±−= Binomial expansion nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− ......21)( 221 , where n is a positive integer and .! )1(...)1( !)!( ! r rnnn rrn n r n +−−=−=      2. TRIGONOMETRY Identities AAec AA AA 22 22 22 cot1cos tan1sec 1cossin += += =+ A AA AAAAA AAA BA BABA BABABA BABABA 2 2222 tan1 tan22tan sin211cos2sincos2cos cossin22sin tantan1 tantan)tan( sinsincoscos)cos( sincoscossin)sin( −= −=−=−= = ±=± =± ±=±   Formulae for ∆ABC C c B b A a sinsinsin == Abccba cos2222 −+= Area of ∆ = Abc sin2 1

Greendale Secondary School 3 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 Answer ALL questions. 1 The maximum value of the expression 2 10ax x c++ is 7. Find a pair of possible integer values of a and c. Show your working clearly. [4]

Greendale Secondary School 4 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 2 The equation of a curve is 2 644 ,y ax x a= ++− where a is a constant. (a) In the case a = 3, find the set of values of x for which the curve lies completely above the line y = 17. [2] (b) In the case where 1 ,2a= show that the line 84yx= − is a tangent to the curve. [3] (c) The straight line L meets the curve at one point only. Given that L is not a tangent to the curve, what can be deduced about L? [1]

Greendale Secondary School 5 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 3 (a) Solve the equation 232 2 4 0.xx +− += [3] (b) The price of a watch was $24500 on 1 Jan 2014. The price of the watch appreciates by the formula, 0.0224500 , tPe= where t is the time in years after purchase of the watch and P is the price of the watch after t years. Estimate (i) the price of the watch on 1 Jan 2024. [1] (ii) the year in which the price of the watch is double the initial price. [2]

Greendale Secondary School 6 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 4 The diagram shows two curves 12 and ,CC one of which represents lg( 2)yx= + and the other ln( 2).yx= + (a) State the value of a. [1] (b) Explain briefly if 1C represents the graph lg( 2).yx= + [2] (c) Solve the equation 2lg( 2) ln( 2).xx+= + [3]

Greendale Secondary School 7 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 5 The figure below shows part of the graph of cosy a bx c= + for 02 x π<< . (a) Find the value of each of the constants a , b and c . [3] (b) On the same axes, sketch the graph of 4sin 1yx= + for 02 x π<< . [2] (c) Write down the number of solutions to the equation 4sin cos 1 0x a bx c− −+= . [1] x y

Greendale Secondary School 8 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 6 (a) Differentiate 2 3 35 4 xx x − with respect to x. [3] (b) Integrate 2 1 3 xx  − with respect to x. [3]

Greendale Secondary School 9 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 7 A rhombus ABCD has coordinates ( 1, 5)A − , ( ,8)Bp , (7,13C ) and ( ,10)Dq . (a) Find the value of the gradient of the line BD. [2] (b) Find the coordinates of B and of D. [4] (c) Find the area of the rhombus ABCD. [2]

Greendale Secondary School 10 Sec 4 Express / 5 Normal Academic Preliminary Examination 2024 Additional Mathematics Paper 1 8 (a) Show that tan15 2 3°= − . [4] (b) Hence, express 2cosec 15 ° in the form 3ab+ , where a and b are integers. [4]