2026 GDLSS P1 QP

Name:_______________________________________ ( ) Write in BLOCK Letters Class: S____ TG:______ This document consists of 17 printed pages including this cover page. Greendale Secondary School 2026 GREENDALE SECONDARY SCHOOL Preliminary Examination 2026 Additional Mathematics 4049/01 Paper 1 17 August 2026 Secondary 4 Express 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 6 7 8 9 10 11 12 13 Strand Marks 90

Greendale Secondary School 2 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −−= Binomial expansion nrrnnnnn bbarnbanbanaba ++++++=+ −−− ......21)( 221 , where n is a positive integer and .! )1(...)1(!)!( ! r rnnnrrn nrn +−−=−= 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 sin21

Greendale Secondary School 3 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 Answer ALL questions. 1 The area of a circle is increasing at a uniform rate of 8 cm2/s. Find the rate of increase of the radius when its circumference is 96 cm. [3] 2 (a) Differentiate 52lnxx with respect to x, where x > 0. [2]

Greendale Secondary School 4 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 (b) Hence find 2 4 1 ln x x dx . [4] 3 A, B and C are angles of a triangle. Given that tan 3A= and tan 1B= , without the use of a calculator, evaluate tan C . [5]

Greendale Secondary School 5 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 4 The curve 1 1 1 2xy+= intersects the line 2 3 0xy+ + = at the point A and B. Explain why a line joining points A and B is perpendicular to the line 2 4 0yx− − = . [6]

Greendale Secondary School 6 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 5 Given the term independent of x in the binomial expansion of 6 2 mx x + is 1215. (i) Find the value of the positive constant m. [4] (ii) Using your value of m, show that the coefficient of 3x in the expansion of ( ) 6 321 mxx x++  is 1755. [3]

Greendale Secondary School 7 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 6 In the diagram, the line AF is tangent to the circle at the point E. Given that BCDE is a parallelogram, show, giving all reasons, that (a) angle EGH = angle EDC, [2] (b) triangle BCE and triangle GEH are similar, [2] (c) EGECEHED = . [2] B E D F H G C A O

Greendale Secondary School 8 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 7 A right circular cone has a vertical height of ( )46− cm and a slant height of l cm. The volume of the cone is ( )8 3 6 + cm3. Without using a calculator, express 2l in the form of ( )6ab+ cm2, where a and b are constants. [6]

Greendale Secondary School 9 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 8 A closed cylinder is made from a metal sheet of negligible thickness. The cylinder has radius r m, height h m, and volume of 128 m3. (a) Show that the external surface area of the cylinder, S m2, can be expressed as 2 2562Sr r=+ . [3] Given that r can vary, (b) find the value of r where S is stationary and determine the nature of this stationary value. [4]

Greendale Secondary School 10 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 1 9 (a) (i) Express 2ax bx c++ in the form ( ) 2 a x h k++ where a, h and k are constants. [2] (ii) Hence, state the coordinates of the turning point in terms of a, b and c. [1] (b) Find the range of values of the constant k for which the equation 241x x k− − = has no real roots. [3]