2026 GDLSS P2 QP

Name:_______________________________________ ( ) Write in BLOCK Letters Class: S____ TG:______ This document consists of 19 printed pages including this cover page. Greendale Secondary School 2026 GREENDALE SECONDARY SCHOOL Preliminary Examination 2026 Additional Mathematics 4049/02 Paper 2 20 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 Strand Marks 90

Greendale Secondary School 2 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 = + +c bx ax, a ac b bx 2 42 − ± −= Binomial expansion nr r nnnn n b b arnb anb ana b a + ++ +++ = + −−− ......21) ( 2 21 , where n is a positive integer and .! ) 1 ( ... ) 1 (! )! (! r r n n nr r nnrn + − −=−= 2. TRIGONOMETRY Identities AAec AA A A 22 22 22 cot1cos tan1sec 1cossin + = + = = + A AA AA A A A A A A B A B AB A B A B A B A B A B A B A 2 2222 tan1 tan22tan sin2 1 1cos2sin cos2cos cos sin2 2sin tan tan1 tan tan)tan( sin sin cos cos)cos( sin cos cos sin)sin( −= − = − = − = = ±= ± = ± ±= ±   Formulae for ∆ABC C c B b A a sin sin sin= = A bc c b acos22 2 2− + = Area of ∆ = A bcsin21

Greendale Secondary School 3 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 Answer ALL questions. 1 A flock of 50 cuckoos was introduced to an island where it is not a native species. The population of cuckoos is predicted to increase so that after a period of t years, the population, P, is given by 0.141 t kP e−= + , where k is a constant. (i) Find the number of cuckoos present after 9 years. Give your answer correct to the nearest integer. [2] (ii) Find the value of P as t becomes very large. Explain the significance of this value. [2]

Greendale Secondary School 4 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 2 Find the range of values of the constant k for which the line ( )52 3y kx= +− lies entirely below the curve ( ) 2 92yx k x=++ − . [5]

Greendale Secondary School 5 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 3 Solve the equation ( )3 93log 18 4log log 2 4 2xx+ = ++ . [5]

Greendale Secondary School 6 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 4 A curve is such that 2 21 2 d 4ed xyx −+= and the gradient at ( ) 32, e− is 32 4e−− . (a) Find ddyx in terms of x. [3] (b) Explain why the curve has no stationary points. [1] (c) Find the equation of the curve. [3]

Greendale Secondary School 7 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 5 (a) Given that 23 1 3 2 2 62 23323 ab − ×= ×× , find the values of a and b. [3] (b) Given that n is a positive integer, explain why the largest prime factor of 122(3 ) 4(3 ) 3n nn++ −+ is 11. [3]

Greendale Secondary School 8 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 6 The equation of a circle, 1C , with centre A, is 22 4 6 12 0xy xy+++−= . (a) Find the coordinates of A and the radius of 1C . [3] Given that the circle pass through a point P ( 5, 7)−− and a point Q such that PQ is the diameter of the circle. (b) Find the coordinates of Q. [1] The tangent to the circle at point Q intersects the x-axis at point R. A second circle, 2C , centre B, is drawn passing through A, Q and R. (c) Show that the coordinates of R is 7 ,03 . [3]

Greendale Secondary School 9 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 (d) (i) Show that the coordinate of B is 13,62 − . [3] (ii) Find the radius of 2C in exact form. [1] (e) State the equation of 2C . [1]

Greendale Secondary School 10 Sec 4 Express Preliminary Examination 2026 Additional Mathematics Paper 2 7 (a) The term containing the highest power of x and the term independent of x in the polynomial f(x) are 4x and 6− respectively. Given that 2 6xx+− is a quadratic factor of f(x) and the remainder when f(x) is divided by ( )2x+ is 36− . Find an expression for f(x) in descending powers of x. [4]