East Spring Secondary 4051/02 QP

Setter: Ms Mindy Yue EAST SPRING SECONDARY SCHOOLTowards Excellence and Success Name: ……………………………………………………………………….……………( ) Class: ……………….N Level Preliminary Examination 2025Secondary 4 Normal Academic ADDITIONAL MATHEMATICS (SYLLABUS A)4051/02 Paper 2 1 AUGUST 20251 hour 45 minutes FRIDAY1005 – 1150 Candidates answer on the Question Paper. No Additional Materials are required.READ THESE INSTRUCTIONS FIRSTWrite your name, class and register number in the spaces provided above, and on all the work you hand in.Write in dark blue or black pen.You may use an HB pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid.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 number of marks for this paper is 70. 70This question paper consists of 17 printed pages including the cover page.

2 2025 ESSS Prelim 4NA A MATH P2 Mathematical Formulae1.ALGEBRAQuadratic EquationFor the equation ax2 + bx + c = 0,24.2bbacxa2.TRIGONOMETRYIdentities22sincos1AA22sec1tanAA22cosec1cotAAsinsincoscossinABABABcoscoscossinsinABABABmtantantan1tantanABABABmsin22sincosAAA2222cos 2cossin2cos112sinAAAAA22tantan 21tanAAAFormulae for ABCsinsinsinabcABC2222cos.abcbcA1sin.2bcA

3 2025 ESSS Prelim 4NA A MATH P2 1Solve the simultaneous equations.221,7.xyxyxy [5]

4 2025 ESSS Prelim 4NA A MATH P2 2(a)A cosine graph with equation cosyabxc, where x is in degrees, has period 180° and has a minimum value of – 4 and a maximum value of 2. Find the values of the integers a, b and c. [3] (b)Sketch, on the axes below, the graph of the curve 4sin21y for 02. [3]xy2322246– 2– 4– 6O

5 2025 ESSS Prelim 4NA A MATH P2 3(a)Find the range of values of p for which 2(2)5yxxpis always positive for all real values of p. [4] (b)James claims that the curve 231yxx is always positive. By using your answer in (a), justify whether his claim is correct. [1]

6 2025 ESSS Prelim 4NA A MATH P2 4A cubic curve has stationary points at (– 2, – 3) and (2, a), where a is a constant.(a)Explain why 2d(4)dykxx, where k is a constant. [2] (b)Given that the curve passes through (– 1, 2), determine its equation. [6]

7 2025 ESSS Prelim 4NA A MATH P2 (iii)Find the value of a. [1]

8 2025 ESSS Prelim 4NA A MATH P2 5In triangle TUX, TU= 51 cm and TX = 352 cm.(i)Given that the area of the triangle TUX is 6 cm2, find the value of sin XTU, giving your answer in the form of 5abcwhere a, b and c are integers. [6] (ii)Hence or otherwise, calculate the possible values of angle XTU. [1]

9 2025 ESSS Prelim 4NA A MATH P2 6The function f()xis defined by 32f()12xxpxqxfor all real x. Given that 3xis a factor of f()xand that when f()xis divided by 2x the remainder is 10.(a)Find the value of each of the constants p and q, [4]

10 2025 ESSS Prelim 4NA A MATH P2 (b)Express f()xas the product of linear factors. [3]