East Spring Secondary 4051/01 QP

Setter: Mrs Jan Yap EAST SPRING SECONDARY SCHOOLTowards Excellence and SuccessName: …………………………………………………………………………………… ( ) Class: ……………….N Level Preliminary Examination 2025 Secondary 4 Normal AcademicADDITIONAL MATHEMATICS4051/01PAPER 130 JULY 20251 hours 45 minutesWEDNESDAY1040 – 1225Candidates 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 questions.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.This question paper consists of 16 printed pages including the cover page. 70

2 2025 ESSS Prelim 4N AM P1 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 4N AM P1 1(a)Given that 5sin13 where 102, find the exact value of (i)tan [1] (ii)sin2 [2] (b)Do not use a calculator in answering this question.State, in terms of π, the principal value of 12cos2. [1]

4 2025 ESSS Prelim 4N AM P1 2Factorise 314112x. [3]

5 2025 ESSS Prelim 4N AM P1 3Circle C has equation 2242200xyxy.(a)Find the radius and the coordinates of the centre of the circle. [3] (b)Hence, show that the centre of the circle lies on the line 715yx. [1]

6 2025 ESSS Prelim 4N AM P1 4Find the range of values of x which satisfies both the inequalities 23716xxx [3] 5Express 224712xxxx in partial fractions. [4]

7 2025 ESSS Prelim 4N AM P1 6(a)Show that 2f()2610xxx can be written as 2f()xaxbc, where a, b and c are constants to be found.[2] (b)Hence, find the co-ordinates of the minimum point.[1](c)Determine if the curve lie completely above or below the x-axis or otherwise. Explain your answer.[1]

8 2025 ESSS Prelim 4N AM P1 7Do not use a calculator in answering this question.Solve the equation , where , giving your answer in its simplest surd form. [4]

9 2025 ESSS Prelim 4N AM P1 8(a)Express in the form , where R > 0 and [3] (b)Hence find the maximum and minimum values of 8sin7cos and the corresponding values of  for oo0360.[3]

10 2025 ESSS Prelim 4N AM P1 9A cone of radius r cm and vertical height h cm has volume 213Vrh and 32hr.Find the rate of increase of the height of this cone when the radius is 6 cm and the volume is increasing at a rate of 4cm³/s.[6]