Sembawang Secondary 4051/02 QP 2025

[Turn Over NSEMBAWANG SECONDARY SCHOOLPRELIMINARY EXAMINATION 2025SECONDARY FOUR NORMAL (ACADEMIC) CANDIDATENAME CLASS:INDEXNUMBERADDITIONAL MATHEMATICSPaper 2 4051/0201 August 2025Paper 21 hour 45 minutes0800 – 0945Additional Materials: READ THESE INSTRUCTIONS FIRSTWrite your class, index number and name 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, glue or correction fluid.Answer all questions.If working is needed for any question it must be shown with the answer.Omission of essential working will result in loss of marks.The use of an approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π.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 70.FOR EXAMINER’S USETOTAL70Setter: Ms Adeline LimThis document consists of 16 printed pages.

2Mathematical Formulae1.ALGEBRAQuadratic EquationFor the equation ,02cbxax x = aacbb2)4(2Binomial Theorem,......21)( 221 nrrnnnnn bbarnbanbanabawhere n is a positive integer and .!)1)......(1(!)!(!rrnnnrrnnrn2. TRIGONOMETRYIdentitiesAAAAAA222222cot1cosectan1sec1cossinBABABAsincoscossin)sin(BABABAsinsincoscos)cos(BABABAtantan1tantan)tan(AAAAAAAAAAA22222tan1tan22tansin211cos2sincos2coscossin22sinFormulae for ABCCcBbAasinsinsinAbccbacos2222Abcsin21

3 [Turn Over Answer all the questions.1Factorise completely338125ab. [3] 2A line has equation 7yx and a curve has equation2351yxx. Determine whether the line intersects, is a tangent to, or does not intersect the curve. Give a reason for your answer. [3]

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5 [Turn Over 3Given that cos302sin60yy, find the value of tany without the use ofcalculator. [5]

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7 [Turn Over 4The equation 0222kkxx, where k is a constant, has real roots.(a)Show that 022kk. [2] (b)Find the range of values of kand represent the values on a number line. [3]

85 In triangleXYZ, angle 90XYZ, 43cmYZ and 431cmXY.(a)Find the area of triangle XYZ, leaving your answer in the form 3ab where a and bare constants. [3] (b)Find the length of XZ, giving your answer in the simplest exact form. [4]

9 [Turn Over 6A piece of wire of length 100 cm is bent into the shape of a trapezium PQRS. Given that PQ = SR = x cm, 60PQASRB∘and PABS is a rectangle. (a)Show that 10032xPS. [3]

10(b)Show that the area of the rectangle ABSP, A cm2, is given by2310034Axx. [3] (c)Given that x can vary, find the value of x for which A is maximum. [4]