Sembawang Secondary 4051/01 QP 2025

[Turn Over NSEMBAWANG SECONDARY SCHOOLPRELIMINARY EXAMINATION 2025SECONDARY FOUR NORMAL (ACADEMIC) CANDIDATENAME CLASS:INDEXNUMBERADDITIONAL MATHEMATICSPaper 1 4051/0131 July 2025Paper 11 hour 45 minutes1100 – 1245Additional 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.1Express 57237 in the form of 7pq, where p and q are rational numbers. [3] 2Given that cot2qA where A is acute, express each of the following in terms of q.(a)secA [2](b)sin2A [2]

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5 [Turn Over 3Solve the simultaneous equations22xyy,21yx. [5]

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7 [Turn Over 4 The volume, V m3, of water in a river may be modelled by the equation 323Vx , where x m is the depth of the water in the river. During a period of rainfall, the volume of water in the river increases at a rate of 0.5 m3/h. Find the rate at which the depth of the water in the river is increasing when x = 0.8. [4]

85(a) Find the values of m and n if 432f219xxxxmxn has a factor of 29x. [4] (b)Hence, express f(x) as the product of linear factors. [3]

9 [Turn Over 6Express 232(1)xxx as partial fractions. [4]

107Find the equation of the normal to the curve 2(3)2yxx at the point where x = 2. [5]