WMA02_01_que_201401271.pdf

www.dynamicpapers.com Write your name here Surname Other names Centre Number Candidate Number Pearson Edexcel International Advanced Level Core Mathematics C34 Advanced Monday 27 January 2014 – Morning Paper Reference Time: 2 hours 30 minutes WMA02/01 You must have: Total Marks Mathematical Formulae and Statistical Tables (Blue) Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. Instructions tt Use black ink or ball-point pen. If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). Coloured pencils and highlighter pens must not be used. t Fill in the boxes at the top of this page with your name, centre number and candidate number. t clearly Answer all questions and ensure that your answers to parts of questions are labelled. t Answer the questions in the spaces provided – there may be more space than you need. t without You should show sufficient working to make your methods clear. Answers working may not gain full credit. t degree When a calculator is used, the answer should be given to an appropriate of accuracy. Information tt The The total mark for this paper is 125. marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Advice tt Read each question carefully before you start to answer it. Try to answer every question. t Check your answers if you have time at the end. Turn over P44966A ©2014 Pearson Education Ltd. *P44966A0144* 5/5/5/5/ www.dynamicpapers.com Leave blank 2x , 1. f ( x) = x  x +3 2 Find the set of values of xIRUZKLFKIƍx)  0 You must show your working. Solutions based entirely on graphical or numerical methods are not acceptable.) 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Solve, for 0 - x - 270°, the equation tan 2 x + tan 50° =2 1 − tan 2 x tan 50° Give your answers in degrees to 2 decimal places. 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Given that 4x3 + 2x2 + 17x + 8 ŁAx + B.dynamicpapers. www.com Leave blank 3. x2 + 4) + Cx + D  D. (4)  E. ILQGWKHYDOXHVRIWKHFRQVWDQWVA. C and D. B.  +HQFHILQG ∫ 4 x 3 + 2 x 2 + 17 x + 8 4 dx 1 x2 + 4 giving your answer in the form p + ln q. 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(2)  E.  6WDWHWKHUDQJHRIJ (2)  F.  )LQGJ–1x) and state its domain. (4) *LYHQWKDWWKHHTXDWLRQIx) = k. has exactly two roots.  G. where k is a constant.  VWDWHWKHUDQJHRISRVVLEOHYDOXHVRIk. 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D.dynamicpapers. www.  3URYHE\XVLQJORJDULWKPVWKDW d x (2 ) = 2 x ln 2 dx (3) The curve C has the equation 2x + 3y 2 + 3x 2y + 12 = 4 × 2x The point PZLWKFRRUGLQDWHV. OLHVRQC.  E.  )LQGDQHTXDWLRQRIWKHWDQJHQWWRC at P. 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___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Q5 (Total 9 marks) 17 *P44966A01744* Turn over . www.dynamicpapers. Given that the binomial expansion. www.com Leave blank 6. of 6 3 . x < √ (9 + Ax 2 ) √A 2 2 is B− x + Cx 4 + ! 3  D. in ascending powers of x.dynamicpapers. B and C. (7)  E. ILQGWKHYDOXHVRIWKHFRQVWDQWVA.  +HQFHILQGWKHFRHIILFLHQWRIx6 (2) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 18 *P44966A01844* . dynamicpapers.com Leave blank Question 6 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Q6 (Total 9 marks) 19 *P44966A01944* Turn over . www. where Ix) = 2xx) ln x. www.dynamicpapers. y O x A Figure 3 Figure 3 shows a sketch of part of the curve with equation y = Ix).com Leave blank 7. x0 The curve has a minimum turning point at A.  D.  )LQGI ƍx) (3)  E.  +HQFHVKRZWKDWWKHx coordinate of A is the solution of the equation 1+ x − x=e 1+ 2 x (3)  F. 46 to find the values of x1. 8VHWKHLWHUDWLRQIRUPXOD 1+ xn − 1+ 2 xn xn +1 = e . (3)  G. x2 and x3 to 4 decimal places. x0 = 0.  8VH\RXUDQVZHUWRSDUWF. 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D.com Leave blank 8. www.dynamicpapers.  3URYHWKDW nπ 2cosec 2A – cot AŁWDQA. n ' 2 (4) π  E. Az .  +HQFHVROYHIRU0  θ  2   L.  FRVHFș – cot 2ș = ¥   LL. 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___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Q8 (Total 10 marks) 27 *P44966A02744* Turn over .dynamicpapers. com Leave blank 9.dynamicpapers. www. D.  E. 8VHWKHVXEVWLWXWLRQu = 4 – ¥x to find dx ∫ 4 − √x (6) A team of scientists is studying a species of slow growing tree. The rate of change in height of a tree in this species is modelled by the differential equation dh 4 − √h = dt 20 where h is the height in metres and t is the time measured in years after the tree is planted.  )LQGWKHUDQJHLQYDOXHVRIh for which the height of a tree in this species is increasing. (2)  F. 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Write your answer to 3 significant figures. *LYHQWKDWRQHRIWKHVHWUHHVLVPHWUHKLJKZKHQLWLVSODQWHGFDOFXODWHWKHWLPHLW would take to reach a height of 10 metres. com Leave blank Question 9 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 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With respect to a fixed origin O.  D. the lines l1 and l2 are given by the equations l1 : r i + 5j + 5k) + Ȝi + j – k) l2 : r j + 12k) + ȝi – j + 5k) where Ȝ and ȝ are scalar parameters. (6)  E. 6KRZWKDWl1 and l2 meet and find the position vector of their point of intersection. lies on l1 The point B is the image of A after reflection in the line l2  F. 6KRZWKDWl1 and l2 are perpendicular to each other. with position vector 5i + 7j + 3k. (2) The point A.  )LQGWKHSRVLWLRQYHFWRURIB. 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The curve C has parametric equations π π x = 10 cos 2t. www. − t 2 2 The point AZLWKFRRUGLQDWHV.dynamicpapers. y = 6 sin t. OLHVRQC.  D. (1)  E. )LQGWKHYDOXHRIt at the point A.  6KRZWKDWDQHTXDWLRQRIWKHQRUPDOWRC at A is 3y = 10x – 41 (6) The normal to C at A cuts C again at the point B.  F.  )LQGWKHH[DFWFRRUGLQDWHVRIB. 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This shaded region is rotated through 2ʌ radians about the x-axis to form a 4 solid of revolution.com Leave blank 12. is bounded by the curve. 0 x 4 The finite region R. the x-axis and the π line x = . π ∫ 4  D. y R O x π x= 4 Figure 4 Figure 4 shows a sketch of part of the curve with equation π y = x(sin x + cos x). shown shaded in Figure 4. with volume V. www.  $VVXPLQJWKHIRUPXODIRUYROXPHRIUHYROXWLRQVKRZWKDWV = πx 2 (1 + sin 2 x)d x 0 (3)  E. You must show your working.) (9) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 40 *P44966A04044* . +HQFHXVLQJFDOFXOXVILQGWKHH[DFWYDOXHRIV.   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___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 42 *P44966A04244* .dynamicpapers. www. com Leave blank Question 12 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 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___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 43 *P44966A04344* Turn over . www.dynamicpapers. com Leave blank Question 12 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 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___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Q12 (Total 12 marks) TOTAL FOR PAPER: 125 MARKS END 44 *P44966A04444* . www.dynamicpapers.