ࡱ> @J?MNzq  5bjbjt+t+ ZlAA$G]^^^$PLe-&('' '*-,-,-,-,-,-,-$.0JP-^'$'''P-'*&'*'*'*'"^*-'*-'*'*, -r^*-,P}lg("- Paper Reference (complete below)Centre No.6663/01Candidate No. Paper Reference(s) 6663 Edexcel GCE Core Mathematics C2 Advanced Subsidiary Set A: Practice Paper 2 Time: 1 hour 30 minutesExaminers use onlyTeam Leaders use onlyQuestion NumberLeave Blank123456Materials required for examinationItems included with question papers7Mathematical Formulae NilCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Thus candidates may NOT use calculators such as the Texas Instruments TI-89, TI-92, Casiocfx9970G, Hewlett Packard HP48G.Instructions to Candidates In the boxes above, write your centre number, candidate number, your surname, initials and signature. You must write your answer for each question in the space following the question. If you need more space to complete your answer to any question, use additional answer sheets. Information for Candidates A booklet Mathematical Formulae and Statistical Tables is provided. Full marks may be obtained for answers to ALL questions. This paper has nine questions. Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled. You must show sufficient working to make your methods clear to the examiner. Answers without working may gain no credit.TotalTurn over EMBED Word.Picture.8  1. f(x) = px3 + 6x2 + 12x + q. Given that the remainder when f(x) is divided by (x 1) is equal to the remainder when f(x) is divided by (2x + 1), (a) find the value of p. (4 marks) Given also that q = 3, and p has the value found in part (a), (b) find the value of the remainder. (1 marks)  2. Figure 1 y (a, b) 5 O 4 x The circle C, with centre (a, b) and radius 5, touches the x-axis at (4, 0), as shown in Fig. 1. (a) Write down the value of a and the value of b. (1 marks) (b) Find a cartesian equation of C. (2 marks) A tangent to the circle, drawn from the point P(8, 17), touches the circle at T. (c) Find, to 3 significant figures, the length of PT. (3 marks)  3. (a) Expand (2(x + 3)2. (2 marks) (b) Hence evaluate  EMBED Equation.3 , giving your answer in the form a + b(2, where aandb are integers. (5 marks)  4. The first three terms in the expansion, in ascending powers of x, of (1 + px)n, are 1 18x + 36p2x2. Given that n is a positive integer, find the value of n and the value of p. (7 marks) (7 marks)  5. Find all values of ( in the interval 0 ( ( < 360 for which (a) cos (( + 75)( = 0. (3 marks) (b) sin 2( ( = 0.7, giving your answers to one decima1 place. (5 marks)  6. Given that log2 x = a, find, in terms of a, the simplest form of (a) log2 (16x), (2 marks) (b) log2 EMBED Equation.3 . (3 marks) (c) Hence, or otherwise, solve log2 (16x) log2 EMBED Equation.3  =  EMBED Equation.3 , giving your answer in its simplest surd form. (4 marks)  7. The curve C has equation y = cos  EMBED Equation.3 , 0 ( x ( 2(. (a) Sketch C. (2 marks) (b) Write down the exact coordinates of the points at which C meets the coordinate axes. (3 marks) (c) Solve, for x in the interval 0 ( x ( 2(, cos  EMBED Equation.3  = 0.5, giving your answers in terms of (. (4 marks)  8. Figure 2  y B    R   x O A Figure 2 shows part of the curve with equation y = x3 6x2 + 9x. The curve touches the x-axis at A and has a maximum turning point at B. (a) Show that the equation of the curve may be written as y = x(x 3)2, and hence write down the coordinates of A. (2 marks) (b) Find the coordinates of B. (5 marks) The shaded region R is bounded by the curve and the x-axis. (c) Find the area of R. (5 marks)  9  Fig. 3 Triangle ABC has AB = 9 cm, BC 10 cm and CA = 5 cm. A circle, centre A and radius 3 cm, intersects AB and AC at P and Q respectively, as shown in Fig. 3. (a) Show that, to 3 decimal places, (BAC = 1.504 radians. (3 marks) Calculate, (b) the area, in cm2, of the sector APQ, (2 marks) (c) the area, in cm2, of the shaded region BPQC, (3 marks) (d) the perimeter, in cm, of the shaded region BPQC. 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