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Answer ALL questions,1 Show that can be written in the form. 5x 1 2x 5 5x 1 2x 5,Find the values of the constants A and B. 2 Use proof by contradiction to show that there exist no integers a and b for which 25a 15b 1. 3 A curve has parametric equations x cos 2t y sin t t. a Find an expression for in terms of t,Leave your answer as a single trigonometric ratio. b Find an equation of the normal to the curve at the point A where t. Showing all steps find cot 3x dx, 5 A triangle has vertices A 2 0 4 B 2 4 6 and C 3 4 4. By considering the side lengths of the triangle show that the triangle is a right angled triangle. 6 The functions p and q are defined by p x x 2 and q x 5 2 x. a Given that pq x qp x show that 3x2 10 x 10 0,b Explain why 3x2 10 x 10 0 has no real solutions.

7 Prove by contradiction that there are infinitely many prime numbers. 8 In a rainforest the area covered by trees F has been measured every year since 1990 It was found that. the rate of loss of trees is proportional to the remaining area covered by trees. Write down a differential equation relating F to t where t is the numbers of years since 1990. 9 At the beginning of each month Kath places 100 into a bank account to save for a family holiday Each. subsequent month she increases her payments by 5 Assuming the bank account does not pay interest. a the amount of money in the account after 9 months. Month n is the first month in which there is more than 6000 in the account. b Show that n, Maggie begins saving at the same time as Kath She initially places 50 into the same account and plans. to increase her payments by a constant amount each month. c Given that she would like to reach a total of 6000 in 29 months by how much should Maggie. increase her payments each month,Find cos2 6 x dx,tan x sec x p. 11 a Prove that sec x x 2n 1,tan x sec x, b Hence solve in the interval 0 x 2 the equation 2. 12 A large arch is planned for a football stadium The parametric equations of the arch are x 8 t 10. y 100 t 2 19 t 10 where x and y are distances in metres Find. a the cartesian equation of the arch,b the width of the arch. c the greatest possible height of the arch,x 3 8x 2 9x 12 D.

13 Ax 2 Bx C,Find the values of the constants A B C and D. 14 The volume of a sphere V cm3 is related to its radius r cm by the formula V r The surface area of. the sphere is also related to the radius by the formula S 4 r 2 Given that the rate of decrease in surface. area in cm2 s 1 is 12,find the rate of decrease of volume. Find sin 3 x dx,16 h t 40ln t 1 40sin t 2 t 0, The graph y h t models the height of a rocket t seconds after launch. a Show that the rocket returns to the ground between 19 3 and 19 4 seconds after launch. b Using t0 19 35 as a first approximation to apply the Newton Raphson procedure once to h t to. find a second approximation to giving your answer to 3 decimal places. c By considering the change of sign of h t over an appropriate interval determine if your answer to. part b is correct to 3 decimal places, 17 a Show that in KLM with KL 3i 0 j 6k and LM 2i 5j 4k KLM 66 4 to one decimal. b Hence find LKM and LMK,TOTAL FOR PAPER IS 93 MARKS.

Pearson Edexcel Level 3 GCE Mathematics Advanced Level Paper 1 or 2 Pure Mathematics Practice Paper F Time 2 hours Paper Reference s 9MA0 01 or 9MA0 02 You must have Mathematical Formulae and Statistical Tables calculator Candidates may use any calculator permitted by Pearson regulations Calculators must not have the facility for algebraic manipulation differentiation and integration

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