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Name:……………………………………………………Stream:………………. Additional Maths P1 2 ½ hrs. Mengo Senior School Beginning of Term 2 Examination May, 2010 S.4 Additional Maths Paper 1 Time: 2 ½ hrs. Instructions: Answer any eight questions. log 2 ( 2 6 28) 10 1. a) Solve the equation: b) Evaluate i) log 2 3 log 27 ii) log 9 2. a) If (x + 1) and (x – 2) are factors of x3 + ax2 – 5x + b . Find the values of a and b and hence find the remaining factor. b) The polynomial x3 + 4x2 – 2x + 1 and x3 + 3x2 – x + 7 leave the same remainder when divided by x – p. Find the possible values of p. 3. a) If x = 2 Sinθ and 3y = Cos θ . Show that x2 + 36y2 = 4. b) Without using tables or calculators, show that tan 15o = 2 - 3 c) Prove that Cos 3θ = 4Cos3θ - 3 Cos θ . 4. a) Find the following integrals with respect to x. i) (2x + 3/2x)2 iii) x2 (2x3 – 5) iii) Cos3x 1 5. α and β are the roots of the equation 2x2 5x – 1 = 0. Find a) the value of α 2 and β 2 b) the equation whose roots are 1 ,1 c) the equation whose roots are 1 and 1 2 2 6. a) Differentiate the follloiwng: i) x2 – 2x (ii) (2x + 3)5 x+2 2 b) Find the value of x for which d y dx 2 If y = x2 (3 – x) 7. a) Find the sum of the odd numbers beteen 100 and 200. b) Find the sum of the even numbers upto and including 100. c) The fourth term of a G.P is -6 and the seventh term is 48. Write down the first three terms of the progression. 8. At the instant from which time is measured a particle is passing through O and traveling towards A along a straight line OA. It’s s metres from O after t seconds where s = t (t - 2)2. a) When, t is again at 0? b) When and where is it momentarily at rest. c) What is the particle’s greatest displacement from O and how far does it move during the 1st 2 seconds. d) What is the average velocity during the 3rd second. 9. a) Find the area of the segment out off from the curve y = x2 – 6x + 9 and the line y = 1. b) The area of a circle is increasing at the rate of 3cm2/s. Find the rate of change of the circumstance when the radius is 2cm. 10. Given the curve y = 3x2 – x3 a) Find the turning points and distinguish them. b) Sketch the curve. 2 11. a) Simplify the expression in the form a + b c 2 2 3 2 3 b) Evaluate log3 2.56121. c) Solve for x in 2(22x) + 2x – 10 = 0 12. a) Find the sums and products of the roots of x + 1/x = 4 b) Find the nature of the turning points of the curve in (a) above. c) Sketch the curve. End End 3