Additional Maths P1 2 hrs by x3V7WxJi

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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.


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