# Additional Maths P1 2 hrs by x3V7WxJi

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2 ½ hrs.

Mengo Senior School
Beginning of Term 2 Examination May, 2010

Time: 2 ½ hrs.

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

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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.

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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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