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Form 4 KCSE 2023 Mathematics Paper 2 Mock Examination

Published on November 10th 2023 | 1 min , 174 words

Section I (50 Marks)


1. Solve for x  (4mks)

(log3x)212log3x=32

solution

letlog3xbey

y212y=32

2y2y3=0

(2y3)(y+1)=0

y=32ory=1

 log3x=32 

or

 log3x=1  

x=(3)32 

or  

 x=(3)1  

 x=5.196  or  x=13  

2. In the figure below PT is a tangent to the circle from an external point P. 𝑃𝑇 = 24 𝑐𝑚 and 𝑂𝑃 = 25 𝑐𝑚.

Tangent
Calculate the area of the shaded region correct to 2 decimal places  [4𝑚𝑎𝑟𝑘𝑠]

OT2=252242

OT2=49

 OT=7 

let  TOPbex

tan x =247

x= 73.74

Area of PTO=12×24×7

=84

Area of sector = 73.74360×227×72

=31.54

Area of the shaded region =8431.54

=52.46cm2

3. Find the value of 𝑤 in the expression wx232x+116 is a perfect square, given that 𝑤 is a constant [2𝑚𝑎𝑟𝑘𝑠]

b2=4ac

(32)2=4×116w

94=14w

w=9

4. Simplify

 45+2352 

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