Form 4
KCSE 2023 Mathematics Paper 2 Mock Examination
![](https://edufocus.co.ke/storage/OYEAjAbI2w01YXrATKsBNp6WJ9sBERiZTacX35Bw.png)
Tangent Calculate the area of the shaded region correct to 2 decimal places [4𝑚𝑎𝑟𝑘𝑠]
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Published on November 10th 2023 | 1 min , 174 words
Section I (50 Marks)
1. Solve for x (4mks)
(log3x)2−12log3x=32
solution
letlog3xbey
y2−12y=32
2y2−y−3=0
(2y−3)(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.
![](https://edufocus.co.ke/storage/OYEAjAbI2w01YXrATKsBNp6WJ9sBERiZTacX35Bw.png)
OT2=252−242
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 =84−31.54
=52.46cm2
3. Find the value of 𝑤 in the expression wx2−32x+116 is a perfect square, given that 𝑤 is a constant [2𝑚𝑎𝑟𝑘𝑠]
b2=4ac
⇒(32)2=4×116w
94=14w
w=9
4. Simplify
4√5+√2−3√5−√2