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KCSE Mathematics Paper 1 Revision Questions and Answers Set 8
Solve for x in the equation
#9^(x-1) × 3^(2x+1)=243#
(2m 17s)
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1.
Without using calculator, evaluate, #(9 1/2 -3 1/3 div 5/9)/(3/5 of 6 1/4 + 1 1/2)#
2.
Factorise completely #5x^2-45#
3.
Find all the integral values of x which satisfy the inequalities #5-3xlex-7<11-2x#
4.
A straight line passes through the points P(1,9) and Q(-1,3). a) Find the equation of the line PQ in the form of y=mx+c b) Hence calculate to 2 decimal places the size of the acute angle this line makes with the x-axis
5.
An alloy is made of aluminium,Zinc and copper in the ratio 2:3:5 by mass. Find the mass of aluminium in a piece of the alloy which contains 5.75kg of copper.
6.
Use substitution method to solve the simultaneous equations 5x-3y=7 2x+y=5
7.
The figure below shows a right angled triangle PQR. The diamensions of the triangle are given in centimetres and in terms of x Find the value of x and hence calculate the perimeter of the triangle.
8.
Kyalo,Onyango and Wafula contributed sh. 20 000, sh 40 000 and sh 90 000 respectively to start a business. They shared the profit realized each month in the ratio of their contributions. At the end of a certain month onyango reveived sh 16 200 as his share of profits. How much more did Wafula receive than Kyalo during that month.
9.
The figure below shows a sector of a circle of radius 18 cm which subtends an angle of 280 degrees at the centre of the circle. The sector represents the net of the curved surface of a solid cone. a) Calculate the base radius of the cone b) Calculate the total surface area of the cone
10.
Kamau is now four times as old as his son. Five years ago Kamau was exactly one and half times as old as his son will be ten years from now. Determine kamau’s present age
11.
A rectangular tank measuring 2.5m long and 2 m wide initially contains water to a depth of 15 cm. water flows into the tank continuously from 11:43 a.m to 12:28 p.m at the rate of 50 litres per minute. Calculate the new height of water in the tank.
12.
Solve for x in the equation #9^(x-1) × 3^(2x+1)=243#
13.
The curved surface area of a cylindrical container is 1320 cm2 . If the radius of the container is 15cm, calculate the capacity of the container in litres (Take #pi=22/7#)
14.
In a fund raising meeting there were 500 people present. Each man contributed sh. 300 and each woman sh 250. The meeting raised a total of sh 136 800. Find the number of men present in the meeting.
15.
Solve the silmutaneous inequality below. #2x-5=10-3x < x+18#
16.
The figure below shows triangle OPQ in which OP=p and OQ =q. M and N are points on OQ and OP respectively such that ON:NP=1:3 and OM:MQ=2:1 a)Express the following vectors in terms of p and q. i)PM ii) QN iii) PQ
17.
Solve the simultaneous equation, 3a+2b=13 5a-3b=9
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