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KCSE Mathematics Paper 2 Revision Questions and Answers Set 5
Use matrices to solve the simultaneous equations
4x – 5y = 13
3x – 2y = 8
(5m 30s)
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1.
The figure above shows an isosceles triangle ABC in which BC = AC and angle ACB = #100^0#. Given that the area of triangle ABC = 70.91 #cm^2#, calculate to the nearest whole number, the length of BC.
2.
Three quantities Q, h and r are such that Q varies jointly with h and the square of r. When h = 15 and r = 3, Q = 675. Find a) An equation connecting Q, h and r. b) The value of Q when h = 12 and r = 4.
3.
A particle moves so that its velocity v ms-1 after a time t in seconds is given by v = #2t^2# – 3t + 5 Determine the total distance moved by the particle between time t = 0 to t = 6 seconds
4.
Two trucks A and B travelling at 28 km/h and 26 km/h respectively approach one another on a straight stretch of road. Truck A is 10 metres long while truck B is 8 metres long. Determine the time in seconds that elapses before the two trucks completely pass each other.
5.
Without using a mathematical table or a calculator, evaluate the expression #2log_10 25 - 2log_10 8 + 5log_10 4#
6.
Chebet deposited sh 50 000 in a saving account which paid compound interest at the rate of 15% per annum. Calculate to the nearest year the time she would have to wait for her money to double.
7.
Given the vectors a = 3i – 5j, b = 2i – 4j and c = 5i – 7j Find the values of parameters m and n such that ma – nb = c
8.
If the ratio x : y = 5 : 3, determine the ratio (2x – y) : (x + y).
9.
Simplify as far as possible #3/(x -y) - 1/(x +y)#
10.
Solve the equation #5/(2x) - 1/(4x) = (2x^2)/3#
11.
In the figure PQ is parallel to RS and the line PS and RQ meet at T. Given that PT : TS = 2: 3 and that RQ = 10 cm, show that triangle PTQ and STR are similar and hence find the length of RT.
12.
The length and width of a rectangle are stated as 18.5 cm and 12.4 cm respectively. Both measurements are given to the nearest 0.1 cm. a) Determine the lower and upper limit of each measurement. b) Calculate the percentage error in the area of the rectangle.
13.
Given matrix P =#[[4,1],[2,3]]#, find #P^2#. b) Find matrix Q such that P2 = 3P + Q.
14.
Use matrices to solve the simultaneous equations 4x – 5y = 13 3x – 2y = 8
15.
Find the values of x which make the following inequality true. 3 – 5x < 2x + 17
16.
A closed cylindrical container, designed such that its volume is 250?? #cm^3#, is made from a metal sheet. Find the radius of the container which will require minimum area of metal sheet.
17.
An export-import company in Kenya owes a firm in the United states USD 55 600. The company can pay this debt in Kenya shillings (Ksh) or in sterling pounds (€) through their account in Britain. The bank in Kenya charges a commission of 5% while the British bank charges 3% commission on the transaction. The currency exchange rate is: 1 USD = Ksh 54.36 1 Sterling € = USD 1.624 1 Sterling € = Ksh 88
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