KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 Mathematics
There are three cars A,B and C in a race. A is twice as likely to win as B while B is twice as likely to win as c. Find the probability that.
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Form 1 Mathematics
Using a ruler and a pair of compasses only.
a) Construct triangle ABC in which BC = 8cm, angle ABC = 1050 and BAC =450
b) Drop a perpendicular from A to meet CB produced at p. Hence find the area of triangle ABC. Form 3 Mathematics
Solve the equation 3tan 2x – 4tan x - 4 = 0 for 00 ≤ x ≥ 1800 (4mks)
Form 3 Mathematics
In June of a certain year, an employee's basic salary was Ksh 17000. The employee was also paid a house allowance of Ksh 6000, a commuter allowance
of Ksh 2500 and a medical allowance of Ksh 1 800. In July of that year, the employee's basic salary was raised by 2%. (a) Calculate the employees: (i) basic salary for July; (ii) total taxable income in July of that year. (b) In that year, the Income Tax Rates were as shown in the table below:
Given that the Monthly Personal Relief was Ksh 1056, calculate the net tax paid by the employee.
Form 3 Mathematics
In triangle OPQ below, OP = p, OQ = q. Point M lies on OP such that OM : MP = 2 : 3 and point N lies on OQ such that ON : NQ = 5:1. Line PN
intersects line MQ at X.
(a) Express in terms of p and q:
(i) PM (ii) QM. (c) Given that PX = kPN and QX = rQM, where k and r are scalars: (i) write two different expressions for OX in terms of p, q, k and r; (ii) find the values of k and r; (iii) determine the ratio in which X divides line MQ. Form 4 MathematicsForm 1 Mathematics
Amaya was paid an initial salary of Ksh 180 000 per annum with a fixed annual increment. Bundi was paid an initial salary of Ksh 150000 per annum with a
10% increment compounded annually. (a) Given that Amaya's annual salary in the 11th year was Ksh 288 000, determine: (i) his annual increment; (ii) the total amount of money Amaya earned during the 11 years. (b) Determine Bundi's monthly earnings, correct to the nearest shilling, during the eleventh year. (c) Determine, correct to the nearest shilling: (i) the total amount of money Bundi earned during the 11 years. Form 4 MathematicsForm 3 MathematicsForm 4 MathematicsForm 3 Mathematics
(a) Expand (1 + x)7 up to the 4th term.
(b) Use the expansion in part (a) above to find the approximate value of (0.94)7 Form 3 Mathematics
The base and height of a right angled triangle were measured as 6.4cm and 3.5 cm respectively. Calculate the maximum absolute error in the area of the triangle.
Form 2 Mathematics
The masses in kilograms of 20 bags of maize were;
90, 94, 96, 98, 99, 102, 105, 91, 102, 99, 105, 94, 99, 90, 94, 99, 98, 96, 102 and 105. Using an assumed mean of 96kg, calculate the mean mass, per bag, of the maize. Form 1 Mathematics
Kago deposited Ksh 30 000 in a financial institution that paid simple interest at the rate of 12% per annum. Nekesa deposited the same amount of money
as Kago in another financial institution that paid compound interest. After 5 years, they had equal amounts of money in the financial institutions. Determine the compound interest rate per annum, to 1 decimal place, for Nekesa's deposit. Form 1 Mathematics
Construct a circle centre x and radius 2.5 cm. Construct a tangent from a point P, 6 cm from x to touch the circle at R. Measure the length PR.
Form 2 Mathematics
Given that P = 2i- 3j + k, Q = 3i – 4j- 3k and R = 3P + 2 Q, find the magnitude of R to 2 significant figures.
Form 1 Mathematics
An inlet tap can fill an empty tank in 6 hours. It takes 10 hours to fill the tan kwhen the inlet tap and an outlet tap are both opened at the same time. Calculate
the time the outlet tap takes to empty the full tank when the inlet tap is closed. Form 3 Mathematics
Give that x = 2i +j – 2k,y = - 3i +4j –k and z = - 5i +3j +2k and that p = 3x – y +2z. Find the magnitude of vector p to 3 significant figures.
Form 2 MathematicsForm 3 Mathematics
A water pump costs Kshs. 21600 when new. At the end of first year its value depreciates by 25%. The depreciation by the second year is 20% and thereafter the rate of the depreciation is 15% yearly. Calculate the exact value of the water pump at the end of the fourth year.
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