KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 1 Mathematics
A number m is formed by writing all the prime numbers between 0 and 10 in an ascending order. Another number n is formed by writing all the square numbers between 0 and 10 in a descending order:
a) Find m – n; b) Express (m – n) as a product of its prime factors.
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Form 3 Mathematics
Given that sin (x + 20)0 = - 0.7660, find x, to the nearest degree, for 00≤ x ≥ 3600.
Form 2 Mathematics
Chelimo’s clock loses 15 seconds every hour. She sets the correct time on the clock at 0700h on a Monday. Determine the time shown on the clock when the correct
time was 1900h on Wednesday the same week. Form 4 MathematicsForm 1 Mathematics
A wholesaler sold a radio to a retailer making a profit of 20%. The retailer later sold the radio for Ksh 1,560 making a profit of 30%. Calculate the amount of money the
wholesaler had paid for the radio. Form 2 Mathematics
The production of milk, in litres, of 14 cows on a certain day was recorded as follows
22, 26, 15, 19, 20, 16, 27, 15, 19, 22, 21, 20, 22 and 28. a) The mode; b) The median. Form 2 Mathematics
Two straight paths are perpendicular to each other at point p.One path meets a straight road at point A while the other meets the same road at B. Given that PA is 50 metres while PB is 60 metres. Calculate the obtuse angle made by path PB and the road.
Form 1 MathematicsForm 2 Mathematics
The length of a solid prism is 10cm. Its cross section is an equilateral triangle of side 6cm.
Find the total surface area of the prism. 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.
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
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.
Form 1 MathematicsForm 2 Mathematics
In the figure below, PQ is parallel to RS. The lines PS and RQ intersect at T. RQ = 10 cm, RT:TQ = 3:2, angle PQT = 40° and angle RTS - 80°.
(a) Find the length of RT.
(b) Determine, correct to 2 significant figures: (i) the perpendicular distance between PQ and RS; (ii) the length of TS. (c) Using the cosine rule, find the length of RS correct to 2 significant figures. (d) Calculate, correct to one decimal place, the area of triangle RST. Form 1 Mathematics
Three pegs R, S and T are on the vertices of a triangular plain field. R is 300 m from S on a bearing of 300° and T is 450 m directly south of R.
(a) Using a scale of 1 cm to represent 60 m, draw a diagram to show the positions of the pegs. (b) Use the scale drawing to determine: (i) the distance between T and S in metres: (ii) the bearing of T from S. (c) Find the area of the field, in hectares, correct to one decimal place. Form 4 Mathematics
The equation of a curve is y = 2x3 + 3x2.
(a) Find: (i) the x - intercept of the curve; (ii) the y - intercept of the curve. (b) (i) Determine the stationery points of the curve. (ii) For each point in (b) (i) above, determine whether it is a maximum or a minimum. (c) Sketch the curve. Form 2 Mathematics
The vertices of quadrilateral OPQR are O (0,0), P(2,0), Q(4,2) and R(0,3).
The vertices of its image under a rotation are O'(l, -1), P'(l, -3), Q'(3, -5) and R'(4, -1). (a) (i) On the grid provided, draw OPQR and its image O'P'Q'R'. (ii) By construction, determine the centre and angle of rotation. (b) On the same grid as (a) (i) above, draw O"P"Q"R", the image of O'P'Q'R' under a reflection in the line y = x. (i) directly congruent; (ii) oppositely congruent. |
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