KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 Mathematics
(a) solve the equation;
(b) The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136m2.
i. Calculate the perimeter of the floor. ii. A rectangular carpet is placed on the floor of the hall leaving an area of 64m2. If the length of the carpet is twice its width, determine the width of the carpet.
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Form 1 Mathematics
A farmer had 540 bags of maize each having a mass of 112kg. After drying the maize, the mass decreased in the ratio 15:16.
a) Calculate the total mass lost after the maize was dried. b) A trader bought and repacked the dried maize in 90 kg bags. He transported the maize in a lorry which could carry a maximum of 120 bags per trip. i. Determine the number of trips the lorry made. ii. The buying price of a 90 kg bag of maize was Ksh 1,500. The trader paid Ksh 2,500 per trip to the mket. He sold the maize and made a profit of 26 %. Calculate the selling price of each bag of the maize. Form 2 Mathematics
Given the inequalities x – 5 ≤ 3 x – 8 < 2 x – 3.
a) Solve the inequalities; b) Represent the solution on a number line. Form 2 MathematicsForm 2 Mathematics
A cylindrical pipe 2 ½ metres long has an internal diameter of 21 millimetres and an external diameter of 35 millimetres. The density of the material that makes the pipe is 1.25 g/cm3.
Calculate the mass of mass of the pipe in kilograms. (Take π = 22/7). Form 2 Mathematics
A triangle ABC is such that AB = 5 cm, BC = 6 cm and AC = 7 cm.
a) Calculate the size of angle ACB, correct to 2 decimal places. b) A perpendicular drawn from A meets BC at N. calculate the length AN correct to one decimal place. Form 2 Mathematics
A straight line passes through points (-2, 1) and (6, 3).
Find: a) equation of the line in the form y = mx + c; b) the gradient of a line perpendicular to the line in (a) Form 1 Mathematics
The interior angles of an octagon are 2x,1/2?, (x + 40)0, 1100, 1350, 1600, (2x + 10)0 and 1850.
Find the value of x. Form 1 MathematicsForm 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. 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 4 Mathematics
The acceleration of a body moving along a straight line is (4 - t) m/s2 and its velocity is v m/s after t seconds.
(a) (i) If the initial velocity of the body is 3 m/s, express the velocity v in terms of t. (ii) Find the velocity of the body after 2 seconds. (b) Calculate: (i) the time taken to attain maximum velocity; (ii) the distance covered by the body to attain the maximum velocity. Form 3 Mathematics
A box contains 3 brown, 9 pink and 15 white clothes pegs. The pegs are identical except for the colour.
(a) Find the probability of picking: (i) a brown peg; (ii) a pink or a white peg. (b) Two pegs are picked at random, one at a time, without replacement. Find the probability that: (i) a white peg and a brown peg are picked; (ii) both pegs are of the same colour. Form 4 Mathematics
A tourist took 1 h 20 minutes to travel by an aircraft from town T(3°S, 35°E) to town U(9°N, 35°E). (Take the radius of the earth to be 6370km and π =22/7
(a) Find the average speed of the aircraft. (b) After staying at town U for 30 minutes, the tourist took a second aircraft to town V(9°N, 5°E). The average speed of the second aircraft was 90% that of the first aircraft. Determine the time, to the nearest minute, the aircraft took to travel from U to V (c) When the journey started at town T, the local time was 0700h. Find the local time at V when the tourist arrived. Form 1 Mathematics
(a) on the same diagram construct:
(i) triangle ABC such that AB = 9 cm, AC= 7 cm and angle CAB = 60°; (ii) the locus of a point P such that P is equidistant from A and B; (iii) the locus of a point Q such that CQ ≤ 3.5cm. (b) On the diagram in part (a): (i) shade the region R, containing all the points enclosed by the locus of P and the locus of Q, such that AP ≥ BP; (ii) find the area of the region shaded in part (b)(i) above. 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. |
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