KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 1 Mathematics
Two taps A and B can each fill an empty tank in 3 hours and 2 hours respectively. A drainage tap R can empty the full tank in 6 hours; taps A and R are opened for 5 hours then closed.
(a) Determine the fraction of the tank is still empty (b) Find how long it would take to fill the remaining fraction of the tank if all the three taps are opened
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Form 3 Mathematics
Two machines, M and N produce 60% and 40% respectively of the total number of items manufactured in a factory. It is observed that 5% of the items produces
by machine M are defective while 3% of the items produced by machine N are defective. If an item is selected at random from the factory, find the probability that it is defective Form 2 Mathematics
The position vectors of points F, G, and H are f, g, and h respectively. Point H divides FG in the ratio 4:-1. Express h in terms of f and g
Form 3 Mathematics
(a) expand (1 − ?)5
(b) Use the expansion in (a) up to the term in x3 to approximate the value of (0.98)5 Form 3 Mathematics
The equation of a circle is given by x2 +4x +y2 -2y – 4 = 0. Determine the centre and radius of the circle
Form 1 MathematicsForm 3 Mathematics
A quadratic curve passes through the points (-2, 0) and (1, 0). Find the equation of the curve in the form y = ax2 +bx +c, where a, b and c are constants
Form 3 Mathematics
The sum of n terms of the sequence; 3, 9, 15, 21, … is 7500. Determine the value of n
Form 4 MathematicsThe velocity Vms-1 of particle in motion is given by V =3t2 – t +4, where t is time in seconds. Calculate the distance traveled by the particle between the time t=1 second and t=5 seconds. Form 2 MathematicsThree points O, A and B are on the same horizontal ground. Point A is 80 metres to the north of O. Point B is located 70 metres on a bearing of 0600 from A. A vertical mast stands at point B. The angle of elevation of the top of the mast from o is 200. Calculate: a) The distance of B from O. (2mks) b) The height of the mast in metres (2mks) Form 1 Mathematics
Form 2 MathematicsThe length of a hallow cylindrical pipe is 6 metres. Its external diameter is 11cm and has a thickness of 1cm. Calculate the volume in cm3 of the material used to make the pipe. Take П as 3.142 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. |
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