KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 3 MathematicsForm 4 MathematicsThe diagram below is a sketch of the curve y =x2 + 5.
Form 2 MathematicsForm 4 MathematicsForm 2 Mathematics
A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is three – quarters full of milk.
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 2 Mathematics
The figure below represents a cone of height 12 cm and base radius of 9 cm from which a similar smaller cone is removed, leaving a conical hole of height 4 cm.
a) Calculate:
i. The base radius of the conical hole; ii. The volume, in terms of π, of the smaller cone that was removed. b) (i) Determine the slant height of the original cone. (ii) Calculate, in terms of it, the surface area of the remaining solid after the smaller cone is removed. Form 2 Mathematics
(a) On the grid provided, draw the square whose verticals are A (6, -2), B (7, -2), C (7, -1) and D (6, -1).
(b) On the same grid, draw: i. AʹBʹCʹDʹ, the image of ABCD, under an enlargement scale factor 3, centre (9, -4); ii. AʹʹBʹʹCʹʹDʹʹ, the image of AʹBʹCʹDʹ, under a reflection in the line x = 0; iii. AʹʹʹBʹʹʹCʹʹʹDʹʹʹ, the the image of AʹʹBʹʹCʹʹDʹʹ under a rotation of + 90 about (0,0) (c) Describe a single transformation that maps AʹBʹCʹDʹ onto AʹʹʹBʹʹʹCʹʹʹDʹʹʹ Form 3 Mathematics
In the figure below, OABC is a trapezium. AB parallel to OC and OC = 5AB. D is a point on OC such that OD: DC = 3:2
a) Given that OA = p and AB = q, express in terms of p and q:
i. OB; ii. AD; iii. CB; b) Lines OB and AD intersect at point X such that AX = kAD and OX = rOB, where k and r are scalars. Determine the values k and r. Form 4 Mathematics
The displacement, s metres, of a moving particle from a point O, after t seconds is given by, s = t3 – 5t2 + 3t + 10
a) Find s when t =2. b) Determine: i. The velocity of the particle when t = 5 seconds; ii. The value of t when the particle is momentarily at rest. c) Find the time, when the velocity of the particles is maximum. Form 2 Mathematics
Two towns, A and B are 80km apart. Juma started cycling from town A to town B at 10.00 am at an average speed of 40 km/h. Mutuku started his journey from
town B to town A at 10.30 am and travelled by car at an average speed of 60 km/h. a) Calculate: i. The distance from town A when Juma and Mutuku met; (5 mks) ii. The time of the day when the two met. (2 mks) b) Kamau started cycling from town A to town B at 10.21 am. He met Mutuku at the same time as Juma did. Determine Kamau’s average speed. Form 4 Mathematics
A trader bought 2 cows and 9 goats for a total of Ksh 98, 200. If she had bought 3 cows and 4 goats she would have spent Ksh 2,200 less.
a) Form two equations to represent the above information. b) Use matrix method to determine the cost of a cow and that of a goat. c) The trader later sold the animals she had bought making a profit of 30% per cow and 40% per goat. i. Calculate the total amount of money she received. ii. Determine, correct to 4 significant figures, the percentage profit the trader made from the sale of the animals 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. 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 Mathematics |
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