KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 4 Mathematics
Two places P and Q are at ( 360N, 1250W) and 360N, 1250W) and 360 N, 1250W) and 360 N, 550E) respectively. Calculate the distance in nautical miles between P and Q measured along the great circle through the North pole.
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Form 4 Mathematics
A particle moving in a straight line passes through a fixed point O with a velocity of 9m/s. The acceleration of the particle, t seconds after passing through O is given by a = ( 10 – 2t) m/s2.Find the velocity of the particle when t – 3 seconds
Form 3 MathematicsForm 1 Mathematics
The figure below is drawn to scale. It represents a field in the shape of an equilateral triangle of side 80m
The owner wants to plant some flowers in the field. The flowers must be at most, 60m from A and nearer to B than to C. If no flower is to be more than 40m from BC, show by shading, the exact region where the flowers may be planted
Form 3 Mathematics
The points which coordinates (5,5) and (-3,-1) are the ends of a diameter of a circle centre A
Determine:
(a) the coordinates of A
(b) The equation of the circle, expressing it in form x2 + y2 + ax + by + c = 0 where a, b, and c are constants Form 3 MathematicsForm 4 MathematicsForm 3 Mathematics
The data below represents the ages in months at which 6 babies started walking:
9,11, 12, 13, 11, and 10. Without using a calculator, find the exact value of the variance Form 3 Mathematics
By correcting each number to one significant figure, approximate the value of 788 x 0.006. Hence calculate the percentage error arising from this approximation.
Form 2 MathematicsForm 2 MathematicsForm 4 Mathematics
A particle moves along straight line such that its displacement S metres from a given point is S = t3 – 5t2 + 4 where t is time in seconds
Find
(a) the displacement of particle at t = 5 (b) the velocity of the particle when t = 5 (c) the values of t when the particle is momentarily at rest (d) The acceleration of the particle when t = 2 Form 2 Mathematics
The figure below is a model representing a storage container. The model whose total height is 15cm is made up of a conical top, a hemispherical bottom and the middle part is cylindrical. The radius of the base of the cone and that of the hemisphere are each 3cm. The height of the cylindrical part is 8cm.
(a) Calculate the external surface area of the model
(b) The actual storage container has a total height of 6 metres. The outside of the actual storage container is to be painted. Calculate the amount of paint required if an area of 20m2 requires 0.75 litres of the paint Form 3 Mathematics
In the diagram below, the coordinates of points A and B are ( 1,6) and (15,6) respectively)
Point N is on OB such that 3 ON = 2OB. Line OA is produced to L such that OL = 3 OA
(a) Find vector LN
(b) Given that a point M is on LN such that LM: MN = 3: 4, find the coordinates of M (c) If line OM is produced to T such that OM: MT = 6:1 (i) Find the position vector of T (ii) Show that points L, T and B are collinear Form 2 Mathematics
The figure below represents a quadrilateral piece of land ABCD divided into three triangular plots The lengths BE and CD are 100m and 80m respectively. Angle ABE = 300,angle ACE = 450and angle ACD = 1000
Find to four significant figures:
(i) The length of AE (ii) The length of AD (iii) the perimeter of the piece of land (b) The plots are to be fenced with five strands of barbed wire leaving an entrance of 2.8 m wide to each plot. The type of barbed wire to be used is sold in rolls of lengths 480m. Calculate the number of rolls of barbed wire that must be bought to complete the fencing of the plots Form 4 Mathematics
Bot juice Company has two types of machines, A and B, for juice production. Type A machine can produce 800 litres per day while type B machine produces 1,600 litres per day.
Type A machine needs 4 operators and type B machine needs 7 operators. At least 8,000 litres must be produced daily and the total number of operators should not exceed 41. There should be 2 more machines of each type. Let x be the number of machines of type A and Y the number of machines for type B,
Form 2 Mathematics
The diagram below represents a pillar made of cylindrical and regular hexagonal parts. The diameter and height of the cylindrical part are 1.4m and 1m respectively. The side of the regular hexagonal face is 0.4m and height of hexagonal part is 4m.
Form 4 MathematicsThe displacement x metres a particle after seconds given by:
x = t3- 2t2 + 6t > 0.
Form 4 Mathematics
a) Complete the table given below in the blank spaces.
Give your answer to the nearest degree.
Form 2 MathematicsAn electric pylon is 30m high. A point S on top of the pylon is vertically above another point on the ground . Points A and B are on the same horizontal ground as R. Point A is due south of the pylon and the angle of elevation of S from A is 260. Point B is due west of the pylon and the angle of elevation of S from B is 320.
Form 3 Mathematics
The nth term of a sequence is given by 2n+3
Sn = n2 +4n Form 2 MathematicsThe marks obtained by 10 pupils in an English test were 15,14,13,12,P,16,11,13,12 and 17.The sum of the squares of the marks, ∑x = 21,794
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