KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 2 Mathematics
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Form 2 Mathematics
The internal and external diameters of a circular ring are 6cm and 8cm respectively. Find the volume of the ring if its thickness is 2 millimetres.
Form 2 MathematicsForm 2 MathematicsForm 2 Mathematics
The diagram below represents a conical vessel which stands vertically. The which stands vertically,. The vessels contains water to a depth of 30cm. The radius of the surface in the vessel is 21cm. (Take π=22/7).
a) Calculate the volume of the water in the vessels in cm3
b) When a metal sphere is completely submerged in the water, the level of the water in the vessels rises by 6cm. Calculate: (i) The radius of the new water surface in the vessel; (ii) The volume of the metal sphere in cm3 (iii) The radius of the sphere. Form 2 Mathematics
The diagram below shows a triangle ABC with A (3, 4), B (1, 3) and C (2, 1).
a) Draw triangle A'B'C' the image of ABC under a rotation of +900+ about (0, 0).
b) Drawn triangle A"B" the image of A"B'C" under a reflection in the line y=x. c) Draw triangle A"B" C. the image under a rotation of -900 about (0, 0) d) Describe a single transformation that maps triangle ABC"" onto angle A"""B"""C""" e) Write down the equations of the lines of symmetry of the quadrilateral BB"A""A Form 2 Mathematics
The diagram below represents two vertical watch-towers AB and CD on a level ground. P and Q are two points on a straight road BD. The height of the tower AB is 20m road a BD is 200m.
a) A car moves from B towards D. At point P, the angle of depression of the car from point A is 11.3. Calculate the distance BP to 4 significant figures.
b) If the car takes 5 seconds to move from P to Q at an average speed of 36 km/h, calculate the angle of depression of Q from A to 2 decimal places c) Given that QC=50.9m, calculate; (i) The height of CD in meters to 2 decimal places; (ii) The angle of elevation of A from C to the nearest degree. Form 2 Mathematics
The equation of line L1 is 2y-5x-8=0 and line L2 passes through the points (-5, 0) and (5,-4). Without drawing the lines L1 and L2 show that the two lines are perpendicular to each other.
Form 2 Mathematics
Given that log 4=0.6021 and log 6=0.7782, without using mathematical tables or a calculator, evaluate log 0.096.
Form 2 Mathematics
A rectangular and two circular cut-outs of metal sheet of negligible thickness are used to make a closed cylinder. The rectangular cut-out has a height of 18cm. Each circular cu-out has a radius of 5.2cm. Calculate in terms of pi, the surface area of the cylinder
Form 2 Mathematics
Three vertices of a rhombus ABCD are; A(-4,-3), B(1,-1) and c are constants.
a) Draw the rhombus on the grid provided below. b) Find the equation of the line AD in the form y = mx + c, where and c are constants. Form 2 Mathematics
An angle of 1.8 radians at the centre of a circle subtends an area of length 23.4cm
Find; a) The radius of the circle b) The area of the sector enclosed by the arc and the radii. Form 2 Mathematics
A liquid spray of mass 384g is packed in a cylindrical container of internal radius 3.2cm. Given that the density of the liquid is 0.6g/cm3, calculate to 2 decimal places the height of the liquid in the container.
Form 2 Mathematics
Mapesa traveled by train from Butere to Nairobi. The train left Butere on a Sunday at 23 50 hours and traveled for 7 hours 15 minutes to reach Nakuru. After a 45 minutes stop in Nakuru, the train took 5 hours 40 minutes to reach Nairobi.
Find the time, in the 12 hours clock system and the day Mapesa arrived in Nairobi. Form 2 MathematicsForm 2 Mathematics
The figure below represents a right prism whose triangular faces are isosceles. The base and height of each triangular face are 12cm and 8cm respectively. The length of the prism is 20cm.
Calculate the:
Form 2 Mathematics
Solve the following inequalities and represent the solutions on a single number line:
3 – 2x < 5 4 – 3x ≥ -8 Form 3 Mathematics
In this question use a ruler and a pair of compasses only
In the figure below, AB and PQ are straight lines
(a) Use the figure to:
(i) Find a point R on AB such that R is equidistant from P and Q (ii) Complete a polygon PQRST with AB as its line of symmetry and hence measure the distance of R from TS. (b) Shade the region within the polygon in which a variable point X must lie given that X satisfies the following conditions I: X is nearer to PT than to PQ II: RX is not more than 4.5 cm III. angle PXT > 90 Form 2 Mathematics
Vector q has a magnitude of 7 and is parallel to vector p. Given that
p= 3 i –j + 1 ½ k, express vector q in terms of I, j, and k. Form 2 Mathematics
Water and milk are mixed such that the ratio of the volume of water to that of milk is 4: 1. Taking the density of water as 1 g/cm3 and that of milk as 1.2g/cm3, find the mass in grams of 2.5 litres of the mixture.
Form 2 Mathematics
Find the equation of a straight line which is equidistant from the points ( 2,3) and ( 6, 1), expressing it in the form ax + by = c where a, b and c are constants
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