KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 2 Mathematics
A small cone of height 8cm is cut off from a bigger cone to leave a frustum of height 16cm. If. the volume of the smaller cone is 160cm3, find the volume of the frustum.
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Form 2 MathematicsForm 2 Mathematics
The volume of a cube is 1728 cm3. Calculate, correct to 2 decimal places, the length of the diagonal of a face of the cube.
Form 2 Mathematics
The figure below shows a right pyramid VABCDE. The base ABCDE is regular pentagon. AO = 15cm and VO = 36 cm.
Calculate:
(a) The area of the base correct to 2 decimal places (b) The length AV (c) The surface area of the correct to 2decimal places (d) The volume of the pyramid correct to 4 significant figures Form 2 Mathematics
The figure below shows a rectangular container of dimensions 40cm by 25cm by 90cm. a cylindrical pipe of radius 7.5cm is fitted in the container as shown.
Water is poured into the container in the space outside the pipe such that the water level is 80% the height of the container. Calculate the amount of the
water, in litres, in the container in 3 significant figures. Form 2 Mathematics
The mass of solid cone of radius 14cm and height 18cm is 4.62kg. find its density in g/cm3
Form 2 Mathematics
A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is three – quarters full of milk.
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 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 MathematicsForm 2 Mathematics
A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 12 cm and the slanting height of the cone is 10 cm.
(a) Calculate correct to two decimal places: (i) the surface area of the solid; (ii) the volume of the solid (b) If the density of the material used to make the solid is 1.3 g/cm3, calculate its mass in kilograms. Form 2 Mathematics
A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm, if the volume of the smaller cone is 160 cm3, find the
volume of the frustum Form 2 Mathematics
The external length, width and height of an open rectangular container are 41 cm, 21 cm and 15.5 cm respectively. The thickness of the material making the container is 5 mm. If the container has 8 litres of water, calculate the
internal height above the water level. Form 2 Mathematics
A carpenter constructed a closed wooden box with internal measurements 1.5 metres long, 0.8 metres wide and 0.4 metres high. The wood used in constructing the box was 1.0 cm thick and had a density of 0.6 gcm3.
(a) Determine the: (i) volume, in cm3, of the wood used in constructing the box; (ii) mass of the box, in kilograms, correct to 1 decimal place. (b) Identical cylindrical tins of diameter 10 cm, height 20cm with a mass of 120 g each were packed in the box. Calculate the: (i) maximum number of tins that were packed; (ii) total mass of the box with the tins. 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 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
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
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 1 Mathematics
Two cylindrical containers are similar. The larger one has internal cross- section area of 45cm2 and can hold 0.945 litres of liquid when full. The smaller container has internal cross- section area of 20cm2
(a) Calculate the capacity of the smaller container (b) The larger container is filled with juice to a height of 13 cm. Juice is then drawn from is and emptied into the smaller container until the depths of the juice in both containers are equal. Calculate the depths of juice in each container. (c) On fifth of the juice in the larger container in part (b) above is further drawn and emptied into the smaller container. Find the difference in the depths of the juice in the two containers. 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 2 Mathematics
The diagram below ( not drawn to scale) represents the cross- section of a solid prism of height 8.0 cm
(a) Calculate the volume of the prism
(b) Given that the density of the prism is 5.75g/cm3, calculate its mass in grams (c) A second prism is similar to first one but is made of a different materials. The volume of the second is 246.24cm3 (i) calculate the area of the cross section of the second prism (ii) Given that the ratio of the mass of the first to that of the second is 2: 5 and the density of the second prism Form 2 Mathematics |
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