KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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 Mathematics
A line with gradient of -3 passes through the points (3 , k) and (k, 8). Find the value of k and hence express the equation of the line in the form ax + by = c ,
where a, b and c are constant Form 2 Mathematics
A minor arc of a circle subtends an angle of 105 at the centre of the circle. If the radius of the circle is 8.4 cm, find the length of the major arc (Take π= 22/7).
Form 2 Mathematics
A students obtained the following marks in four tests during a school term: 60%, 75%, 48% and 66%. The tests were weighted as follows: 2,1, 4 and 3 respectively.
Calculate the students weighed mean mark of the tests Form 2 Mathematics
Two trains T1 and T2 traveling in the opposite directions, on parallel tracks are just beginning to pass one another. Train T1 is 72 m long and traveling at 108 km/h. T2 is 78 m long and is traveling at 72 km/h.
Form 2 Mathematics
A bus travelling at an average speed of 63 km / h left a station at 8:15 am. A car later left the same station at 9.00 am and caught up with the bus at 10.45 am.
Find the average speed of the car. Form 2 Mathematics
A man who can swim at 5km/h in still water swims towards the east to cross a river. If the river flows from north to south at the rate of 3km/h
a) Calculate: i) The resultant speed ii) The drift b) If the width of the river is 30m, find the time taken, in seconds, for the man to cross the river. Form 2 Mathematics
A triangular plot ABC is such that the length of the side AB is two thirds that of BC. The ratio of the lengths AB:AC = 4:9 and the angle at B is obtuse.
a) The length of the side BC
b)
i) The area of the plot
iii) The size of ∠ABC Form 2 Mathematics
The figure below represents a model of a solid structure in the shape of a frustum of a cone with hemispherical top. The diameter of the hemispherical part is 70cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 28cm and slant height of 60cm.
Calculate
Form 2 Mathematics
P(5,-4) and Q (-1,2) are points on a straight line. Find the equation of the perpendicular bisector of PQ: giving the answer in the form y = mx + c.
Form 2 MathematicsForm 2 Mathematics
A school decided to buy at least 32 bags of maize and beans. The number of bags of maize were to be more than 20 and the number of bags of beans were to
be at least 6. A bag of maize costs Ksh 2500 and a bag of beans costs Ksh 3500. The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information. Form 2 Mathematics
Find the value of x given that log (x - 1) + 2 = log (3x + 2) + log 25.
Form 2 Mathematics
The figure below represents a conical flask. The flask consists of a cylindrical part and a frustum of a cone. The diameter of the base is 10cm while that of the neck is 2 cm. the vertical height of the flask is 12cm.
Calculate, correct to 1 decimal place
a) The slant height of the frustum part b) The slant height of the smaller cone that was cut off to make the frustum part c) The external surface area of the flask. (Take π =3.142) Form 2 Mathematics
On the grid below, an object T and its image T’ are drawn
a) Find the equation of the mirror lien that maps T onto Tʹ.
b i)Tʹ is mapped onto Tʺ by positive quarter turn about (0,0). Draw Tʺ ii) Describe a single transformation that maps T onto Tʺ c) Tʺ is mapped onto Tʺʹ by an enlargement, centre (2,0), scale factor -2 . Draw Tʺʹ d) Given that he area of Tʺʹ is 12cm2, calculate the area of Tʺʹ . Form 2 Mathematics
(a) A straight line L, whose equation is 3y — 2x = —2 meets the x-axis at R.
Determine the co-ordinates of R. b) A second line L2 is perpendicular to L1 at R. Find the equation of L2 in the form y = mx + c, where m and c are constants. (c) A third line L3 passes through (—4,1) and is parallel to L2 Find: (i) the equation of L3 in the form y = mx + c, where m and c are constants (ii) the co-ordinates of point S, at which L intersects L Form 2 MathematicsForm 2 Mathematics
Musa cycled from his home to a school 6km away in 20 minutes. He stopped at the school for 5 minutes before taking a motorbike to a town 40km away.
The motorbike travelled at 75km/h. On the grid provided, draw a distance-time graph to represent Musa's journey. Form 1 Mathematics
The cost of 2 jackets and 3 shirts was Ksh 1800. After the cost of a jacket and that of a shirt were increased by 20%, the cost of 6 jackets and 2 shirts was
Ksh 4 800. Calculate the new cost of a jacket and that of a shirt. Form 2 MathematicsForm 2 Mathematics
The sum of interior angles of a regular polygon is 24 times the size of the exterior angle.
(a) Find the number of sides of the polygon. (b) Name the polygon |
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