KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

​A dam containing 4158m-cubed of water is to be drained. A pump is connected to a pipe of radius 3.5cm and the machine operates for 8 hours per day. Water flows through the pipe at the rate of 1.5m per second. Find the number of days it takes to drain the dam. (3mks)

​Atieno is now four times as old as her daughter and six times as old as her son. Twelve years from now, the sum of the ages of her daughter and son will differ from her age by 9 years. What is Atieno’s present age? (3mks)

​Two grades of coffee one costing sh.42 per kilogram and the other costing sh.47 per kilogram are to be mixed in order to produce a blend worth sh.46 per kilogram in what proportion should they be mixed.     (3mks)

Worked Answer:

​A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm². Calculate the actual area in hectares of the land. (3mks)

​​​Worked Answer:

(a) A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below. ​

​(i) Using a scale of 1cm to 10m make an accurate drawing of the map of the field.         (4mks)

​(ii) Find the area of the field. (3mks)

(iii) Assuming that the baseline in (a) runs in a northern direction give the position of D relative to A using bearing and distance.    (3mks)

(a) Using the scale: 1cm represents 10km, construct a diagram showing the positions of B, C, Q and D. (5mks)

(b) Determine the 
(i) Distance between B and C           (1mk)

(ii) Bearing of D from B                      (2mks)

(c) Find the distance and bearing of D from C.  (2mks)

​(a) The diagram represents a solid frustum with base radius of 35cm and top radius of 21cm.The frustum is 22.5cm high and is made of a metal whose density is 4g/cm³.  
Taking  = 22/7, calculate

​(i) The volume of the metal that makes the frustum. (6mks)

​(ii) The mass of the frustum.                      (2mks)

​(b) The frustum is melted in down and recast into a solid cube in the process 20% of the metal is lost.  Calculate to 2d.p the length of each side of the cube.                                                                    (2mks)

​From a reservoir, water flows through a cylindrical pipe of diameter 0.2m at a rate of 0.35m per second.

​(a) Determine the number of liters of water discharged from reservoir in one hour.         (4mks)

(b) The water flows from the reservoir for 18 hours per day for 25 days per month and serves a population of 2500 families.  Determine the average consumption of water per family per month giving your answer to the nearest 100 litres.      (4mks)

(c) The water is charged at the rate of sh.4.50 per 100 litres.  Calculate the average water bill per family per month.  (2mks)

​The figure below is a cone whose base radius is 3.5cm and slant height 7cm.  The net of the cone is a sector of a circle.

​(a) Find the angle subtended at the centre of the sector.   (2mks)

(b) Draw the net of the solid.               (1mk)

​A Kenya company received US Dollars M.  The money was converted into Kenya Shillings in a bank which buys and sells foreign currencies.

​(a) If the company received Ksh.15, 132,000, calculate the amount, M received in US Dollar.         (2mks)

(b) The company exchanged the above Kenya shillings into Sterling pounds to buy a car in Britain. Calculate the cost of the car to the nearest Sterling pound.   (2mks)

The interior angles of a hexagon are 2x + 5, 4x - 5, 4x + 5, 3x, 4x - 20 and 2x. Find the value of x.    (3mks)

​Agnes paid rent which was 1/10 of her net salary. She used ½ of the remaining amount to make a down payment for a plot. She gave her mother Kshs. 2,500 and did shopping worth Kshs. 7,500 for herself. She saved the remainder which was Ksh. 12,500. How much was the down payment that she made. (4mks)

Worked Solution

​Find the distance round the figure given below.  

Worked solution

From a point 20m away on a level ground the angle of elevation to the lower window line is 25° and the angle of elevation to the top line of the window is 34°.  Calculate the height of the window.   [3 marks]

Worked solution

Worked Solution