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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

QUESTION AND ANSWER ON VOLUME AND SURFACE AREA MODEL06012023018

5/1/2023

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THE FIGURE BELOW SHOWS A RECTANGULAR BASED RIGHT PYRAMID, USE IT TO ANSWERS QUESTIONS THAT FOLLOW:

2/1/2023

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Two inlet taps P and Q opened at the same time can fill a tank in 2 1/2 h. The two taps were opened together at the same time and after 1 hour 10 minutes tap Q was closed and P continued alone and filled the tank after a further 4 hours. Find:

2/1/2023

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QUESTIONS

Two inlet taps P and Q opened at the same time can fill a tank in 2 1/2 h. The two taps were opened together at the same time and after 1 hour 10 minutes tap Q was closed and P continued alone and filled the tank after a further 4 hours. Find:
a) The fraction of the tank filled by both taps for 1 hour.     (1 marks)  
b) The fraction of the tank filled by tap P after Q was closed.  (2 marks)    
c) The time which each tap working alone would have taken to fill the tank.   (7 marks)    

ANSWERS

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A piece of wire, 18 cm long is cut into two parts. The first part is bent to form the four sides of a rectangle having length x cm and breath 1 cm.

27/12/2022

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A piece of wire, 18 cm long is cut into two parts. The first part is bent to form the four sides of a rectangle having length x cm and breath 1 cm.
a). State two expressions in terms of x only for the perimeter of the square and the rectangle.       (2 marks)

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If the sum of the areas of the square and the rectangle is A cm2, show that
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If A =8 cm2, Solve the equation in (b) above for x, hence find the possible dimensions of the two pieces of wire. (6 marks)
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If the bucket above has a hole and 1.1 cm3 of water leaks out every 5 seconds and collects in a cylindrical can of base radius and height 10 cm and 25 cm respectively. Calculate how long it takes to fill the cylindrical can.   (4 marks)

27/12/2022

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The diagram below shows a bucket in the shape of a frustum of a cone with diameters 36 cm and 24 cm and a vertical height of 28 cm. The bucket contains water such that the diameter of the water surface is 30cm. Calculate the volume of the bucket.  (6 marks)
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If the bucket above has a hole and 1.1 cm3 of water leaks out every 5 seconds and collects in a cylindrical can of base radius and height 10 cm and 25 cm respectively. Calculate how long it takes to fill the cylindrical can.   (4 marks)
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A cylinder of radius 15 cm and height 24 cm is filled with water. A solid hemisphere of radius 7cm is submerged into the cylinder and removed. Find the change in height of water level in the cylinder.  (4 marks)

11/12/2022

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​A cylinder of radius 15 cm and height 24 cm is filled with water. A solid hemisphere of radius 7cm is submerged into the cylinder and removed. Find the change in height of water level in the cylinder.     (4 marks)
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A wall clock that gains 20 seconds after every hour was set to read the correct time on Tuesday at 03 25.  Determine the time the wall clock will read on Thursday 03 25 h.    (3 marks)

11/12/2022

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​A wall clock that gains 20 seconds after every hour was set to read the correct time on Tuesday at 03 25.  Determine the time the wall clock will read on Thursday 03 25 h.    (3 marks)  
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A dealer sells a mobile phone at a profit of 25%. The customer sells it to a friend at ksh 60,000, making a profit of 20 %. Find the cost prize of the mobile phone.             (3 marks)

11/12/2022

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​A dealer sells a mobile phone at a profit of 25%. The customer sells it to a friend at ksh 60,000, making a profit of 20 %. Find the cost prize of the mobile phone.             (3 marks) 
A DEALER SELLS A MOBILE PHONE AT A PROFIT OF 25%. THE CUSTOMER SELLS IT TO A FRIEND AT KSH 60,000, MAKING A PROFIT OF 20 %. FIND THE COST PRIZE OF THE MOBILE PHONE.

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A three-digit number is such that twice the hundreds digit is more than the tens digit by 2.the unit digit is thrice the hundred digit. When the digits are reversed, the number is increased by 594.Find the number.

9/12/2022

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​A three-digit number is such that twice the hundreds digit is more than the tens digit by 2.the unit digit is thrice the hundred digit. When the digits are reversed, the number is increased by 594.Find the number.
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Evaluate without using mathematical tables or calculator

9/12/2022

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​Evaluate without using mathematical tables or calculator 

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Simplify:

9/12/2022

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Simplify:

3 marks
Simplify:

Worked Solution

Simplify:

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​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.

28/11/2021

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RATES, RATIO, PROPORTION AND PERCENTAGE | RATES | FORM 1 LEVEL | PAPER 2 QUESTIONS | SECTION A

​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)



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​Atieno is now four times as old as her daughter and six times as old as her son.

28/11/2021

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RATES, RATIO, PROPORTION AND PERCENTAGE | RATES | FORM 3 | PAPER 2 QUESTIONS | SECTION A

​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)



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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.

27/11/2021

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​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:

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A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm-square. Calculate the actual area in hectares of the land.

26/11/2021

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​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:

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

23/11/2021

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

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)

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

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(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)

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Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60degreesE from Q. Point D is equidistant from B, Q and C.

23/11/2021

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Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60oE from Q. Point D is equidistant from B, Q and C.

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

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

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

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

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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/cm-cubic.

23/11/2021

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​(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

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/cm-cubic.

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



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

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​(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)

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

22/11/2021

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​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)

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(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)

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(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)

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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.

21/11/2021

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​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.

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)

Find the angle subtended at the centre of the sector.

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

Draw the net of the solid.



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

21/11/2021

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

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

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(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)

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

21/11/2021

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


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Agnes paid rent which was a tenth of her net salary. She used half of the remaining amount to make a down payment for a plot.

20/11/2021

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​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

Agnes paid rent which was a tenth of her net salary. She used half of the remaining amount to make a down payment for a plot.



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Find the distance round the figure given below.

20/11/2021

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​Find the distance round the figure given below.  

take pie to be 22/7
find the perimeter of this figure

Worked solution

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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.

19/11/2021

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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

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