KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

(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)

PAPER 1, SECTION B, STATISTICS II, FORM 4 LEVEL, 10 MARKS

​A number of people are asked to cut 20cm lengths of string without measuring. Later 100 pieces are collected and measured correct to the nearest 1/10cm. the data below was collected.

​Using 19.7 as a working mean calculate:

​(a) Mean (4mks)

​(b) Standard deviation (5mks)

​(c) State the modal class (1mk)

Paper 1, Section B

​A bus left Nairobi at 7.00 am and traveled towards Eldoret at an average speed of 80Km/hr. At 7.45 a.m a car left Eldoret towards Nairobi at an average speed of 120Km/hr. The distance between Nairobi and Eldoret is 300 km. Calculate:

(a) The time the bus arrived at Eldoret.   (2mks)

(b) The time of the day the two met.   (4mks)

(c) The distance of the bus from Eldoret when the car arrived in Nairobi.   (2mks)

(d) The distance from Nairobi when the two met. (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)

(a) Given that y = 7 + 3x-x², complete the table below.(2mks)

Worked Solution

(b) On the grid provided and using a suitable scale draw the graph of y = 7 + 3x-x². (2mks)

(c) On the same grid draw the straight line and use your graph to solve the equation x² - 4x– 3 = 0.    (3mks)

(d) Determine the coordinates of the turning point of the curve. (2mks)

Worked Solution:

​A straight line L1 has a gradient ˉ½ and passes through point P (-1, 3).  Another line L2 passes through the points Q (1, -3) and R (4, 5).  Find. 

​(a) The equation of L1.         (2mks)

​(b) The gradient of L2.                        (1mk)

(c) The equation of L2.                      (2mks)

​(d) The equation of a line passing through a point S (0, 5) and is perpendicular to L2.                      (3mks)

(e) The equation of a line through R parallel to L1. (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)

A line passes through the point (-1, 2) and has gradient -½. Write down its equation in the form ax + by = c  (3mks)

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

A chord PQ of length 15cm subtends an angle of 65º at the circumference centre O.  Find the radius of the circle.  (3mks)

Worked Solution

​The figure below is a velocity time graph for a car.

​(a) Find the total distance traveled by the car.

​(b) Calculate the deceleration of the car.

​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