KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Comprehensive Answers and Marking Schemes KNEC Certified
Form 3 Mathematics
Amina carried out an experiment to determine the average volume of a ball bearing. He started by submerging three ball bearings in water contained in a
measuring cylinder. She then added one ball a time into the cylinder until the balls were nine. The corresponding readings were recorded as shown in the table below
a) i) On the grid provided, Plot (x, y) where x is the number of ball bearings and y is the corresponding measuring cylinder, reading.
ii) Use the plotted points to draw the line of best fit b) Use the plotted points to draw the line of best fit. i) The average volume of a ball bearing; ii) The equation of the line. c) Using the equation of line in b(ii) above, determine the volume of the water in the cylinder.
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Form 3 Mathematics
a)The first term of an Arithmetic Progression (AP) is 2. The sum of the first 8 terms of the AP is 156
i) Find the common difference of the AP. ii) Given that the sum of the first n terms of the AP is 416, find n. b) The 3rd, 5th and 8th terms of another AP form the first three terms of a Geometric Progression (GP) If the common difference of the AP is 3, find: i) The first term of the GP; ii) The sum of the first 9 terms of the GP, to 4 significant figures. Form 4 MathematicsForm 3 Mathematics
The table below shows income tax rates.
In certain year, Robi‟s monthly taxable earnings amounted to Kshs. 24 200.
a) Calculate the tax charged on Robi‟s monthly earnings. b) Robi was entitled to the following tax reliefs: I: monthly personal relief of Ksh 1 056; II: Monthly insurance relief at the rate of 15% of the premium paid. Calculate the tax paid by Robi each month, if she paid a monthly premium of Kshs 2 400 towards her life insurance policy. Form 4 Mathematics
Triangle PQR shown on the grid has vertices p(5,5), Q(10, 10) and R(10,15)
a) Find the coordinates of the points p‟, Q‟ and R‟ and the images of P, Q and R respectively under transformation M whose matrix is
b) Given that M is a reflection;
i) draw triangle P‟Q‟R‟ and the mirror line of the reflection; ii) Determine the equation of the mirror line of the reflection c) Triangle P” Q” R” is the image of triangle P‟Q‟R‟ under reflection N is a reflection in the yaxis. i) draw triangle P”Q”R” ii) Determine a 2 x2 matrix equivalent to the transformation NM iii) Describe fully a single transformation that maps triangle PQR onto triangle P”Q”R” Form 4 Mathematics
The table below shows the number of goals scored in handball matches during a tournament.
Draw a cumulative frequency curve on the grid provided
b) Using the curve drawn in (a) above determine; i) The median; ii) The number of matches in which goals scored were not more than 37; iii) The interquartile range Form 3 Mathematics
At the beginning of the year 1998, Kanyingi bought two houses, one in Thika and the other one Nairobi, each at Ksh 1 240 000. The value of the house in Thika appreciated at the rate of 12% p.a
a) Calculate the value of the house in thirika after 9 years, to the nearest shilling. b) After n years, the value of the house in Thika was Kshs 2 741 245 while the value of the house in Nairobi was Kshs 2 917 231. i) Find n ii) Find the annual rate of appreciation of the house in Nairobi. Form 1 Mathematics
A water vendor has a tank of capacity 18900 litres. The tank is being filled with water from two pipe A and B which are closed immediately when the tank is full. Water flows at the rate of
a) If the tank is empty and the two pipes are opened at the same time, calculate the time it takes to fill the tank. b) On a certain day the vendor opened the two pipes A and B to fill the empty tank. After 25 minutes he opened the outlet to supply water to his customers at an average rate of 20 Liters per minute i) Calculate the time it took to fill the tank on that day. ii) The vendor supplied a total of 542 jerricans, each containing 25 litres of water , on the day. If the water that remained in the tank was 6 300 litres, calculate, in litres, the amount of water that was wasted. Form 4 MathematicsForm 3 MathematicsForm 4 Mathematics
Point P (40^{0}S, 45^{0}E) and point Q (40^{0}S, 60^{0}W) are on the surface of the Earth.
Calculate the shortest distance along a circle of latitude between the two points. Form 3 Mathematics
On a certain day, the probability that it rains is 1/7 . When it rains the probability that Omondi carries an umbrella is 2/3. When it does not rain the probability that Omondi carries an umbrella is 1/6. Find the Probability that Omondi carried an umbrella that day.
Form 3 Mathematics
A circle whose equation is (x – 1)^{2} + (y k)^{2} = 10 passes through the point (2,5). Find the coordinates of the two possible centres of the circle.
Form 3 Mathematics
a) Expand and simplify the binomial expression (2 –x)^{7} in ascending powers of x.
b) Use the expansion up to the fourth term to evaluate (1.97)^{7} correct to 4 decimal places Form 1 Mathematics
In a certain commercial bank, customer may withdraw cash through one of the two tellers at the counter. On average, one teller takes 3 minutes while the other teller takes 5 minutes to serve a customer. If the two tellers start to serve the customers at the same time, find the shortest time it takes to serve 200 customers
Form 2 MathematicsForm 3 MathematicsForm 1 MathematicsForm 3 Mathematics
find a quadratic equation whose roots are 1.5 + sq root 2 and 1.5  sq root 2, expressing it in the form ax^{2} + bx + c =0, where a, b and c are integers
Form 1 Mathematics
A farmer feed every two cows on 480 Kg of hay for four days. The farmer has 20 160 Kg of hay which is just enough to feed his cows for 6 weeks. Find the number of cows in the farm.
Form 3 Mathematics
a) On the grid provided, draw a graph of the functionY= ½ x^{2} – x + 3 for 0 ≤ x ≤ 6
b) Calculate the midordinates for 5 strips between x= 1 and x=6, and hence Use the midordinate rule to approximate the area under the curve between x= 1, x=6 and the xaxis. c) Assuming that the area determined by integration to e the actual area, calculate the percentage error in using the midordinate rule. Form 1 Mathematics
Three points P, Q and R are on a level ground. Q is 240 m from P on a bearing of 230^{0} . R is 120 m to the east of P
a) Using a scale of 1 cm to represent 40 m, draw a diagram to show the positions of P, Q and R in the space provided below. b) Determine i) The distance of R from Q ii) The bearing of R from Q c) A vertical post stands at P and another one at Q. A bird takes 18 seconds to fly directly from the top of the post at q to the top of the post at P. Given that the angle of depression of the top of the post at P from the top of the post at Q is 9^{0}, Calculate: i) The distance to the nearest metre, the bird covers; ii)The speed of the bird in Km/h 
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