KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Comprehensive Answers and Marking Schemes KNEC Certified
Form 4 Mathematics
The equation of a curve is y = 2x^{3} + 3x^{2}.
a)Find i)The x – intercept of the curve ii) theyintercept of the curve b i)Determine the stationary points of the curve ii)For each point in (b) (i) above, determine whether it is a maximum or a minimum c) Sketch the curve.
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Form 1 Mathematics
Using a pair of compasses and ruler only, construct
a)i)Triangle ABC in which AB= 5 cm, <BAC=30 and <ABC = 105. ii)A circle that passes through he vertices of the triangle ABC. Measure the radius iii)the height of triangle ABC with AB as the base. Measure the height b) Determine the area of circle that lies outside the triangle correct to 2 decimal places Form 1 Mathematics
a)The ratio of Jumas and Akinyis earning was 5:3. Jumas earnings rose to Kshs 8400 after an increase of 12%
Calculate the percentage increase in Akinyis earnings given that the sum of their new earnings was kshs 14,100. b) Juma and Akinyi contributed all the new earnings to buy maize at Kshs 1175 per bag. The maize was then sold at Kshs 1762.50 per bag. The two shared all the money from the sales of the maize in the ratio of their contributions. Calculate the amount hat Akinyi got. Form 3 Mathematics
In the diagram below, the coordinates of points A and B are (1,6) and (15, 6) respectively.
Point N is on OB and that 30N = 2OB. Line OA is produced to L such that OL = 3OA.
a)Find vector LN b) Given that a point M is on LN such that LM: MN = 3: 4 find the coordinate of M c) If line OM is produced to T such a that OM: MT= 6:1 i)Find the position vector of T ii) Show that points L, T and B are collinear Form 2 Mathematics
The frequency table below shows the daily wages paid to casual workers by a certain company
a) In the grid provided, draw a histogram to represent the above information
b.i)State the class in which the median wage lies ii) Draw a vertical line, in the histogram, showing where the median wage lies c) Using the histogram, determine the number of workers who earn shs 450 or less per day Form 3 Mathematics
Three business partners: Asha, Nangila and Cherop contributed Ksh 6 000, Ksh 85 000 and Ksh 105 000 respectively. They agreed to put 25% of the profit back into business each year. They also agreed to put aside 40% of the remaining profit to cater for taxes and insurance. The rest of the profit would then be shared among the partners in the ratio of their contributions. At the end
of the first year, the business realised a gross profit of Ksh 225 000. (a) Calculate the amount of money Cherop received more than Asha at the end of the first year. (b) Nangila further invested Ksh 25 000 into the business at the beginning of the second year. Given that the gross profit at the end of the second year increased in the ratio10:9 calculate Nangila's share of the profit at the end of the second year. Form 3 Mathematics
a)Solve the equation
b) The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136m^{2}
.i)Calculate the perimeter of the floor ii)A rectangular carpet is placed on the floor of the wall leaving an area of 64m^{2}. If the length of a carpet is twice its width, determine the width of the carpet. Form 2 Mathematics
Given that Log 4 = 0.6021 and log 6 = 0.7782, without using mathematical tables on a calculator, evaluate log 0.096.
Form 2 Mathematics
The production of milk, in litres, of 14 cows on a certain day was recorded as follows:
22, 26, 15, 19, 20, 16,27, 15, 19, 22, 21, 20, 22 and 28. Determine: (a) the mode; (b) the median. 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 160cm^{3}, find the volume of the frustum.
Form 1 Mathematics
In this question, mathematical tables should not be used. A Kenyan bank buys and sells foreign currencies as shown below:
Buying Selling (In Kenya Shillings) (In Kenya Shillings) 1 Hong Kong Dollar 9.74 9.77 1 South African Rand 12.03 12.11 A tourist arrived in Kenya with 105 000 Hong Kong Dollars and changed the whole amount to Kenya Shillings. While in Kenya, she spent Sh 403 879 and changed the balance to South African Rands before leaving for South Africa. Calculate the amount in South African Rand, that she received, Form 1 Mathematics
Points L and M are equidistant from another point K.; The bearing of L form K is 330. The bearing of M from K is 220.
Calculate the bearing of M from L 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 4 Mathematics
The gradient of the tangent to the curve y = ax^{3} + bx at the point (1,1) is 5 , Calculate the values of a and b.
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 3 Mathematics
Given that x is an acute angle and cos x = 2/5 √5 find, without using mathematical tables or a calculator, tan (90x).
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 3 Mathematics
Give that OA =2i a + 3 j and OB = 3i 2j, find the magnitude of AB to one decimal place
Form 1 MathematicsForm 1 Mathematics
The external length, width and height of an open rectangular container are 41 cm and 15.5 cm respectively. The thickness of the materials making the container is
5mm. if the container has 8 lit res of water, calculate the internal height above the water level. 
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