KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 4 Mathematics
(a)On the grid provided, draw a graph of the function y = 1/2 x2 - x + 3 for 0 ≤ x ≤ 6.
b) Calculate the mid ordinates for five strips between x = 1 and x = 6, and hence use the mid- ordinate rule to approximate the area under the curve between x = 1, x = 6 and the x = axis c) Assuming that the area determined by integration to be the actual area, calculate the percentage error in using the mid ordinate rule Form 4 Mathematics
The equation of a curve is y = 2x3 + 3x2.
a)Find i)The x – intercept of the curve ii) they-intercept 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. 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 136m2
.i)Calculate the perimeter of the floor ii)A rectangular carpet is placed on the floor of the wall leaving an area of 64m2. 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 160cm3, find the volume of the frustum.
Form 1 Mathematics
An industrialist has 450 litres of a chemical which is 70% pure. He mixes it with a chemical of the same type but 90% pure so as to obtain a mixture which is 75% pure.
Find the amount of the 90% pure chemical used Form 3 Mathematics
A group of 5 people can do a piece of work in 6 hours. Calculate the time a group of people. Working at half the rate of the first group would take to complete the same work.
Form 3 Mathematics
(a) Expand (1 + x)5
(b) Use the first three terms of the expansion in (a) to find the approximate value of (0.98)5 Form 3 Mathematics
Use matrices to solve the simultaneous equations
4x + 3 y = 18 5x – 2y = 11 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 = ax3 + bx at the point (1,1) is -5 , Calculate the values of a and b.
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