KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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Form 4 Mathematics
A hotel buys beef and mutton daily. The amount of beef bought must be at least 30kg and that of mutton at least 20 kg. The total mass of beef and mutton bought should not exceed 100 kg. The beef is bought at Ksh 360 per kg and the mutton at Ksh 480 per kg.
The amount of money spent on both beef and mutton should not exceed Ksh 43 200 per day. Let x represent the number of kilograms of beef and y the number of kilograms of mutton. (a) Write the inequalities that represent the above information. (b) On the grid provided, draw the inequalities in (a) above. (c) The hotel makes a profit of ksh 50 on each kg of beef and ksh 60 on each kg of mutton. Determine the maximum profit the hotel can make
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Form 3 Mathematics
The table below shows monthly income tax rates for a certain year.
In that year a monthly personal tax relief of Ksh 1 280 was allowed. In a certain month of that year, Sila earned a monthly basic salary of Ksh 52 000, a house allowance of Ksh 7 800 and a commuter allowance of Ksh 5 000.
(a) Calculate: (i) Sila’s taxable income; (ii) the net tax payable by Sila in that month; (b) In July that year, Sila’s basic salary was raised by 4%. Determine Sila’s net salary in July. Form 4 Mathematics
The figure below is a model of a watch tower with a square base of side 10 cm. Height PU is 15 cm and slanting edges UV = TV = SV = RV = 13 cm.
Giving the answer correct to two decimal places, calculate:
(a) length MP;
(b) the angle between MU and plane MNPQ; (c) Length of VO; (d) The angle between planes VST and RSTU; Form 4 Mathematics
The table below shows some values of the curves y = 2 cos x and y = 3 sin x.
(a) Complete the table for values of y = 2 cos x and y = 3 sin x, correct to 1 decimal place.
On the grid provided, draw the graphs of y = 2 cos x and y = 3 sin x for 0° ≤ x ≤ 360°, on the same axes.
(c) Use the graph to find the values of x when 2 cos x — 3 sin x = 0 (d) Use the graph to find the values of y when 2 cos x = 3 sin x. Form 1 Mathematics
(a) Using a ruler and a pair of compasses only, construct:
(i) a parallelogram ABCD, with line AB below as part of it, such that AD = 7 cm and angle BAD = 60°;
(ii) the locus of points equidistant from AB and AD;
(iii) the perpendicular bisector of BC. (b) (i) Mark the point P that lies on DC and is equidistant from AB and AD. (ii) Measure BP. (c) Describe the locus that the perpendicular bisector of BC represents. (d) Calculate the area of trapezium ABCP. Form 4 Mathematics
The table below shows the frequency distribution of heights of 40 plants in a tree nursery.
(a) State the modal class.
(b) Calculate: (i) the mean height of the plants; (ii) the standard deviation of the distribution. (c) Determine the probability that a plant taken at random has a height greater than 40 cm. Form 3 Mathematics
(a)Complete the table below for the equation y = x^{2}4x+2
(b) On the grid provided draw the graph y = x^{2}  4x + 2 for 0 ≤ x ≤ 5. Use 2 cm to represent 1 unit on the xaxis and 1 cm to represent 1 unit on the yaxis.
(c) Use the graph to solve the equation, x^{2} 4x + 2 = 0 (d) By drawing a suitable line, use the graph in (b) to solve the equation x^{2} 5x + 3 = 0. Form 3 Mathematics
The 5th and 10th terms of an arithmetic progression are 18 and 2 respectively.
(a) Find the common difference and the first term. (b) Determine the least number of terms which must be added together so that the sum of the progression is negative. Hence find the sum. Form 3 Mathematics
In a certain firm there are 6 men and 4 women employees. Two employees are chosen at random to attend a seminar. Determine the probability that a man and a woman are chosen.
Form 3 MathematicsForm 4 Mathematics
The position of two points C and D on the earth’s surface are (θ°N, l0°E) and (θ°N, 30°E)
respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. Form 4 Mathematics
The mass, in kilograms, of 9 sheep in a pen were: 13, 8, 16, 17, 19, 20, 15, 14 and 11.
Determine the quartile deviation of the data. Form 4 Mathematics
State the amplitude and the phase angle of the curve y = 2 sin ( 3/2 x — 30°)
Form 3 MathematicsForm 3 Mathematics
Use completing the square method to solve 3x^{2} + 8x — 6 = 0, correct to 3 significant figures.
Form 3 MathematicsForm 4 MathematicsForm 1 Mathematics
Asia invested some money in a financial institution. The financial institution offered 6% per annum compound interest in the first year and 7% per annum in the second year. At the end of the second
year, Asia had Ksh 170 130 in the financial institution. Determine the amount of money Asia invested. Form 3 Mathematics
A variable P varies directly as t^{3} and inversely as the square root of s. When t = 2 and s = 9, P = 16. Determine the equation connecting P, t and s, hence find P when s = 36 and t=3.
Form 4 Mathematics
The equation of a curve is given as y=1/3x^{3}4x+5
Determine: (a) The value of y when x = 3; (b) The gradient of the curve at x = 3; (c) The turning points of the curve and their nature. Form 1 Mathematics
Three business partners Abila, Bwire and Chirchir contributed Ksh 120 000, Ksh 180 000 and Ksh 240 000 respectively, to boost their business.
They agreed to put 20% of the profit accrued back into the business and to use 35% of the profits for running the business (official operations). The remainder was to be shared among the business partners in the ratio of their contribution. At the end of the year, a gross profit of Ksh 225 000 was realised. (a) Calculate the amount: (i) put back into the business; (ii) used for official operations (b) Calculate the amount of profit each partner got. (c) If the amount put back into the business was added to individuals’s shares proportionately to their initial contribution, find the amount of Chirchir’s new shares. 
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