KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 1 MathematicsA salesman earns a basic salary of Kshs. 9,000 per month In addition he is also paid a commission of 5% for sales above Kshs 15,000 In a certain month he sold goods worth Kshs. 120,000 at a discount of 2 ½ % Calculate his total earnings that month ( 3 marks)
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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 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 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. Form 1 MathematicsPipe a can fill an empty water tank in 3 hours while, pipe B can fill the same tank in 6 hours, when the tank is full it can be emptied by pipe C in 8 hours. Pipes A and B are opened at the same time when the tank is empty. If one hour later, pipe C is also opened, find the total time taken to fill the tank (4 marks) Form 1 MathematicsIn a fund- raising committee of 45 people, the ratio of men to women is 7: 2. Find the number of women required to join the existing committee so that the ratio of men to women is changed to 5: 4 ( 3 marks) Form 2 Mathematics
A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively.
(a) Calculate the area of the curved surface of the tank, correct to 2 decimal places. (b) Find the capacity of the tank, in litres, correct to the nearest litre. (c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water. Form 1 Mathematics
A photograph print measuring 24cm by 15 cm is enclosed in a frame. A uniform space of width x cm is left in between the edges of the photograph and the frame. If the area of the space i‹ 270cm2, find the value of x.
Form 1 Mathematics
A Kenyan businessman intended to buy goods worth US dollar 20 000 from South Africa
Calculate the value of the goods to the nearest South Africa (S.A) Rand given that 1 US dollar = Ksh 101.9378 and 1 S.A Rand = Ksh 7.6326. Form 2 MathematicsForm 1 Mathematics
(a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle.
(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres. Form 1 Mathematics
A two digit number is such that, the sum of its digits is 13. When the digits are interchanged, the original number is increased by 9. Find the original number.
Form 1 Mathematics
The lengths of three wires were 30m, 36 m and 84m. Pieces of wire of equal length were cut from the three wires. Calculate the least number of pieces obtained.
Form 1 MathematicsForm 2 Mathematics
The length of a room is 3 m shorter than three times its width. The height of the room is a quarter of its length. The area of the floor is 60 m2.
(a) Calculate the dimensions of the room. (b) The floor of the room was tiled leaving a border of width y m, all round. If the area of the border was 1.69m2, find: (i) the width of the border; (ii) the dimensions of the floor area covered by tiles. Form 1 Mathematics
Using a ruler and a pair of compasses only, construct:
(a) a triangle LMN in which LM = 5 cm, LN = 5.6 cm and MLN = 45° (b) the circle that touches all the sides of the triangle. Form 1 MathematicsThe size of each interior angle of a regular polygon is five times the size of the exterior angle. Find the number of sides of the polygon. Form 1 MathematicsForm 1 Mathematics
A miller was contracted to make porridge flour to support a feeding program. He mixed millet, sorghum, maize and Omena in the ration 1:2:5:1. The cost per kilogram of millet was Ksh 90, sorghum Ksh 120, maize Ksh 30 and omena Ksh 150.
Calculate: (a) the cost of one kilogram of the mixture; (b) the selling price of 1 kg of the mixture if the miller made a 30% profit. Form 1 Mathematics
The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°.
(a) Using a scale of 1cm to represent 1km, draw a diagram to show the positions of A, B, C and D. (b) Use the scale drawing to determine: (i) the bearing of A from D; (ii) the distance BD in kilometres. |
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