KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 1 Mathematics
Using a ruler and a pair of compass only, construct a rhombus PQRS such that PQ = 6cm and SPQ = 75°.
Measure the length of PR.
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Form 1 Mathematics
A tourist converted 5820 US dollars into Kenya Shillings at the rate of Ksh 102.10 per dollar. While in Kenya, he spent Ksh450 000 and converted the balance into dollars at the rate of Ksh 103.00 per dollar.
Calculate the amount of money, to the nearest dollar, that remained. Form 3 Mathematics
Given that sin 2x = cos (3x — 10°), find tan x, correct to 4 significant figures.
Form 1 Mathematics
A retailer bought a bag of tea leaves. If the retailer were to repack the tea leaves into smaller
packets of either 40 g, 250g or 350 g, determine the least mass, in grams, of the tea leaves in the bag. Form 1 Mathematics
Three villages A, B and C rife Such that B is 53 km on a bearing of 295° from A and C is 75 km east of B.
(a) Using a scale of 1 cm to represent 10 km, draw a diagram to show the relative positions of villages A, B and C. (b) Determine the distance, in km, of C from A. Form 4 Mathematics(a) BCD is a rectangle in which AB = 7.6 cm and AD = 5.2 cm. draw the rectangle and construct the lucus of a point P within the rectangle such that P is equidistant from CB and CD ( 3 marks) (b) Q is a variable point within the rectangle ABCD drawn in (a) above such that 600 ≤ AQB≤ 900 On the same diagram, construct and show the locus of point Q, by leaving unshaded, the region in which point Q lies Form 3 MathematicsAbdi and Amoit were employed at the beginning of the same year. Their annual salaries in shillings progressed as follows: Abdi: 60,000, 64 800, 69, 600 (a) Calculate Abdi’s annual salary increment and hence write down an expression for his annual salary in his nth year of employment( 2 marks) (b) Calculate Amoit’s annual percentage rate of salary increment and hence write down an expression for her salary in her nth year of employment. ( 2 marks) (c) Calculate the differences in the annual salaries for Abdi and Amoit in their 7th year of employment ( 4 marks) Form 4 MathematicsTriangles ABC and A”B”C” are drawn on the Cartesian plane provided. Triangle ABC is mapped onto A”B”C” by two successive transformations (a) Find R ( 4 marks) (b) Using the same scale and axes, draw triangles A’B’C’, the image of triangle ABC under transformation R ( 2 marks) (c) Describe fully, the transformation represented by matrix R ( 2 marks) Form 1 MathematicsForm 2 Mathematics
Juma left his home at 8.30a.m. He drove a distance of l40km and arrived at his aunt’s home at 10.15 a.m.
Determine the average speed, in km/h, for Juma’s journey. Form 2 MathematicsForm 1 MathematicsForm 3 MathematicsExpand and simplify (3x – y)4. Hence use the first three terms of the expansion to approximate the value of (6-0.2)4 ( 4 marks) 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) Form 4 MathematicsTwo lines L1 and L2 intersect at a point P. L1 passes through the points (-4,0) and (0,6). Given that L2 has the equation: y = 2x – 2, find, by calculation, the coordinates of P. ( 3 marks) 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 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. |
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