KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 MathematicsThe diagram below represents a cuboid ABCDEFGH in which FG= 4.5 cm, GH = 8cm and HC = 6 cm Calculate: (a) The length of FC ( 2 marks) (b) (i) the size of the angle between the lines FC and FH ( 2 marks) (ii) The size of the angle between the lines AB and FH ( 2 marks) (c) The size of the angle between the planes ABHE and the plane FGHE (2mks)
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Form 3 Mathematics(a) complete the table below, giving your values correct to 2 decimal places ( 2 marks) (b) On the grid provided, using the same scale and axes, draw the graphs of y = sin x^{0} and y = 1 – cos x^{0} ≤ x ≤ 180^{0} Take the scale: 2 cm for 300 on the x axis 2 cm for I unit on the y axis (c) Use the graph in (b) above to (i) Solve equation 2 sin x^{o} + cos x^{0} = 1 ( 1 mark) (ii) Determine the range of values x for which 2 sin xo > 1 – cos x^{0} ( 1 mark) Form 1 MathematicsA boat at point x is 200 m to the south of point Y. The boat sails X to another point Z. Point Z is 200m on a bearing of 310^{0} from X, Y and Z are on the same horizontal plane. (a) Calculate the bearing and the distance of Z from Y ( 3 marks) (b) W is the point on the path of the boat nearest to Y. Calculate the distance WY ( 2 marks) (c) A vertical tower stands at point Y. The angle of point X from the top of the tower is 6^{0} calculate the angle of elevation of the top of the tower from W (3 marks) Form 4 MathematicsA curve is represented by the function y = ^{1}/_{3} x^{3} + x^{2} – 3x + 2 (a) Find ^{dy}/_{dx} (1 mark) (b) Determine the values of y at the turning points of the curve y = ^{1}/_{3} x^{3} + x^{2} – 3x + 2 ( 4 marks) Form 4 MathematicsDiet expert makes up a food production for sale by mixing two ingredients N and S. One kilogram of N contains 25 units of protein and 30 units of vitamins. One kilogram of S contains 50 units of protein and 45 units of vitamins. If one bag of the mixture contains x kg of N and y kg of S. (a) Write down all the inequalities, in terms of x and representing the information above ( 2 marks) 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 n^{th} 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 n^{th} year of employment. ( 2 marks) (c) Calculate the differences in the annual salaries for Abdi and Amoit in their 7^{th} 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 3 MathematicsExpand and simplify (3x – y)^{4}. Hence use the first three terms of the expansion to approximate the value of (60.2)^{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 L_{1} and L_{2} intersect at a point P. L_{1} passes through the points (4,0) and (0,6). Given that L_{2} has the equation: y = 2x – 2, find, by calculation, the coordinates of P. ( 3 marks) Form 4 MathematicsA stone is thrown vertically upwards from a point O After t seconds, the stone is S metres from O Given that S= 29.4t – 4.9t^{2}, Find the maximum height reached by the stone ( 3 marks) Form 1 MathematicsSuccessive moving averages of order 5 for the numbers 9,8.2, 6.7,5.4, 4.7 and k are A and B. Given that A – B = 0.6 find the value of k. Form 3 MathematicsGiven that Cos 2x^{0} = 0.8070, find x when 0^{0} < x < 360^{0} ( 4 marks) Form 2 Mathematics
The volumes of two similar solid cylinders are 4752 cm^{3} and 1408 cm^{3}. If the area of the curved surface of the smaller cylinder is 352 cm^{2}, find the area of the curved surface of the larger cylinder. ( 4 marks)
Form 3 MathematicsFind, without using Mathematical Tables the values of x which satisfy the equation Log_{2} (x^{2} – 9) = 3 log_{2} (2 + 1) (4 marks) 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 3 MathematicsThe first three consecutive terms of a geometrical progression are 3, x and 5 ^{1}/_{3}. Find the value of x. ( 2 marks) Form 2 MathematicsForm 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 MathematicsThe diagram below represents a rectangular swimming pool 25m long and 10m wide. The sides of the pool are vertical. The floor of the pool slants uniformly such that the depth at the shallow end is 1m at the deep end is 2.8 m. (a) Calculate the volume of water required to completely fill the pool. (b) Water is allowed into the empty pool at a constant rate through an inlet pipe. It takes 9 hours for the water to just cover the entire floor of the pool. Calculate: (i) The volume of the water that just covers the floor of the pool ( 2 marks) (ii) The time needed to completely fill the remaining of the pool ( 3 marks) 
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