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) 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 MathematicsThe density of a solid spherical ball varies directly as its mass and inversely as the cube of its radius. When the mass of the ball is 500g and the radius is 5 cm, its density is 2 g per cm^{3} Calculate the radius of a solid spherical ball of mass 540 density of 10g per cm^{3}. 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. 
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