KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 MathematicsThe points P, Q, R and S have position vectors 2p, 3p, r and 3r respectively, relative to an origin O. A point T divides PS internally in the ratio 1:6 (a) Find, in the simplest form, the vectors OT and QT in terms P and r ( 4 marks) (i) Show that the points Q, T, and R lie on a straight line ( 3 marks)
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Form 3 Mathematics(a) (i) Complete the table below for the function y = x^{3} + x^{2} – 2x (2 marks) (ii On the grid provided, draw the graph of y = x3 + x2 – 2x for the values of x in the interval – 3 ≤ x ≤ 2.5 (2 marks) (iii) State the range of negative values of x for which y is also negative (1 mk) (b) Find the coordinates of two points on the curve other than (0,0) at which x coordinate and y coordinate are equal (3 marks) Form 2 MathematicsA boat which travels at 5 km/h in still water is set to cross a river which flows from the north at 6km/h. The boat is set on a course of x^{0} with the north. (a) Given that cos x^{0} = ^{3}/_{5} , calculate (i) The resultant speed of the boat ( 2 marks) (ii) The angle which the track makes with the north ( 2 marks) (b) If the boat is to sail on a bearing of 135^{0}, calculate the bearing of possible course on which it can be set ( 4 marks) Form 4 MathematicsForm 4 MathematicsThe gradient of a curve at point (x,y) is 4x – 3. the curve has a minimum value of – 1/8 (a) Find (i) The value of x at the minimum point ( 1 mark) (ii) The equation of the curve ( 4 marks) (b) P is a point on the curve in part (a) (ii) above. If the gradient of the curve at P is 7, find the coordinates of P ( 3 marks) Form 4 MathematicsThe table below gives some of the values of x for the function y = ½ x ^{2} + 2x + 1 in the interval 0≤ x ≤ 6. (a) Use the values in the table to draw the graph of the function ( 2 marks) (b) (i) Using the graph and the mid – ordinate rule with six (6) strips, estimate the area bounded by the curve, the x axis, the y axis and the line = 6 (ii) If the exact area of the region described in (b) (i) above is 78cm^{2}, calculate the percentage error made when the mid – ordinate rule is used. Give the answer correct to two decimal places ( 2 marks) Form 2 MathematicsThe distance between towns M and N is 280 km. A car and a lorry travel from M to N. The average speed of the lorry is 20 km/h less than that of the car. The lorry takes 1 h 10 min more than the car to travel from M and N. (a) If the speed of the lorry is x km/h, find x ( 5 marks) Form 4 Mathematics
The acceleration, a ms^{2}, of a particle is given by a =25 – 9t^{2}, where t in seconds after the particle passes fixed point O.If the particle passes O, with velocity of 4 ms^{1}, find:
(a) An expression of velocity V, in terms of t ( 2 marks)
(b) The velocity of the particle when t = 2 seconds ( 2 marks) Form 3 MathematicsA bank either pays simple interest as 5% p.a or compound interest 5% p.a on deposits. Nekesa deposited Kshs P in the bank for two years on simple interest terms. If she had deposited the same amount for two years on compound interest terms, she would have earned Kshs 210 more. Calculate without using Mathematics Tables, the values of P ( 4 marks) Form 2 MathematicsForm 3 MathematicsPoint T is the midpoint of a straight line AB. Given the position vectors of A and T are ij + k and 2i+ 1 ½ k respectively, find the position vector of B in terms of i, j \ and k. ( 3 marks) Form 2 MathematicsA cylindrical piece of wood of radius 4.2 cm and length 150 cm is cut length into two equal pieces. Calculate the surface area of one piece (Take ∏ as ^{22}/_{7} (4mks) Form 2 MathematicsForm 3 Mathematics
Make P the subject of the formula P^{2} = (P – q) (Pr) ( 3 marks)
In this question Mathematical Tables should not be used
The base and perpendicular height of a triangle measured to the nearest centimetres are 6 cm and 4 cm respectively. Find (a) The absolute error in calculating the area of the triangle (b) The percentage error in the area, giving the answer to 1 decimal place (2mks) Form 3 Mathematics
Two teachers are chosen randomly from a staff consisting 3 women and 2 men to attend a HIV/AIDs seminar. Calculate the probability that the two teachers chosen are:
(a) Of the same sex
(b) Of opposite sex Form 2 Mathematics
Given that sin (90 – x)^{0} = 0.8, where x is an acute angle, find without using mathematical tables the value of tan x^{0}.
Form 3 MathematicsA point R divides a line PQ internally in the ration 3:4. Another point S, divides the line PR externally in the ration 5:2. Given that PQ = 8cm, calculate the length of RS, correct to 2 decimal places. 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 2 MathematicsThe area of a rhombus is 60cm^{2}. Given that one of its diagonals is 15 cm long, calculate the perimeter of the rhombus Form 1 Mathematics 
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