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)
Answer
Form 3 Mathematics(a) (i) Complete the table below for the function y = x3 + x2 – 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)
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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 x0 with the north. (a) Given that cos x0 = 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 1350, calculate the bearing of possible course on which it can be set ( 4 marks)
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Form 4 MathematicsThe data below shows the masses in grams of 50 potatoes 
(a) On the grid provide, draw a cumulative frequency curve for the data (4mks) (b) Use the graph in (a) above to determine (i) The 60th percentile mass (ii) The percentage of potatoes whose masses lie in the range 53 g to 68g (3mks)
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Form 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)
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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 78cm2, calculate the percentage error made when the mid – ordinate rule is used. Give the answer correct to two decimal places ( 2 marks)
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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)
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Form 4 Mathematics
The acceleration, a ms-2, of a particle is given by a =25 – 9t2, 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)
Answer
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)
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Form 2 Mathematics
The figure below shows a quadrilateral ABCD in which AB = 8 cm, DC = 12 cm, ∠BAD = 450, ∠CBD = 900 and ∠BCD = 300.
Find: (a) the length of BD ( 1 mark) (b) The size of the angle ADB (2 marks)
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Form 3 MathematicsPoint T is the midpoint of a straight line AB. Given the position vectors of A and T are i-j + k and 2i+ 1 ½ k respectively, find the position vector of B in terms of i, j \ and k. ( 3 marks)
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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)
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Form 2 MathematicsOn the diagram below, the line whose equation is 7y – 3x + 30 = 0 passes though the points A and B. Point A on the x- axis while point B is equidistant from x- and y – axes. 
Calculate the co-ordinates of the points A and B (3mks)
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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
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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 x0.
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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.
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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.
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Form 2 MathematicsThe area of a rhombus is 60cm2. Given that one of its diagonals is 15 cm long, calculate the perimeter of the rhombus
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Form 1 MathematicsExpress the numbers 1470 and 7056, each as a product of its prime factors Hence evaluate 
Leaving the answer in prime form
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