Form 2 Mathematics
In the figure below, PQ is parallel to RS. The lines PS and RQ intersect at T. RQ = 10 cm, RT:TQ = 3:2, angle PQT = 40° and angle RTS  80°.
(a) Find the length of RT.
(b) Determine, correct to 2 significant figures: (i) the perpendicular distance between PQ and RS; (ii) the length of TS. (c) Using the cosine rule, find the length of RS correct to 2 significant figures. (d) Calculate, correct to one decimal place, the area of triangle RST. Form 1 Mathematics
Three pegs R, S and T are on the vertices of a triangular plain field. R is 300 m from S on a bearing of 300° and T is 450 m directly south of R.
(a) Using a scale of 1 cm to represent 60 m, draw a diagram to show the positions of the pegs. (b) Use the scale drawing to determine: (i) the distance between T and S in metres: (ii) the bearing of T from S. (c) Find the area of the field, in hectares, correct to one decimal place. Form 4 Mathematics
The equation of a curve is y = 2x^{3} + 3x^{2}.
(a) Find: (i) the x  intercept of the curve; (ii) the y  intercept of the curve. (b) (i) Determine the stationery points of the curve. (ii) For each point in (b) (i) above, determine whether it is a maximum or a minimum. (c) Sketch the curve. Form 2 Mathematics
The vertices of quadrilateral OPQR are O (0,0), P(2,0), Q(4,2) and R(0,3).
The vertices of its image under a rotation are O'(l, 1), P'(l, 3), Q'(3, 5) and R'(4, 1). (a) (i) On the grid provided, draw OPQR and its image O'P'Q'R'. (ii) By construction, determine the centre and angle of rotation. (b) On the same grid as (a) (i) above, draw O"P"Q"R", the image of O'P'Q'R' under a reflection in the line y = x. (i) directly congruent; (ii) oppositely congruent. Form 3 MathematicsForm 1 Mathematics
Two alloys, A and B, are each made up of copper, zinc and tin. In alloy A, the ratio of copper to zinc is 3:2 and the ratio of zinc to tin is 3:5.
(a) Determine the ratio, copper: zinc: tin, in alloy A. (b) The mass of alloy A is 250 kg. Alloy B has the same mass as alloy A but the amount of copper is 30% less than that of alloy A. Calculate: (i) the mass of tin in alloy A; (ii) the total mass of zinc and tin in alloy B. (c) Given that the ratio of zinc to tin in alloy B is 3:8, determine the amount of tin in alloy B than in alloy A. Form 2 Mathematics
The figure below represents a solid cuboid ABCDEFGH with a rectangular base, AC= 13cm, BC = 5 cm and CH = 15cm.
(a) Determine the length of AB,
(b) Calculate the surface area of the cuboid. (c) Given that the density of the material used to make the cuboid is 7.6 g/cm3, calculate its mass in kilograms. (d) Determine the number of such cuboids that can fit exactly in a container measuring 1.5 m by 1.2 m by 1 m. Form 2 MathematicsForm 1 Mathematics
Bukra had two bags A and B, containing sugar. If he removed 2 kg of sugar from bag A and added it to bag B, the mass of sugar in bag B would be four times the
mass of the sugar in bag A. If he added 10 kg of sugar to the original amount of sugar in each bag, the mass of sugar in bag B would be twice the mass of the sugar in bag A. Calculate the original mass of sugar in each bag. Form 2 MathematicsForm 1 Mathematics
A Forex Bureau in Kenya buys and sells foreign currencies as shown below:
Buying Selling Currency (Ksh) (Ksh) Chinese Yuan 12.34 12.38 South African Rand 11.28 11.37 A businesswoman from China converted 195 250 Chinese Yuan into Kenya shillings. (a) Calculate the amount of money, in Kenya shillings, that she received. (b) While in Kenya, the businesswoman spent Ksh 1 258 000 and then converted the balance into South African Rand. Calculate the amount of money, to the nearest Rand, that she received. Form 2 Mathematics
A line L passes through point (3,1) and is perpendicular to the line 2y = 4x + 5.
Determine the equation of line L. Form 3 Mathematics
Without using mathematical tables or a calculator, solve the equation,
2log_{10}x – 3log_{10}2 + log_{10}32 = 2 
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