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Form 4 Mathematics Paper 1 Exam Revision Questions With Answers

The diagram shows a cylindrical tank surmounted with a hemispherical dome. The cylindrical part has the same diameter as the hemispherical part. The cylindrical part is 1.5 m high and has a diameter of 2.8 m.

a) Calculate to 2 decimal places
i. the area of the hemispherical part.
ii. the curved surface area of the cylindrical part
iii. the total surface area of the tank
b) Find the cost of painting the tank at the rate of sh 150 per square metre.
c) Calculate the capacity of the tank in litres.

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74. The figure shows a rectangular metal sheet ABCD in which AB = 90 cm and BC = 70 cm. The sheet is 1.8 mm thick and is made of metal whose density is 2.5 g/#cm^3#. A square of side t cm is removed from each corner as shown and the remaining part folded along the dotted line to form an open cuboid. a) Given that the area of the unshaded part is #A cm^2#, write down an equation for A in terms of t.
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78. A truck which consumes diesel at the rate of 1 litre for every 5 km uses 72 litres of diesel for a certain journey. A bus uses 45 litres of diesel for the same journey. Find the distance the bus covers for every litre of diesel.
79. Solve for y in the equation #8^((2y-1))×32^y=16^((y+1))#
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81. The sum of the interior angles of an n-sided polygon is 1080°. Find the value of n and hence deduce the name of the polygon.
82. The wheel of a bicycle is rotating at the rate of 130 revolutions per minute. If the speed of the bicycle is 18.4 km/h, calculate to the nearest whole number, the diameter of the wheel in centimetres. (Take p = 3.142).
83. A straight line passes through the points P (5 , 3) and Q(0 , 6). Find equation of the line in the form y = mx + c and hence find its double intercept equation.
84. Form the quadratic equation whose roots are #y= 3/5 and y= -1#
85. Find the values of x which make the following inequality true. #9-3/4 x<2/3 x+4 3/4#
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