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Form 4 Mathematics Paper 1 Exam Revision Questions With Answers

The diagram represents a solid hemispherical dome of diameter 42cm. The dome is painted on all faces at a cost of sh 500 per square metre and has a mass of 48.5kg.

Calculate:
a) The total surface area of the dome.
b) The cost of painting the dome.
c) The volume of the material making the dome.
d) The density of the material in kg/m3.

(4m 55s)

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1. Without using logarithms or a calculator evaluate: #sqrt((0.8064 ×6.048)/(1.008×0.1344))#
2. Without using mathematical tables evaluate: #(sin60°·tan30°·cos 60° + sin30°·cos45°·sin 45°)/(sin90°·cos45°·sin45°- sin60°· cos30°· sin30°)#

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72. The diagram represents a solid frustum with base radius 21 cm and top radius 14 cm. The frustrum is 15 cm high and is made of a metal whose density is 2 g/#cm^3#. a) Calculate i. the volume of metal in the frustrum ii. the mass of the frustrum in kg. b) The frustrum is melted down and recast into a solid cube. In the process 20% of the metal is lost.
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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.
75. Simplify# ((4x+2y)^2-(2y-4x)^2)/((2x+y)^2-(y-2x)^2 )#
76. The figure shows an equilateral triangle ABC in which all the dimensions are given in centimetres. Determine the value of x and hence calculate the area of the triangle
77. A solid metal sphere of radius 7.5 cm is melted down and recast into a solid cylinder of height 15 cm. In the process 4% of the metal is lost. Calculate a) in terms of p the volume of metal used to make the cylinder. b) the radius of the cylinder.
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))#
80. The distance between two towns P and Q is 480 km. At 10.28 a.m a bus left town P and travelled towards town Q at an average speed of s km/h. A car left town Q at the same time and travelled towards town P along the same road. The two vehicles met at 1.40 p.m. Given that on average the car travelled 30 km/h faster than the bus, determine the value of s and hence state the speed of the car.
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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90. In order to start a business, three businesswomen, Amina, Balinda and Chini contributed sh 25 000, sh 35 000 and sh 45 000 respectively as business capital. They also had to pay sh 15 000 more as rental fee for business premises. The rental fee was shared equally among the partners. The three partners agreed to put 25% of the annual profits back in the business and share the rest in the ratio
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