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Form 4 Mathematics Paper 1 Exam Revision Questions With Answers

The figure below shows a circle centre O and radius R cm. The minor arc AB subtends an angle of 105˚ at the centre of the circle and the corresponding sector AOB has an area of # 528cm^2#. (Take π=22/7)

a) Find the radius R of the circle.
b) The sector is removed and folded into a cone, calculate:
i. the area of the cone so formed.
ii. to 2 decimal places the height of the cone.
iii. to the nearest whole number, the volume of the cone.

(6m 6s)

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2. Without using mathematical tables evaluate: #(sin60°·tan30°·cos 60° + sin30°·cos45°·sin 45°)/(sin90°·cos45°·sin45°- sin60°· cos30°· sin30°)#

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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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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#
86. Omondi working alone takes 10 days, Simiyu 15 days and Muiruri 12 days to complete digging a shamba. Omondi and Simiyu started working together and after 3 days Muiruri joined them. Determine how many more days it took the three men to complete digging the shamba.
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