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Form 4 Mathematics Paper 1 Exam Revision Questions With Answers

The model of a closed cylindrical tank is made in such a way that it is similar in shape to the actual tank to be constructed. The capacity of the model is #770cm^3# while that of the proposed tank is #49.28m^3#.
Find:
a) The volume scale factor.
b) The linear scale factor and hence calculate the height of the tank in metres given that the height of the model is 5cm.
c) The area scale factor and hence calculate the total surface area of the tank in square metres given that the total surface area of the model is #528cm^2#.
d) The cost of cementing all the inside surfaces of the tank at the rate of sh. 500 per square metre.

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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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64. Simplify the following expression by reducing it to a single fraction #(2x-5)/4-(1-x)/3-(x-4)/2#
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68. You are given the points P (-3 , -2), Q(-6 , 3) and R(-12 , 13). a) Express PQ and QR as column vectors. b) Use the result in (a) above to explain why the points P, Q and R are collinear.
69. An open cylindrical water reservoir of radius 10.5 metres has a curved surface area of #198 m^2#. The reservoir is to be cemented on all its inside surfaces at a cost of sh 400 per square metre. a) Taking p=22/7, determine (i) the height of the reservoir. (ii) the cost of cementing the reservoir.
70. The above diagram represents a trough which is 6 metres long and whose cross-section is a semicircle of diameter 1.4 metres. a) Calculate i. the cross-sectional area of the trough in #cm^2#. ii. the capacity of the trough in litres b) The trough which is initially empty is filled by a diesel pump which pumps water at the rate of 1.54 litres per second.
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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.
73. After allowing his customer a 5% discount on the marked price a sales agent sold a second hand bus at sh 1 140 000. The owner of the bus received sh 1 003 200 from the sales agent after the latter had deducted his commission. a) Determine the marked price of the bus. b) Calculate the percentage commission the agent received c) By selling the bus this way the owner incurred a loss of 25%.
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#
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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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
91. Without using logarithms or a calculator, evaluate # root(3)((4.536×0.8064×v20.25)/(0.2268×1.134))#
92. Factorise #5x^2 -9x + 4#
93. A South African businessman exchanged 6 000 Rands and received Ksh 56 160 after the bank deducted its commission. Given that the exchange rate was 1 SA Rand = Ksh 9.75, calculate the percentage commission the bank charged him.
94. The base radius of a cone is decreased by 10% while its height is increased by 40%. Find the percentage change in its volume and state whether it is an increase or a decrease.
95. A school used 25% of the money raised in a harambee for renovating classrooms. 35% for building a new laboratory, three-fifths of the remainder for buying laboratory equipment and the rest for installing electricity. If the school bought laboratory equipment worth sh 360 000, calculate the total amount raised at the harambee and hence determine the amount spent for installing electricity.
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97. A rectangular water cistern measuring 2.5 m long, 1.8 m wide and 1.2 m high is initially half full of water. Water is pumped into the cistern at the rate of 1.25 litres per second. Calculate the time in minutes it takes to fill the cistern.
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100. In a meeting there are 200 more women than men. One-third of the men and two-fifths of the women are elderly people. If there are 300 elderly people in the meeting. find how many young people attended the meeting.