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Form 4 Mathematics Paper 1 Exam Revision Questions With Answers

A triangle whose base is 6 cm longer than its height has an area of $80 cm^2$ .
a) Taking h as the height of the triangle, write down a simplified quadratic equation for the area of the triangle.
b) Hence determine the dimensions of the triangle.

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52. Given the ratio a:b= 3:4, find the ratio (6a-b) :(3a+3b)
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54. Given that tan x° = ¾ , write down in fraction form the values of sin x and cos x.
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56. A triangle whose base is 6 cm longer than its height has an area of $80 cm^2$ . a) Taking h as the height of the triangle, write down a simplified quadratic equation for the area of the triangle. b) Hence determine the dimensions of the triangle.
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59. It takes 20 men 10 days to lay 300 metres of pipes. Find how many days it would take 15 men to lay 270 metres of pipes.
60. A retailer usually makes a profit of 50% by selling an article at sh 540. If he reduces the price of the article by sh 54, calculate the percentage profit he will now make.
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63. Factorise completely $(a - 2b) (2a + b) - (a-2b)^2$
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.
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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.
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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 $y= 3/5 and y= -1$
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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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