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KCSE Mathematics Paper 1 Revision Exercise Set 5
Simplify
#((3x+y)^2-(y-3x)^2)/((x+y)^2-(y-x)^2)#
(6m 9s)
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1.
A trader sold an article at 15% discount to a customer who paid sh 510 for it. What was the marked price of the article.
2.
Simplify #((3x+y)^2-(y-3x)^2)/((x+y)^2-(y-x)^2)#
3.
The figure below shows a rectangle PQRS in which all the dimensions are given in centimeters. Find the value of x and hence calculate the area of the rectangle.
4.
Solve for x in the equation #2^(3x - 2) times 8^(x) = 4^(x + 1)#
5.
a) Given that the position vectors of points P, Q and R are p, q and r respectively and that R is the midpoint of PQ, write down a vector equation that relates p, q and r. b) If p =# ((5),(-8))#and q =# ((7),(4))# , find r and hence state the coordinates of point R.
6.
A lorry which consumes 1 litre of diesel for every 9 km uses 108 litres of diesel for a journey. Find how many litres of diesel a trailer which consumes 1 litre of diesel for every 6 km uses for the same journey.
7.
The distance between towns T and S is 418 km. At 9.45 a.m a truck left town T and travelled towards town S. At the same time a car left town S and travelled towards town T along the same road. Given that the car travels 30 km/h faster than the truck and that the two vehicles meet at 1.33 p.m, find the speed of each vehicle
8.
A coil which is made by winding 500 metres of copper wire of cross-sectional diameter 1.26 mm has the same mass as another coil of copper wire whose cross-sectional diameter is 1.4 mm. Find the length of wire in the second coil.
9.
The sum of the interior angles of an n-sided polygon is 1 440°. Find the value of n and hence deduce the name of the polygon.
10.
The wheel of a bicycle has a diameter of 70 cm and makes 2 revolutions per second. Calculate to one decimal place the speed of the bicycle in km/h.
11.
The straight line whose double intercept equation is #x/a + y/b# = 1 Passes through the points P(-4 ,9) and Q(4, -3). Write down the equation of the line in the form y = mx +c and hence determine the value of a and b.
12.
From the quadratic equation whose root are x = #-5/3# and x = 1
13.
Solve the inequality 4 - #3/2x = 5/3x - 2 3/1#
14.
Two pipes P and Q each running alone can fill a trough in 6 hours and 10 hours respectively. A drainage pipe R can empty the full trough in 15 hours. Pipes P and Q are turned on and left running for 121 hours. The drainage pipe R is then opened and all three-left running. Find how much longer it takes to fill the trough.
15.
The figure shows a water tank which consists of a hemispherical part surmounted on top of a cylindrical part. The two part have the same diameter of 2.1 m and the cylindrical part is 1.5 m high as shown. All the surfaces of tank are made of iron sheet. a) Allowing for a 15% wastage on overlapping, calculate to two decimal place the area of iron sheet required. b) Iron sheet cost sh 400 per square
16.
The table below shows the marks stored by form two students in a mathematics test. a) Complete the table b) State the modal class c) Use the completed table to calculate the mean mark for the students.
17.
A spire stand directly across the street from a building. The angle of depression of the top of the building from the top of the spire is #25.8^0# and the angle of elevation of the top of the spire from the foot of the building is #43.5^0#. given that the distance between the spire and the building is 40 metres, calculate to two decimal places: a)The height of the spire. b)The difference in height
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