# KCSE Mathematics Paper 1 Revision Exercise Set 5

KCSE Mathematics Paper 1 Revision Exercise Set 5

Lessons (**17**) * SHARE*

- 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.

2m 9s - 2.
Simplify
#((3x+y)^2-(y-3x)^2)/((x+y)^2-(y-x)^2)#

6m 9s - 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.

2m 39s - 4.
Solve for x in the equation
#2^(3x - 2) times 8^(x) = 4^(x + 1)#

2m 15s - 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.

6m 19s - 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.

1m 47s - 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

5m 29s - 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.

7m 25s - 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.

1m 59s - 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.

5m 22s - 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.

6m 55s - 12.
From the quadratic equation whose root are
x = #-5/3# and x = 1

2m 29s - 13.
Solve the inequality
4 - #3/2x = 5/3x - 2 3/1#

4m 9s - 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.

5m 34s - 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

11m 12s - 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.

5m 18s - 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

9m 53s

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