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KCSE Mathematics Paper 1 Revision Exercise Set 1
Given that a=2, b=-1 and c=3, find the value of
3
a
2
-
2
b
2
c
+
4
b
2
a
c
+
2
b
3
-
3
c
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1.
Without using mathematical tables evaluate.
27.72
×
0.3876
2.09
×
0.4284
2.
(a) Expand the expression (x+4)(2x-3) (b) Without using long multiplication, use the above expansion with an appropriate substitution for x to find the value of
19
×
27
3.
A business woman bought 288 bananas at sh 10 for every 12. She sold all of them at sh 20 for every 18. What was her percentage profit.
4.
Without using logarithm tables find the value of
log
10
96
+
3
log
10
5
-
log
10
12
5.
Given that a=2, b=-1 and c=3, find the value of
3
a
2
-
2
b
2
c
+
4
b
2
a
c
+
2
b
3
-
3
c
6.
Solve the simultaneous equations 3x-2y=7 5x+y=3
7.
In the figure ABCD is a rhombus whose diagonals AC and BD meet at X. given that AC=27.6cm and BD=16.2cm. Calculate the area of the rhombus.
8.
A farmer has twice as many goats as cows and two-thirds as many pigs as goats. (a) If he has x cows, write down a simplified expression in x for the total number of animals. (b) Find the total number of animals given that the farmer has 20 pigs.
9.
Find the size of each exterior angle of a regular octagon.
10.
Given the following currency exchange rate,calculate to 3 significant figures the number of dollars that can be exchanged for 25 sterling pounds. 1 US dollar =ksh 76.85 1 sterling pound = Ksh115.30
11.
The figure alongside shows a vertical pole QR of height 2 metres 85 centimetres standing on a horizontal ground. When the sun is at an elevation of
θ
0
, the pole casts a shadow PQ 5 metres 6.5 centimetres long. Find the value
θ
in degrees and minutes.
12.
The diagram alongside represents a circular flower bed surrounded by a path of uniform width. Given that R=14m and r=12.6m, calculate to the nearest whole number the area of the path. (Take
π
=
22
7
)
13.
(a) Find the range of the values of x which satisfies the following inequalities simultaneously.
4
x
–
6
≥
x
–
12
8
–
3
x
>
2
x
–
7
(b) Represent this range of values of x on a number line.
14.
The figure below shows the map of an estate drawn on a grid of 1cm squares. (a) Estimate the area of the map in square centimeters. (b) If the scale of the map is 1:50 000, calculate the actual area of the estate in hectares.
15.
The average height of 40 students in a class is 155cm. Recently, five students whose average height is 148cm, left the class. What is the new average height of the students in the class?
16.
A cylindrical tank whose diameter is 1.4 metres and height 80cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (Take
π
=
22
7
).
17.
The diagram below shows the cross-section of a structure used as part of building construction design. All dimensions are given in metres and the structure is 6 metres long. (a) Calculate (i) The cross-sectional area of the structure. (ii) The volume of the material used to fill the structure. (b) The material used to fill the structure is concrete made by mixing gravel, sand and cement in the
18.
In the figure below, ABCD is a parallelogram in which BC is produced to X such that BC=CX. Y is the mid-point of DC and AYX is a straight line. (a) Given that AB=a and BC=b, express the following vectors in terms of a and b. (i) CX (ii) AC (iii) AX (iv) DX (b) Use vectors to prove that ACXD is a parallelogram.
19.
Forty students in a form two class were weighed and their masses recorded to the nearest kilogram as shown below. 45 48 56 39 47 36 45 49 50 46 37 46 33 43 51 42 47 39 42 48 47 40 46 41 45 43 46 50 38 45 54 42 51 39 42 45 44 35 52 46 (a) Using class intervals of 5kg tabulate this data in a frequency table. (b) Find the modal class. (c) Modify the table and use it to calculate them mean mass of the
20.
The figure below shows a circle centre O and radius 21cm. The minor arc ABC substends an angle of
120
0
at the centre of the circle. (Take
π
=
22
7
). (a) Find the area of the minor sector OABC. (b) The sector is cut off and folded to form a hollow cone. Find the base radius of the cone. (c) Calculate to one decimal place the vertical height of the cone. (d) Calculate to the nearest whole
21.
The diagram below represents a right cone of base radius 28cm from which a small cone is cut off to form a frustum. The top radius of the frustum is 21cm and its height is 10cm as shown. Calculate to the nearest whole number the total surface area of the frustum
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