1.
Evaluate
without using mathematical tables
(3mks)
2.
Use
reciprocal tables to evaluate f if; (3
mks)
3.
In
the figure below, AB is parallel to DE,
DE bisects angle BDG, angle DCF = 600 and angle CFG = 1100
Find
(a)
< CDF
(2mks)
(b)
<
ABD
(2mks)
Give reasons
for your answers
4. 
The
figure below shows an octagon obtained by cutting off four congruent triangles
from rectangle measuring 19.5 by 16.5 cm
The
figure below shows an octagon obtained by cutting off four congruent triangles
from rectangle measuring 19.5 by 16.5 cm
5. The
size of each interior angle of a polygon is x0 and each exterior
angle is
calculating the number of sides of the polygon. (3 mks)
calculating the number of sides of the polygon. (3 mks)
6. Calculate the density of the material used to make a concrete culvert of
mass 1million grams, internal diameter 0.72m, thickness 70mm and length
(giving your answer in kg/m3 and in standard form) (3 marks)
(giving your answer in kg/m3 and in standard form) (3 marks)
7.
Evaluate the following:
(3
mks)
8.
The marked price of an article is Ksh 1020. A
shopkeeper sold the article to his customer after allowing him a 10% discount
on the marked price. If the shopkeeper still made a profit of 20%. Determine how
much he had paid for it? (3
mks)
9.
From a window 25m above a street, the angle of
elevation of the top of a wall on the opposite side is 150. If the
angle of depression of the base of the wall from the window is 350.
Find;
(i)
The
width of the street. (1
mk)
(ii)The
height of the wall on the opposite side. (2
mks)
10.
The
figure below shows a net of a prism whose cross – section is an equilateral
triangle.
Sketch the prism
(3mks)
State the number of
planes of symmetry of the prism. (1mks)
11. In
fourteen years time, a mother will be twice as old as her son. Four years ago,
the sum of their ages was 30 years. Find how old the mother was, when the son
was born.
( 4 marks)
12 Line AB given below is one side of triangle
ABC. Using a ruler and a pair of
compasses only;
Complete the triangle ABC such that
BC=5cm and ÐABC=450
On
the same diagram construct a circle touching sides AC,BA produced and BC
13 A part B is on a bearing of 0800
from a port A and at a distance of 95 km. A submarine is stationed at a port D,
which is on a bearing of 2000 from A and a distance of 124 km from
B.
A ship leaves B and moves directly
southwards to an island P, which is on a bearing of 140 from A. The submarine
at D on realizing that the ship was heading from the island P, decides to head
straight for the island to intercept the ship
Using a scale 0f 1 cm to represent
10 km, make a scale drawing showing
the relative positions of A, B, D, P. (
2 marks)
Hence find
(i) The distance from A to D ( 2 marks)
(ii) The bearing of the submarine from the ship was setting
off from B
( 1 mark)
(iii) The bearing of the island P from D ( 1 mark)
(iv) The distance the submarine had to cover to reach the
island P
( 2 marks)
14 The
angle of elevation
to the top
of a tower
a from a point
P is 300 .The angle
of elevation to the
top of the
tower from another
point Q which
is nearer to
the foot ( base ) R of
the tower is 450.The distance
between P and Q is
20 metres and
the points P,Qand R
are on the
same level ground.
a)Using a
scale of 1cm
to represent 5cm,
draw an accurate drawing
to represent the
bove information
(4 marks
)
b) Using your scale drawing determine,
i) The height of the tower
(2 marks)
ii) The distance QR
(2 mark)
iii) The distance PR
(2 marks)
15 Four
buildings A, B, C and D stand on a level ground such that B is 240m on a
bearing of 600 from A. C is south east of B and east of A. D is 320m
from C on a bearing of 1500 from A.
a)
i)
Use scales of 1 cm rep 40m draw accurately the points ABCD. (3 marks)
ii) Use the
drawing to find the direction of B and D. (1
mark)
b)
The
height of building A is 200m and that of B is 80m. Determine the angle of
depression of the top of building B from the top of building A. (3 marks)
c)
Enter
the layout of Kamau’s plot shown below in a surveyor’s book. (Unit in metres) (3
marks)
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