Download mathematics paper 1 molo

NAME:……………………………………………………………………………INDEX……...……
CANDIDATE’S SIGNATURE: …………………………………….
DATE: …………………………………….
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MATHEMATICS
PAPER 1
JULY / AUGUST 2008
2 ½ HOURS
MOLO DISTRICT MOCK EXAMINATION
Kenya Certificate of Secondary Education (K.C.S.E) 2008
121 / 1
MATHEMATICS
PAPER 1
JULY / AUGUST 2008
INSTRUCTIONS TO CANDIDATES
1.
2.
3.
4.
5.
6.
Write your name and index number in the spaces provided at the top of this page.
The paper consists of two sections: Section I and Section II.
Answer all questions in section I and any five questions from Section II.
All answers and working must be written on the question paper in the space provided
below each question
Show all the steps in your calculation, giving your answers at each stage in the spaces
below each question.
Non- programmable silent electronic calculators and KNEC Mathematical tables may be
used, except where stated otherwise.
For Examiner’s Use Only
1
SECTION I
2
3
4
SECTION II
17
18 19
20
5
21
6
7
22
23
8
24
9
Total
10
11
12
13
14
15
16
Total
Grand
Total
This paper consists of18 printed pages. Candidates should check the question paper to ensure that all the pages are printed as indicated and no
questions are missing.
© MOLO DISTRICT MOCK EXAMINATION 2008
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2
SECTION I (50 MARKS)
Answer all the questions in this section.
1. Without using Mathematics tables or calculator, evaluate the following leaving your answer as a
0119  0 .256
fraction in its simplest form. 3
(3mks)
0.068 7
2. The H.C.F of two numbers is 12 and their LCM is 180. If one of the two numbers is 36, find the
other number.
(3mks)
3. Two boys and a girl shared some money. The younger boy got 5 of it, the elder boy got 7 of
18
12
the remainder and the girl got the rest. Find the percentage share of the younger boy to the girl’s
share.
(4mks)
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3
4. In the figure below ED and EA are tangents to the circle at D and A. DC is parallel to AB and
BDC  510 .Calculate the value of x
(3mks)
5. From a point P the angle of elevation of the top of a grass thatched house is 150. From another point
Q which is 15m from the base of the house, the angle of elevation of the top of the house is 21.50.
Giving your answer to two decimal places, determine the height of the house from the apex and
hence calculate the distance between P and Q. IP and Q are on the same side of the house and lies
on a straight line with the base of the house.
(3mks)
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4
6. A bank in Kenya buys and sells foreign currencies as follows.
Currency
Buying (Ksh)
Selling (Ksh)
1 sterling pound
132.40
132.75
1 US dollar
70.40
70.84
A tourist arrived in Kenya with US $ 3500. He converted all the dollars to Kenya shillings at the bank.
While in Kenya, he spent Kshs. 115,000 and then converted the remaining amount in Kenya shillings
to sterling pounds. Calculate the amount he received in sterling pounds.
(3mks)
7. Solve for P
2
1
 1
 1  3
2

3
p
 2
4
 
9
(3mks)
8. Find the equation of a line L1 passing through (3,-2) and is perpendicular to another line L2 which
makes an angle of 450with the x-axis.. Give your answer in the form of y  mx  c.
(3mks)
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5
9. Under a certain rotation, triangle XYZ is mapped onto triangle X 1Y 1Z 1 as shown on the figure
below. Describe the rotation fully.
(3mks)
Graph picture
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6
2 2
x  11
3
10.
If x is a positive integer, Find all possible values of x given that 2 
11.
If A is 20km in the direction 0300 from O and B is 25 km in the direction 1200 from O.
a. Using an appropriate scale, draw the diagram showing the position of O, A and B.
(1mk)
(3mks)
b. Using the diagram in (a) above, find.
i. the bearing of B from A
(1mk)
ii. the distance of A from B
© MOLO DISTRICT MOCK EXAMINATION 2008
(1mk)
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7
12.
Draw the net of the solid shown below.
13.
In Sokomoko factory, apiece of work can be completed by 45 workers in 10 days. They
worked for 4 days after which 15 workers were laid off. How many days would it take the
remaining workers to complete the work?
(3mks)
14.
The number of sides of two regular polygons are in the ratio 3:4. The sums of the
interior angles of the two polygons are in the ratio 3:4. The sum of the interior angles of the
two polygons are in the ratio 2:3. Calculate the number of sides of the two polygons. (3mks)
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(2mks)
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8
15.
The table below shows marks obtained in a math’s test by a form IV class.
Marks(X)
8  9 9  11 11    13 13  16 16  20
No of
2
6
8
3
2
students Y
Use the table to represent the information on a histogram
20  21
1
(3mks)
GRID
16.
One kilogram of molten metal A of density 2.5 g/cm3 is mixed with three kilogrammes
of another molten metal B of density 5 g/cm3. Calculate the mass of 1cm3 of the mixture.
(4mks)
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9
SECTION II (50 MARKS)
Answer any five Questions in the section
17.
A slaughter house bought a number of sheep at Sh. 1,200 each and a number of oxen
at sh.15,000 each. They paid a total amount of Sh 135,000. If they had bought twice as
many sheep and three oxen less, they would have saved sh 15,000.
a. Find the number of the each type of animals they bought.
(6mks)
b. The slaughter house sold all the animals at a profit of 30% per sheep and 35% per
oxen. Determine the total profit they made.
(4mks)
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10
18.
(a) Draw the Quadrilateral P(1,0), Q(4,0), R(4,2) and S(1,2) and its image P1Q1R1S 1
1 0

under a transformation whose matrix is 
(2mks)
 0 2
grid
(b) Describe the transformations represented by the matrix in (a)
© MOLO DISTRICT MOCK EXAMINATION 2008
(2mks)
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11
1 0
 and label
(c) Find the image of P1Q1R1S1 under the transformation whose matrix is 
 0 1
the image of the figure as P11Q11R11S11. Draw P11Q11R11S11 on the same diagram as (a)
above
(3mks)
(d) Determine the matrix of the single transformation which maps P11Q11R11S11 onto PQRS .
(3mks)
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12
19.
A solid polyhedron shown below is made up of a pyramid with Isosceles triangles and
a cuboid.
a. Calculate the total surface area of the figure above
(4mks)
b. The whole polyhedron is completely immersed in water contained in a cylindrical drum
of base radius 3.5 cm. Find the height of the water displaced upwards in the drum
(6mks)
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13
20.
(a) Construct triangle PQR in which PQ= 12.5 cm,  QPR= 450,  PQR=600.
Construct also the perpendicular bisector of PQ and perpendicular to QR at R, producing
these lines to meet at S.
(6mks)
(b) Draw a circle passing through points Q, R, S and M, where M is the mid point of PQ.
State the radius of the circle drawn.
(4mks)
(Use a ruler and pair of compasses only)
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14
21.
In the figure below, A and B are centres of two intersecting circles of radii 8cm each.
PQ is a chord common to both circles and is 11.2cm.
a) find the perimeter of the figure
b) find the area of the shaded region
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(4mks)
(6mks)
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15
22.
A particle undergoes an acceleration of -4m/s2 from 50m/s for 8 seconds. It continues
at the constant velocity for 6 seconds. It comes to a retardation after a further 10
seconds.
a. Find the velocity after the first 8 seconds
(2mks)
b. Draw the velocity time graph of the motion
(3mks)
grid
c. What is the deceleration in the last 10 seconds?
(3mks)
d. Calculate the distance traveled or covered by the particle.
(3mks)
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16
23.
x
-2x2
3x
5
y
(a) Fill the table for Y  5  3x  2 x 2 for  2    3.5
-2
-1.5
-1
-0.5
0
0.5
1
-8
-4.5
-2
-0.5
0
-0.5
-2
-6
-3
0
3
5
5
5
5
5
5
5
-9
0
5
6
1.5
4.5
5
5
2
-8
6
5
3
2.5
-12.5
7.5
5
0
3
3.5
25
9
5
5
-10
(2mks)
(3mks)
(b) Draw the graph of y  5  3x  2 x 2 of table in a) above
Grid
(c) Use you graph in b) above to:
(i) Determine the range of values which satisfy the inequality 5  3x  2 x 2  2
(2mks)
(ii) Solve the equation 2 x 2  2 x  3  0
© MOLO DISTRICT MOCK EXAMINATION 2008
(3mks)
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17
24.
The table below shows some values of the function.
Y  8  2 x  x 2 for  4    2
x -4
-3.5 -3 -2.5 -2 -1.5 -1 -0.5
y 0
8
a)
complete the table above
b)
0
8
0.5
1
1.5
2.75
2
(2mks)
Using the completed table and the mid ordinate rule with six ordinates estimate the area
of the region bounded by the curve y  8  2 x  x 2 and x-axis.
(3mks)
Grid
c)
(i) By integration find the actual area of the region in b) above
(ii)
(3mks)
Calculate the percentage error arising from the estimate in b) above(2mks)
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