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121/2
MATHEMATICS
Paper 2
July / August 2008
2 ½ Hours
BUTERE DISTRICT MOCK EXAMINATION - 2008
Kenya Certificate of Secondary Education (K.C.S.E)
121/2
MATHEMATICS
Paper 2
July / August 2008
2 ½ Hours
INSTRUCTIONS TO CANDIDATES
1.
Write your name and index number in the space provided at the top of this page.
2.
The paper contains TWO sections; section I and section II
3.
Answer all the questions in section I and ANY FIVE questions from section II
4.
Show all the steps in your calculations; giving your answers at each stage in the spaces
provided below each question.
5.
Marks may be given for correct working even if the answer is wrong.
6.
Non-programmable silent electronic calculators and KNEC mathematical tables maybe used.
For Examiners use only
Section 1
1
2
3
4
5
6
7
8
9
10
20
21
22
23
24
Total
11
12
13
14
15
Section II
17 18
19
This paper consists of 16 printed pages
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1
Grand Total
16
Total
Candidates should check the question paper to ensure that all the printed pages are printed as indicated and no
questions are missing.
SECTION I ( 50 MARKS)
Answer all the questions in this section
1.
Use logarithm tables to evaluate
(3mks)
13.4  9
12  log 4.82
2.
Two grades of tea costing sh.100 and sh.150 per kg respectively are mixed in the ratio 3:5 by
weight. The mixture is then sold at sh.160 per kg. Find the percentage profit on the cost price.
(4mks)
.
.
3.
Given that a = 1.2, b = 0.02 and c = 0.2 express ac  b in the form m/n where m and n are
integers.
(3mks)
4.
A quantity P is partly constant and partly varies inversely as Q. Q=9 when P = 3 and Q = 18
when P = 9. Find P when Q = 12.
(4mks)
5.
Find the time for which Ksh. 200,000 at 15% p.a. accumulates to Ksh.314,175.
(3mks)
6.
Find the value of x that satisfy the equation
Log(x + 5) = log 4 – log (x + 2)
(3mks)
7.
Find the equation of the normal to the curve y = x2 + 4x – 3 at point (1, 2).
8.
A point T divides line AB internally in the ratio 1;3. Given that A is ( 3, 2) and R is (11, 6).
Find the co-ordinates of T.
9.
(3mks)
(3mks)
Given that ABD is a similar triangle to triangle ACB.  ABD = ACB. Calculate the
length AC.
(2mks)
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10.
In the figure below RS is a tangent to the circle at S.
Given that LTPQ = 1080 and LTSU = 560, find LQRS.
11.
(4mks)
The probability that a day is rainy is ¼ . The probability that a teacher carries an umbrella on
a rainy day is 1/7 and that he carries an umbrella on a non-rainy day is 2/7. Find the probability
that a teacher carries an umbrella.
(2mks)
12.
Use binomial expansion to determine the value of (1.00)5 correct to 3d.p.
(3mks)
13.
The table below shows corresponding values of x and y for a certain curve.
x
1.0
1.2
1.4
1.6
1.8
2.0
2.2
y
6.5
6.2
5.2
4.3
4.0
2.6
2.4
Using 6 strips and mid-ordinate rule estimate the area between the curve, x-axis, the lines x=1
14.
and x = 2.2
(3mks)
Make s the subject of the formulae.
(3mks)
a
15.
S2  q
p2
The floor of a rectangular room measures 4.8m by 3.2m. Estimate the percentage error in the
area.
16.
(4mks)
Otieno had a bag whose mass was 0.05kg. She put in it two balls, one 5.3kg and another
6005g in mass. Find the total mass of the bag and the balls.
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(2mks)
SECTION II ( 50 MARKS)
Answer any five questions in this section
17.
The figure below shows a pulley belt passing round two pulleys with centres x and y. The radii
of the pulleys are 12cm and 4cm and the distance between their centre is 27cm. The belt is
tangential to the pulleys at M, Q, T, S, P and N.
18.
a) Calculate the length of the belt MQ.
(3mks)
b) Find the angle YXQ.
(2mks)
c) Find the length of the belt that would go round the pulleys (QRSPNM).
(5mks)
Income tax is charged on annual income at the rate shown below
Taxable income (K£)
Rate (shs per K£)
1 – 1500
2
1501 – 3000
3
3001 – 4500
5
4501 - 6000
7
6001 – 7500
9
Over 7500
10
A civil servant earns a monthly basic salary of Ksh.8570. He is housed by the government and
as a result, his taxable income is 15% more than his salary. He is entitled to a tax relief of Ksh.
150 per month.
a) How much tax does he pay in a year.
(6mks)
b) From his salary, the following deductions are also made every month.
WCPS
2% basic salary
NHIF
Ksh 20
Calculate the civil servants net salary per month.
19.
(4mks)
The table below shows the distribution of the wages in a week for a number of employees in a
certain factory.
Wage
Number of
800-899
900-999
1000-1099
1100-1199
1200-1399
1400-1599
3
10
23
9
3
2
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workers
a) Using Kshs. 1049.5 per week as the assumed mean wage,
Calculate the
(i) mean for the group wages.
(4mks)
b) Standard deviation.
(5mks)
c) The week that followed, every employee earned extra Kshs. 100 as wage increment.
Determine the new mean for the group wage.
20.
(1mk)
The figure below represents a model of a tower VPQR. The horizontal base PQR is an
equilateral triangle of side 9cm.
The lengths of the edges are VP=VQ=VR=20.5cm point m is the mid-point of PQ and
VM=20cm point N is on the base and vertically below V
V
Calculate
(a) the length RM.
(2mks)
(b) the height of the model.
(5mks)
(c ) the angle between
21.
(i) plane VPR and the base.
(1mk)
(ii) Line VR and the base
(2mks)
a) A shear parallel to x – axis (x-axis invariant) maps point (1,2) onto point ( 7, 2). T is the
transformation equivalent to this shear followed by a reflection in the line y=x. Find the matrix
which defines T.
(5mks)
b) A transformation P maps points ( 1, 3) and (-2, -3) onto points (2, 4) and (-3, -11)
respectively. Find the matrix of the transformation.
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(5mks)
22.
A bag contains blue, green and red pens of the same type in the ratio 8:2:5 respectively. A pen
is picked at random without replacement and its colour noted.
a) Determine the probability that the first pen picked is
(i) blue
(1mk)
(ii) either green or red.
(1mk)
b) Using a tree diagram, determine the probability that
(i) the first two pens picked are both green.
(3mks)
(ii) Only one of the first two pens picked is red.
(3mks)
c) (i) Draw the probability space for the possible outcomes when a coin is tossed and a die
23.
thrown simultaneously
(1mk)
(ii) Determine the probability of getting a head and an even number.
(1mk)
Complete the table below for the functions y = cosx and y = 2 cos (x + 300) for O0 < x < 3600
x
00
300
600
Cos x
1
0.87
0.5
2 cos
1.73
0
900
-1.0
1200
1500
1800
-0.5
0.87
-1.0
-2.0
-1.73
2100
2400
2700
0.5
0
-1.0
1
3000
1.73
3300
3600
0.87
1
2.00
1.73
(x + 300)
(a) On the same axis, draw the graphs of y = cos x and y = 2 cos (x + 30) for 00 < x < 3600.
(4mks)
(b) (i) State the amplitude of the graph y = cos x0.
(1mk)
(ii) State the period of the graph y = 2 cos (x + 300).
(1mk)
c) Use your graph to solve
Cos x = 2 cos ( x + 300)
24.
(2mks)
A body moves in a straight line with acceleration ( 5 – 12t) m/s2, t seconds after the start.
Given that the body started with a velocity of 3m/s.
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a) Find velocity and displacement in terms of t.
(6mks)
b) How far was the body from its starting point after 2 seconds and its velocity then?
(4mks)
END
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