3.
4.
A motorist took 2 hours to travel from one town to another town and 1 hour 40 minutes to travel
back. Calculate the percentage change in the speed of the motorist. (3 marks)
A square room is covered by a number of whole rectangular slabs of sides 60

MATHEMATICS PAPER 1
2011
SECTION 1 (50 marks)
Answer all the questions in this section in the spaces provided.
1.
Without using a calculator, evaluate;
(3 marks)
2.
The diagonal of a rectangular garden measures 111/4 m while its width measures 63/4 m.
Cal

(i)
the distance between T and S in metres:
(ii)
(c)
24
(a)
the bearing of T from S.
(2 marks)
(1 mark)
Find the area of the field, in hectares, correct to one decimal place.
(4 marks)
In the figure below, PQ is parallel to RS. The lines PS and RQ interse

7.
The external length, width and height of an open rectangular container are 41 cm, 21 cm and 15.5
cm respectively. The thickness of the material making the container is 5 mm. If the container has 8
litres of water, calculate the internal height above th

(3 marks)
22. The displacement, s metres, of a moving particle after,t seconds is given by,
s =2t 3- 5t2 + 4t + 2.
.
Determine:
(c)
(a)
the velocity of the particle when t = 3 seconds;
(b)
the value o f t when the particle is momentarily at rest;
the disp

K.C.S.E
MATHEMATICS ALT A
Paper 1 2012
SECTION 1 (50 marks)
Answer all the questions in this section in the spaces provided.
1.
Without using a calculator, evaluate
(4 marks)
2.
Find the reciprocal of 0.216 correct to 3 decimal places, hence evaluate
(3 m

(iii)
In the third month she earned Ksh 68 000. Find the number of items sold.
(2 marks)
20.
In a triangle ABC, BC =8 cm, AC= 12 cm and angle ABC = 120.
(a)
Calculate the length of AB, correct to one decimal place.
(b)
If BC is the base of the triangle, c

14.
(a)
Express 10500 in terms of its prime factors.
(1 mark)
(b)
Determine the smallest positive number P such that 10500P is a perfect cube.
(2 marks)
15. Three police posts X, Y and Z are such that Y is 50 km on a bearing of 060 from X while Z
is 70 km

(b)
Determine, correct to 2 significant figures:
(i)
the perpendicular distance between PQ and RS;
marks)
(ii)
(c)
(d)
the length of TS.
(2
(2 marks)
Using the cosine rule, find the length of RS correct to 2 significant figures.
(2
marks)
Calculate, corre

Mathematics paper2 2011
SECTION I (50 marks)
Answer all the questions in this section in the spaces provided.
1
Use logarithms, correct to 4 decimal places, to evaluate
(4 marks)
2.
Three grades A, B, and C of rice were mixed in the ratio 3:4:5. The cost

The vertices of its image under a rotation are O'(l, -1), P'(l, -3), Q'(3, -5) and R'(4, -1).
(a) (i) On the grid provided, draw OPQR and its image O'P'Q'R1.
(2 marks)
(ii)
By construction, determine the centre and angle of rotation.
(3 marks)
(b) On the

Use the graph to determine:
(a)
(b)
the average rate of change of distance between t =3 seconds and t =6
seconds;
(2 marks)
the gradient at t = 3 seconds.
(2 marks)

15.
The equation of a circle centre (a, b) is x2 y2 6x - 10y + 30 = 0.
Find the values of a and b.
16.
(a)
(3 marks)
The table below shows values of x and y for the function y = 2 sin 3x in the range
x
0
15
30
y
0
1.4 2
45
60
1.4 0
75
90
-1.4 -2
On the gr

10 . (a) In the figure below, lines NA and NB represent tangents to a circle at points A and B.
Use a pair of compasses and ruler only to construct the circle. (2 marks)
Measure the radius of the circle.
(b)
(1 mark)
11
Expand and simplify the expression.

(a)
Find in terms of a and d:
(i)
BC;
(2 marks)
(ii)
AX;
(2 marks)
(iii)
DX;
(b)
Determine the values of h and k
(1 marks)
(5 marks)
24. The frequency table below shows the daily wages paid to casual workers by a
certain company.
(a)
Wages in shillings
10

17. The table below shows the height, measured to the nearest cm, of 101 pawpaw trees.
(a)
Height in cm.
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
Frequency
2
15
18
25
30
6
3
2
State the modal class.
(1 mark)
(b)
Calculate to 2 decimal places:
(i)
t

22
The figure below represents a rectangular based pyramid VABCD. AB = 12 cm and AD =16
cm. Point O is vertically below V and VA = 26 cm.
Calculate:
(a)
the height, VO, of the pyramid;
(b)
the angle between the edge VA and the plane ABCD;
(4 marks)
(3 mar

(iii) the size of angle ACB.
21.
(2 marks)
(a) Using the trapezium rule with seven ordinates, estimate the area of the region
bounded by the curve y = x2 +,6x+ 1, the lines x = 0, y = 0 and x = 6.
(5 marks)
(b)
Calculate:
(i)
the area of the region in (a)

MATHS P 2 2012
MARKING SCHEME
SECTION I (50 marks)
Answer all the questions in this section in the spaces provided.
1.
giving the answer to 4 significant figures.
2
(2 marks)
Make n the subject of the equation
(3 marks)
3.
An inlet tap can fill an empty t

3.
Make s the subject of the formula.
(3 marks)
4. (a)
(b)
Solve the inequalities 2x 5 > ~ 11 and 3 + 2x < 13, giving the answer as a combined
inequality.
(3 marks)
List the integral values of x that satisfy the combined inequality in (a) above.
(1 mark)

12. (a)
Expand (1 + x)7 up to the 4th term.
(b)
(1 mark)
Use the expansion in part (a) above to find the approximate value of (0.94)7.
(2 marks)
13
The graph below shows the relationship between distance s metres and time t
seconds in the interval 0 < t <

23.
In the figure below, ABCD is a trapezium, AB is parallel to DC, diagonals AC and DB intersect at
X and DC = 2 AB. AB = a, DA = d, AX = k AC and DX = hDB, where h and k are constants.
d

(b)
(i)
(ii)
State the class in which the median wage lies.
(1 mark)
Draw a vertical line, in the histogram, showing where the median wage lies.
(1 mark)
(c)
Using the histogram, determine the number of workers who earn sh 450 or less
per day.
(3 marks)

19
The vertices of a rectangle are A(-l,-l), B(-4 ,-l),C(-4-3) and D(-l,-3).
(a)
On the grid provided, draw the rectangle and its image A' B' C1 D' under a
transformation whose matrix is
(4 marks)
b)
A" B" C" D" is the image of A' B' C' D' under a transfo

4cm, BC = 6 cm, AD = 3 cm, angle ABC = 135 and angle DAB = 60. Measure the size of angle BCD.
(4 marks)
9.
Given that OA = 2i + 3j and OB = 3i - 2j
Find the magnitude of AB to one decimal place.
(3 marks)
10.
Given that tan x = 3/7 find cos (90 - x) givin

(a)
Determine the ratio, copper: zinc: tin, in alloy A.
(2 marks)
(b) The mass of alloy A is 250 kg. Alloy B has the same mass as alloy A but the
amount of copper is 30% less than that of alloy A.
Calculate:
(i)
the mass of tin in alloy A;
(2 marks)
(ii)

(b)
If the density of the material used to make the solid is 1.3 g/cm3, calculate its mass in
kilograms.
(3 marks)
18. Makau made a journey of 700 km partly by train and partly by bus. He started his journey
at 8.00 a.m. by train which travelled at 50 km/

22.
The equation of a curve is y = 2x3 + 3x2.
(a)
Find:
(i)
the x - intercept of the curve;
(ii)
(b)
the y - intercept of the curve.
(i) Determine the stationery points of the curve.
(2 mark)
(1 mark)
(3 marks)
(ii) For each point in (b) (i) above, determ

If the area of the parallelogram is 24 cm3, find its perimeter.
(3 marks)
5.
Given that 92y X 2x = 72, find the values of x and y.
(3 marks)
6.
Three bells ring at intervals of 9 minutes, 15 minutes and 21 minutes. The bells will
next ring
together at 11.

(b)
16.
Determine the distance, in km, of Z from X.
(1 mark)
A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of
height 16 cm, if the volume of the smaller cone is 160 cm3, find the volume of the
frustum
(3 marks)
SECTION II (5

a) Line OB interests AJ at X such that OX = mOB and AX = nAJ.
i)
Express OX in terms of p, r and m.
(1 mark)
ii)
Express OX in terms of p, r and n
(1 mark)
iii)
Determine the value of m and n and hence the ratio in which point x divides line AJ.
(6 marks)

i)
The distance travelled in 5 seconds;
(2 marks)
The time taken to travel a distance of 560 metres.
marks)
ii)
(3
1. In the figure below, P,Q, R and S are points on the circle. Line USTV is a tangent to the circle at
S, <RST = 500 and <RTV = 1500. PRT an

(b)
10.
determine the perpendicular distance between PQ and SR.
(1 mark)
The masses of people during a clinic session were recorded as shown in the table below.
Mass (kg)
No. of people
40-44
1
45-49 50-54
2
12
55-59
10
60-64
65-69
2
2
70-74
1
(3 marks)
Ca

(i)
Determine the coordinates of A", B", C" and D".
(ii)
On the same grid draw the quadrilateral A" B" C" D".
(2 marks)
(1 mark)
(c)
Find the area of A" B" C" D".
20.
A parent has two children whose age difference is 5 years. Twice the sum of the ages of

(3 marks)
12 .
Three vertices of a parallelogram PQRS are P(-l, 2), Q(8, -5) and R (5,0).
(a)
(b)
On the grid provided below draw the parallegram PQRS.
Determine the length of the diagonal QS.
(2 marks)
(1 mark)
13.
In January, Mambo donated 1/6th of his