Four steps to change the world
Bryan Stevenson
Bryan Stevenson is the founder of the Equal Justice Initiative (www.eji.org) and author of Just
Mercy: A Story of Justice and Redemption, at once an unforgettable account of an idealistic,
gifted young lawyer

121/ 1 MATHEMATICS 2005
PAPER 1
SECTION 1 (52 Marks)
Answer all the question in this section
1. Evaluate
+ 1 5/7 of 2 1/3
(1 3/7 5/8 x 2/3 )
( 3 marks)
2. Express the numbers 1470 and 7056, each as a product of its prime factors
Hence evaluate
14702 Leav

y
1
3.5
7
11.5
17
23.5
31
(a) Use the values in the table to draw the graph of the function ( 2 marks)
(b)
(i)
Using the graph and the mid ordinate rule with six (6) strips,
estimate the area bounded by the curve, the x- axis, the y- axis and the line = 6

Monthly taxable income
Tax rate percentage
In ( kshs)
(%) in each shillings
Under Kshs 9681
10%
From Kshs 9681 but under 18801
15%
From Kshs 18801 but 27921
20%
In the tax year 2004, the tax of Kerubos monthly income was Kshs 1916
Calculate Kerubos monthl

20.
The diagram below represents two vertical watch-towers AB and CD on a level ground. P and Q
are two points on a straight road BD. The height of the tower AB is 20m road a BD is 200m.
A
20
M
B
P
Q
D
A car moves from B towards D. At point P, the angle o

(a) Find vector LN
( 3 marks)
(b) Given that a point M is on LN such that LM: MN = 3: 4, find the coordinates of M
( 2 marks)
(c) If line OM is produced to T such that OM: MT = 6:1
(i) Find the position vector of T
(1 mark)
(ii) Show that points L, T and

24.
The diagram on the grid below represents as extract of a survey map showing
two adjacent plots belonging to Kazungu and Ndoe.
The two dispute the common boundary with each claiming boundary along different smooth
curves coordinates ( x, y) and (x, y2)

SECTION II (50MKS)
Answer any five questions in this section.
17.
a)
A trader deals in two types of rice; type A and with 50 bags of type B. If
he sells the mixture at a profit of 20%, calculate the selling price of one bag of the
mixture.
(4mks)
18.
b)
T

1. Two cylindrical containers are similar. The larger one has internal cross- section area of 45cm 2
and can hold 0.945 litres of liquid when full. The smaller container has internal cross- section
area of 20cm2
(a) Calculate the capacity of the smaller c

121/2 MATHEMATICS PAPER 2 2005
SECTION I (52 Marks).
Answer all questions in this section
1.
Find the value of y in the equation
243 x 32y = 81
729 x 3y divide 3(2y 1)
2.
( 3 marks)
Without using mathematical Tables, simplify
63
+
72
_
32
+
28
( 3 marks)

Calculate:
23.
a)
The length of AC;
b)
The angle between the line AG and the plane ABCD;
c)
The vertical height of point V from the plane ABCD;
d)
The angle between the planes EFV and ABCD.
a)The first term of an Arithmetic Progression (AP) is 2. The sum

1. The gradient of the tangent to the curve y = ax 3 + bx at the point ( 1,1) is -5
Calculate the values of a and b
( 4 marks)
2. Simplify the expression 15a2b 10ab2
3a2 5ab + 2b2
( 3 marks)
3. A square brass plate is 2 mm thick and has a mass of 1.05 kg.

(a) Given that A (-6, 5) is mapped onto A (6,-4) by a shear with y- axis invariant
(i)
(b)
draw triangle ABB, the image of triangle ABC under the shear
( 3 marks)
(ii)
Determine the matrix representing this shear ( 2 marks)
Triangle A B C is mapped on to

1 cos x0
(b)
0.5
1
On the grid provided, using the same scale and axes, draw the graphs of
y = sin x0 and y = 1 cos x0 x 1800
Take the scale: 2 cm for 300 on the x- axis
2 cm for I unit on the y- axis
(c)
Use the graph in (b) above to
(i)
Solve equation
2

(a) Calculate the volume of the prism
( 3 marks)
(b) Given that the density of the prism is 5.75g/cm 3, calculate its mass in grams
( 2 marks)
(c) A second prism is similar to first one but is made of a different materials. The volume of the
second is 246

SECTION II ( 48 marks)
Answer any six questions in this section
17.
The distance between towns M and N is 280 km. A car and a lorry travel from M to N. The
average speed of the lorry is 20 km/h less than that of the car. The lorry takes 1 h 10 min
more th

Hadija bought 2 pens and 3 exercise books for Kshs 78. Kagendo bought pens and 4 exercise
books for Kshs 108
Calculate the cost of each item
5.
( 3 marks)
The histogram below represents the distribution of marks obtained in a test.
The bar marked A has a

(4 marks)
7.
Find, without using Mathematical Tables the values of x which satisfy the equation
Log2 (x2 9) = 3 log2 2 + 1
( 4 marks)
8.
The volumes of two similar solid cylinders are 4752 cm 3 and 1408 cm3. If the area of the curved
surface of the smalle

SECTION II (50 MARKS)
Answer any five questions in this section)
5.
(a)
In the year 2001, the price of a sofa set in a shop was Kshs 12,000
Calculate the amount of money received from the sales of 240 sofa sets that year
( 2 marks)
(b) (i)
In the year 200

17. A curve is represented by the function y = 1/3 x3 + x2 3x + 2
(a) Find dy/dx
( 1 mark)
(b) Determine the values of y at the turning points of the curve
y = 1/3 x 3 + x2 3x + 2
18.
( 4 marks)
Triangles ABC and ABC are drawn on the Cartesian plane provi

SECTION II (50 marks)
Answer any five questions in this section
1. Three business partners: Asha Nangila and Cherop contributed Kshs 60,000, Kshs 85,000 and
Kshs 105 000 respectively. They agreed to put 25% of the profit back into business each year.
Thay

(b) (i)
State the group in which the median mark lies
( 1 mark)
(ii) A vertical line drawn through the median mark divides the total area of the histogram
into two equal parts
Using this information or otherwise, estimate the median mark (3mks)
1. A retai

1. A particle moving in a straight line passes through a fixed point O with a velocity of 9m/s. The
acceleration of the particle, t seconds after passing through O is given by a = ( 10 2t) m/s 2.
Find the velocity of the particle when t 3 seconds
( 3 mark

1.
In this question use a ruler and a pair of compasses only
In the figure below, AB and PQ are straight lines
Q
P
(a) Use the figure to:
(i) Find a point R on AB such that R is equidistant from P and Q (1 mark)
(ii) Complete a polygon PQRST with AB as it

K.C.S.E 2006 MATHEMATICS PAPER 121/2
SECTION 1 (50 Marks)
1. In this question, show all the steps in your calculations, giving your answers at each stage
Use logarithms, correct to 4 decimal places, to evaluate
( 4 marks)
3 36.72 x (0.46)2
185.4
2. Make s

points A and B. Point A on the x- axis while point B is equidistant from x- and y
axes.
Calculate the co-ordinates of the points A and B
(3mks)
12. A cylindrical piece of wood of radius 4.2 cm and length 150 cm is cut length into
two equal pieces.
Calcul

Given that PN = 14cm, NB = 4 cm and BR = 7.5 cm, calculate the length of:
(a) NR
( 1 mark)
(b) AN
( 3 marks)
1.
Vector q has a magnitude of 7 and is parallel to vector p. Given that
p= 3 i j + 1 k, express vector q in terms of I, j, and k.
( 2 marks)
2.
T

121/2
MATHEMATICS
Paper 2
Oct/Nov 2008
2 hours
SECTION I (50 MARKS)
Answer all the questions in this section in the spaces provided.
1.
In this question, show all the steps in your calculations, giving the answer each stage. Use
logarithms correct to deci

1.
Two bags A and B contain identical balls except for the colours. Bag A contains 4 red balls
and 2 yellow balls. Bag B contains 2 red balls and 3 yellow balls.
(a) If a ball is drawn at random from each bag, find the probability that both balls
are of t

In a certain month the dealer sold twice as much diesel as petrol. If the total fuel sold that
month was 900,000 litres, find the dealers profit for the month. (3mks)
7.
A liquid spray of mass 384g is packed in a cylindrical container of internal radius 3