NAME…………………………………………………………………	INDEX ……………………………………

CANDIDATE’S SIGN………………………………………………..	DATE………………………………………

SCHOOL………………………………………..…………………….

BUSIA SUB COUNTY JOINT EXAM 2016

Kenya Certificate of Secondary Education (K.C.S.E)

121/1

MATHEMATICS

PAPER 1

JUL/AUG 2016

TIME: 2 ½ HOURS

INSTRUCTIONS TO CANDIDATES

1)	Write your name and index number in the spaces provided above.

2)	Sign and write the date of examination in the spaces provided above.

3)	This paper consists of two section I and II.

4)	Answer ALL questions in section I and only five questions from section II.

5)	Answers and working must be written on the question paper in the spaces provided below each question.

6)	Marks may be given for correct working even if the answer is wrong.

7)	Non-programmable electronic calculators may be used.

FOR EXAMINERS’ USE ONLY.

SECTION I

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	TOTAL

Grand Total SECTION II

17	18	19	20	21	22	23	24	TOTAL

SECTION A – 50 MARKS

Without using tables evaluate	(3mks)

Nekesa, Ouma and Wabwire shared money. Ouma got of it, Wabwire gotof the remainder and Nekesa got the rest. Find the Percentage share of Wabwire to Nekesa`s share. (3mks)

The gradient of a straight line L1 passing through the points P(3,4) and Q(a,b) is -. A line L2 is perpendicular to L1 and passes through the points Q and R(2,-1). Determine the value of a and b	(3mks)

A triangle with vertices of P(3,0) , Q(5,1) and R( 4,4) under goes enlargement scale factor -2 centre (1,0).

Find the co-ordinates of the image P1Q1R1	(3mks)

A water pipe has an external diameter of 8cm and a wall thickness of 0.5cm. If water flows through the pipe at the rate of 5m/s .What is the discharge in litres /h (3mks)

Simplify

(2mks)

Hence find the value of the expression when a=and c =	(2mks)

In the figure below, find the inequalities which describe the unshaded region R apart from x ≥ 0

and y ≥ 0	(4mks)

A motocycle is valued at Kshs. 100,000. If the rate of depreciation is 0.9% per month. Calculate the time it takes for the value to drop to Kshs. 50,000	(3mks)

Five years ago a woman was 4 times as old as her daughter. In four years’ time, the woman will be two and a half times as old as her daughter. Find their present age.	(3mks)

Solve 2x-3 x	(3mks)

A manufacturer made 5,000 packets of detergent powder for Kshs. 60,000. He sold them to a supermarket at a profit of 25% and the supermarket charged customers shs. 19.50 per packet. Calculate the supermarkets percentage profit.	(4mks)

Use matrix method to solve the simultaneous equation

7p + 5q = 11	(3mks)

3q + 4p = 2

Solve the equation sin ( ½ x-500) = cos x for 0 < x < 90.	(2mks)

Each interior angle of a regular polygon is 1200 larger than the exterior angle.

i)Find the number of sides of the polygon	(2mks)

ii) State the name of the polygon	(1mk)

The diagram below represents a right pyramid on a squarebase of side 3cm. The slant height of the pyramid is 4cm

Draw a net of the pyramid	(2mks)

16.Object A of area 20cm2 is mapped onto its image B of area 120cm2 by a transformation whose matrix is given by P = Find the positive value of x	(4mks)

Section B (50 MARKS)

17. The following data was obtained for masses of some group of children

Mass x kg	1-5	6-7	8-13	14-15	16-20
Cumulative frequency of the children	16	36	54	68	83

i) Calculate the mean mass of the children	(4mks)

State the

Median class	(1mk)

Modal class	(1mk)

i) Draw a histogram of the data above	(4mks)

18. The diagram below represents the circular container with a base radius 10cm and a length of

25cm. O is the centre of this cross-section and angle AOC = 1200 . The container contains water

i) Calculate i) the cross-section without water	(5mks)

ii) The volume of water in the cylinder in litres	(5mks)

19.a) The scale of a map is 1: 125000. Calculate the actual distance in Km represented by 16.8cm on the

map	(2mks)

The following are measurements in meters of a dam as indicated in the surveyor`s field book

M

140

F 15	120

100	E 25

70	D 20

C 30	50

20	B 10

A 30	10

N

By using a scale 1cm to represent 10meters . Draw the map of the dam	(3mks)

Calculate the area of the dam in Km	(5mks)

20. In the figure below OPQR is a Trapezium. PQ is a parallel to OR and OR = 5PQ . S. is a point on OR such

that OS:SR = 3:2

x

Given that OP = p and PQ = q, express in terms of p and q

OQ	(1mk)

PS	(2mks)

RQ	(2mks)

Line OQ and line PS intersect at point X such that PX = kPS and OX = rOQ

Where k and r are scalars. Determine the values of k and r.	(5mks)

21. The table below shows values for the function.	Y= 5 + 8x -2x2 for -2 ≤ x ≤ 5

Complete the table below of the function. y=5x + 8x -2x2	(2mks)

X	-2	-1	0	1	2	3	4	5
5	5	5	5	5	5	5	5	5
8x	-16	-8	0	8
-2x2	0	-8
y

Draw the graph of 5+8x-2x2 for -2≤ x ≤5	(3mks)

Use your graph to solve the equation

5+8x -2x2	= 0	(1mk)

-2x2 +5x + 3=0	(3mks)

State the equation of the line of symmetry of the curve y= 5+ 8x -2x2

22. In the figure below PQRS and T are points on the circle. SRW and PQW are straight lines. Angles SWQ =

300 ,SQW = 1100 and PQT = 380

Calculate the size of the angles and

give reasons for each case

TPS	(2mks)

STP	(2mks)

TSP	(2mks)

QSR	(2mks)

b) Given that SR= 5cm RW= 6cm and QW =4cm. Calculate the length of the chord PQ(2mks)

23. A curve whose gradient function is dy/dx = 3x2 +10x +3 passes through point (-2, -3)

a) Find the equation of the curve	(4mks)

b) i) Determine the turning points	(3mks)

ii) Sketch the curve	(3mks)

24. a) using a pair of compass and a ruler only construct triangle PQR Where PR = 8cm, angle PRQ =600 and angle RQP = 750	(3mks)

b)i) Find the locus of a point T which is equidistant from the points P,R and Q	(2mks)

ii) Find the locus of a point M where PM = MQ and angle PMQ = 600	(3mks)

iii) X is a point on PR and QX is the shortest distance from Q to line PR

By construction find the point x	(1mk)

Find the length of QX	(1mk)