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

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

SCHOOL………………………………………..…………………….

BUSIA SUB COUNTY JOINT EXAM 2016

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

121/2

MATHEMATICS

PAPER 2

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 1 (50 marks)

Answer all questions in this section in the spaces provided

Use logarithms to evaluate	(4mks)

Make r the subject of the formula	(3mks)

Simplify the expression leaving your answer in surd form	(4mks)

Determine the semi – interquartile ranges for the following numbers

3,4,9,5,4,7,6,2,1,6,7,8,9	(3marks)

A quantity P varies directly as R and inversely as the square root of Q. Find the percentage change in P if R is increased by 40% and Q decreases by 36%.	(3marks)

In finding the area of a rectangle whose dimensions are 7.28 by 5.49, a student truncated the measurement 1d.p. Find the percentage error arising from this.	(3marks)

Determine the two possible value of a for which	(3marks)

(a) Expand (1-2x)6 in ascending powers of x upto the term in x3	(2mks)

(b) Hence evaluate (1.02) 6 to 4 d.p	(2mks)

The position vectors of A and B are given as and . Find to 2 decimal places the length of the vector AB	( 3mks)

Determine the amplitude, period and the phase angle of the wave represented by the equation sin (2/5x +400)	(3mks)

Find the radius and co – ordinates of the Centre of the circle whose equation is

y2 = 3x -5y -9	( 3mks)

A quantity P varies partly as t and partly as the square of t. when t = 20, p = 45 and when t = 24 and p = 60.

a). Express p in the terms of t	(3mks)

b). Find p when t = 32	( 1mk)

Given that log 3= 1.583 and log 5 = 2.322 evaluate without using table or calculator log 75 ( 2mks)

The distance s metres moved by a particle along a straight line after t seconds in motion is given by s = 7 +8t2 – 2t3. Find the velocity at t = 2 sec.	( 2mks)

Two similar containers have masses 256kg and 108kgs respectively. If the surface area of the smaller container is 810cm, find the corresponding surface area of the larger container. ( 3mks)

A blender mixes two brands of juice A and B to obtain 70ml of the mixture worth Kshs 165 per litre. If brand A was valued at khs 168 per litre bottle and brand B at Kshs 153 per litre bottle. Calculate the ration in which the brands A and B were mixed.	( 3mks)

SECTION II ( 50 MARKS)

Answer only five questions from this section

Mr. Onyango a civil servant on a basic salary of Kshs 18, 000. On top of his salary, he gets a monthly house allowance of Kshs 14, 000, medical allowance of Kshs 3080 and commuter allowances of Kshs. 4640. He has a life insurance policy for which he pays a premium of Kshs. 800 p.m and claims an insurance relief of Kshs 3 for every 20/= on the monthly premiums . He is entitled to a personal relief of Kshs 1056 p.m.

Using the taxable below calculate his PAYE	(7marks)

Income in k£ p.m	Rate %
1-484 485 -940 941-1396 1397-1852 Over 1852	10 15 20 25 30

In addition to PAYE the following deductions are made on his pay every month

WCPS at 2% of his basic salary

NHIF of Kshs 400

Loan repayment of Kshs 4000

Co-op shares of skhs 800

Calculate his total monthly deduction is Khs	( 2mks)

Calculate his net monthly pay in Kshs.	( 1mk)

A tailor takes 4 hours to make a shirt and 6 hours to make a dress. It takes the tailor at least 144 hours to make x shirts and y dresses. The labour cost of making a shirt is kshs 100 and that of a dress is kshs 200. The total labour cost should not exceed kshs. 4,800. The tailor must make at least 16 shirts and more than 10 dresses.

a). Write down inequalities to represent the above information	( 4mks)

b). Draw the inequalities above on the grid provided	( 4mks)

c). The tailor makes a profit of Kshs 40 on the shirt and kshs 100 on a dress. Use the graph to determine the maximum profit the tailor can make.	( 2mks)

The probability of passing KCPE depends on performance in the school mock examination. If the candidate passes in mock, the probability of passing KCPE is 4/5. If the candidate fails in mock, the probability of passing KCPE is 3/5 . If the candidate passes KCPE the probability of getting employed is 1/3, the probability of passing mock is 2/3.

Draw a well labeled tree diagram to represent the above information	( 2mks)

Use the tree diagram in (a) above to find the probability that the candidate

Passes KCPE exam	( 2mks)

Gets employed	(2mks)

Passes KCPE and gets employed.	( 2mks)

Does not pass KCPE	(2mks)

The points AlBlCl are images ABC, A(1,4), B(-2,0), C (4,-2) respectively under a transformation

N presented by Matrix N =	( 4mks)

a). Write down the co-ordinates of AlBlCl

b). AllBllCll are the images of AlBlCl under a transformation represented by matrix M =

Write down the co-ordinates of AllBllCll	( 4mks)

c). A transformation N followed by M can be represented by a single transformation K. determine

the matrix K	( 2mks)

The position of two towns X and Y are given to the nearest degree as

X (450N, 100E) and Y(450N, 700E)

Find :-

The difference in longitude	( 1mk)

The distance between the two towns in	( 4mks)

Kilometres ( take radius of the earth as 6371km)

Nautical miles ( take 1 nautical mile to be 1.85km)	(2mks)

The local time at x when the local time at Y is 2.00pm.	(3mks)

a) The first term of an arithmetic progression ( AP) is 2. The sum of the first 8 terms of the AP is 156.

Find the common difference of the AP	( 2mks)

Given that the sum of the first n terms of the AP is 416, find n	( 3mks)

b). The 3rd, 5th and 8th terms of another AP form the first three terms of a Geometric

Progression (GP). If the common difference of the AP is 3 find

The first term of the GP	( 3mks)

The sum of the first 9 terms of the GP, to 4s.f	( 2mks)

In the figure below, VABCD is a right pyramid on a rectangular base. Point O is vertically below the vertex V. AB = 12cm, BC = 5cm and VA = VB = VC = VD = 18cm.

V

18 CM

C D

5 CM

O

12 CM A B

Calculate

The height VO	(3 mks)

The angle between

V C and the plane ABCD	(3 mks)

The planes VAB and ABCD	(2 mks)

The planes VAD and VBC	(2 mks)

The table below gives some values of y = sin 2x and y = 2cos x in the range - 2250≤ x≤ 2250

a). Complete the table	( 2mks)

X0	-225	-180	-135	-90	-45	0	45	90	135	180	225
Sin 2x	-1.0	0	0	0	1.0
2 cos x	-1.4	0	2.0	0	-1.4

b). on the same axes, draw the graphs of y =sin 2x0 and y =2cosx0	( 5 mks)

c). Use your graph find the values of x for which sin 2x = 2 cos x	( 2mks)

d). Find the difference in period between the two curves	(2mks)