MATHEMATICS

PAPER 2

Instructions

- Sign and write date of examination in the spaces provided above
- This paper consist of two sections; Section I and Section II
- Answer all questions in section I and only 5 questions from Section II
- Show all the steps in your calculations, giving your answers at each stage in the spaces provided below each questions
- Marks may be given for correct working even if the answer is wrong
- Non- programmable silent electronic calculators and KNEC Mathematical tables may be used, except where stated otherwise.

## Questions

SECTION I(50 MARKS)

Answer ALL questions in this section.

- Simplify the following expression. (3 marks)

2x - x-5 - 3x-1

4 2 - In the figure below NC=3.3cm and AB =2.4cm

Find the area of triangle ABC (3marks) - Calculate the percentage error in volume of a cylinder whose diameter is 17.5cm and its height is 32.5cm. (3 marks)
- Evaluate without using mathematical tables or a calculator. (4marks)

1 + 1

1+Cos 45 1-Sin 45º - The roots of a quadratic equation are x= -
^{2}/_{3}and x =4.Form the quadratic equation in the of ax^{2}+bx+c=0 where a, b, and c are integers (3 marks) - What is the length of an arc which subtends an angle of 0.8 radians at the centre of circle given its circumference to be 66 cm.(3marks)
- Solve for x in the equation; (3marks)

log 5-2+log (2x+10) = log(x - 4) - Make x the subject of the formula (3marks)
- In the figure below , BDEF are points on the circumference of a circle centre O. Points ABC and BOE are straight lines. Given that angle BDF= 500 and BF=DF.

Find the values of angles ( 3marks)- FBE
- ABF
- EBD

- Find the equation of the normal to the curve y = x2 + 4x -3 at the point (1, 2). (3marks)
- Using the assumed mean of 50 determine the variance of the following set of numbers

52, 45, 42 ,59 , 50 , 56 ,46 (3marks) - Solve the following simultaneous equations using matrix method. (3marks)

-3y +2x = 7

4x +3y = 5 - Given that OA = a , OB = b and that P divide AB in the ratio 3 : -1 Express OP in terms of vectors a and b (3marks)
- A solid consists of a cylinder and hemisphere of equal radius 10.5cm if the height of the solid is 30 cm find its capacity .(3marks)
- The lines x + 2y = -1 and 2x + 2y = 3 intersect at a point R. Find the equation of a circle, centre R, radius 5, giving your answer in the form x2 +y2 + gx + fy + c = 0, where g, f and c are constants. (3marks)
- Expand and hence find the constant term in the binomial expansion (4marks)

[2x-^{1}/_{x}]^{4}

SECTION II (50 MARKS)

Answer FIVE questions ONLY from this section

- A teacher in a certain school earns ksh.19620 per month. He is also paid a house allowance of sh. 20000 per month and medical allowance of 2476 and commuter allowance of sh.318.In addition to income tax he is deducted sh.392.40 towards a widow and children pension scheme (WCPS) and monthly life insurance premium of ksh.1250.He is entitled to personal tax relief of sh.1162 per month and insurance relief of 10%of premium paid.

Monthly taxable income sh per m Rate of tax in % 0 - 10164 10 10165 - 19740 15 19741 - 29316 20 29317 - 38892 25 Over 38892 30 - Determine the teachers taxable income per month. (2 marks)
- Calculate the tax paid by the teacher each month. (5marks)

- Find the teachers net income per month (3marks)An aircraft leaves airport P(500N,50W) and flies due west for 2400 km to point Q, then 1500 km due south to point R. given that the radius of the earth is 6370 Find
- the position of point Q (3marks)
- the position of point R (3marks)
- A ship leaves Mombasa (40S, 400E) and sails due east for 30 hours to point Q(40S, 520E) in the Indian ocean. Find the average speed of the ship in knots. (4marks)

- The table below shows marks scored by applicants for various positions in an interview.

Marks 20 - 29 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89 No. of people 4 18 22 24 16 12 4 - Draw an ogive to represent the given data. (4 marks)
- Using your ogive estimate;
- the median (1 mark)
- the quartile deviation. (3 marks)
- the range of marks scored by the middle 40% of applicants. (2 marks)

- A die is biased so that when tossed the probability of a number n showing up is given by p(n)=Kn where k is a constant and n=1,2,3,4,5 and 6(the number on the faces of the die)
- Calculate the value of K (2marks)
- What is the probability of getting a number greater than 4 . (2marks)
- What is the probability of getting an even number . (2 marks)
- If the number is rolled twice what is the probability that the sum of the numbers showing up is atleast 11. (4marks)

- Three consecutive terms of geometric progression are 9 2x + 1, 81x and 729 respectively. Calculate:
- The value of x (3marks)
- Find the common ratio (2marks)
- Calculate the sum of the first 10 terms of this series (2marks)
- Given that the fifth and the sixth terms of this G.P forms the first two consecutive terms of arithmetic sequence, calculate the sum of the first 20 terms of this sequence. (3marks)

- Using a ruler and pair of compasses only, construct a parallelogram PQRS such That PQ = 7.5cm, PS = 5cm, and QPS = 67 ½0. (4marks)

On the same diagram, locate;- locus X equidistant from P and Q. (1 mark)
- A point M is such that<QMS = 900. M is on the same side of QS as R. (2marks)
- A region inside the parallelogram in which variable Y lies such that PY, RY and QYS ≥ 900, Shade the region represented by Y. (3marks)

- The diagram below shows a right pyramid with vertex V and a triangular base ABC which is an equilateral triangle of sides 6cm. The length of VA=VB=VC=20 cm .M is the midpoint BC. Point O is at the base and vertically below
- Calculate the length of line AM (2 marks)
- Calculate the angle the line VA makes with the base ABC. (2marks)
- Find the angle between the face VBC and the base ABC. (3 marks)
- Find the volume of the pyramid (3 marks )

- A Lady sells two types of ice creams in cups and sticks. She can store less than ten packets in her cooling box. She sells more cups than sticks but less than 3 items as many cups as sticks. She also knows that she will sell more than 3 packets of sticks. Her profit is Ksh. 8 on a packet of cups and Ksh. 5 on a packet of sticks.
- Form inequalities to represent the above information: (3 marks)

Let x – packets of cups and y – packets of sticks - On the grid provided graph the inequalities and show region R that satisfy the required condition. (4 marks)
- How many packets of cups and sticks should the lady put in her box to give her the maximum profit? (3 marks)

- Form inequalities to represent the above information: (3 marks)

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