KAKAMEGA SOUTH SUB-COUNTY EXAMINATIONS

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121/2

MATHEMATICS PAPER 2

MARCH/APRIL 2014 TIME: 2 ½ HOURS.

KAKAMEGA SOUTH SUB-COUNTY EXAMINATIONS

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

121/2

MATHEMATICS PAPER 2

MARCH/APRIL 2014 TIME: 2 ½ HOURS.

INSTRUCTIONS TO CANDIDATES 1. Write your name, index number, name of your school, date and signature in the space provided

at the top of the page.

2. The paper consists of two sections; Section 1 and Section II.

3. Answer all the questions in section I and any other five from Section II.

4. All answers and workings must be done on the question paper in the spaces provided.

5. Show all the steps in your calculations, giving your answers at each stage in the spaces below

each question.

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

7. Electronic calculators and mathematical (4-figure) tables may be used where stated.

For Examiner’s Use Only SECTION 1

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

Marks

SECTION II

Question 17 18 19 20 21 22 23 24 TOTAL

Marks


This paper consists of 18 printed pages. Candidates must check the question paper to ensure that all pages are printed as

indicted and no questions are missing.

SECTION I: (50 MARKS) Answer ALL questions in this section

1. Use logarithms correct to 4 decimal places to evaluate;

3 0.8942 x (68.22) ½

(59.350) ½ (4 marks)

2. The absolute errors of the radius and height of a cylinder are 3mm and 2mm respectively. If the actual

radius and height of a cylinder are 5 cm and 5.5 cm respectively, calculate the percentage error in the volume. (2 marks)

3. A man standing 20 m away from the foot of a vertical pole observes the top of the pole at an angle of

elevation of 300. He begins to walk along a straight line on a level ground towards the pole. Calculate

how far he walked before the angle of elevation of the top of the pole becomes 800. (4 marks)


4. Solve for x in the equation.

Log2(x – 3) + 2 = Log2(8-x) (3 marks)

5. A quantity x varies directly as the square of Y and inversely as the square root of t. Find the percentage change in t if x increases by 12% and Y decreases by 36%, give your answer correct to 4

significant figures. (3 marks)

6. The value of a new machine is shs.150000. After 5 years its value falls to shs.102000. Find the annual depreciation rate. (3 marks)


7. The position vectors of points A and B are and respectively. A point N divides

AB in the

ratio 2:3. Find the position vector of point N. (3 marks) 8. The end points of a diameter of a circle are (-1,2) and (5,8). Find the equation of the circle in the form

x2 + ax + y

2 + by + c = 0 (3 marks)

9. Solve the equation;

4sin2x = 6cosx when 0

0 x 3600 (4 marks)


10. A fruit dealer mixes two types of juices “Mango” and “Guava” to obtain 35 litres of the mixture worth Ksh.62 per litre. If “Mango” is valued at shs.68 per litre and “Guava” at Ksh.53 per litre.

Calculate the ratio in the simplest form in which the two types of Juice are mixed. (3 marks)

11. Rationalize the denominator leaving your answer in the form a + b√ where a, b and c are real

numbers.

√ tan45 + sin60 (3 marks)

12. Make Y subject of the formula (3 marks)

x = 3 K – KY2

FY2 – 1


13. (a) Expand and simplify (2 – y)6 upto the term y

3 (1 mark)

(b) Use the expansion in (a) above to find the approximate value of (1.6)6 to 2 decimal places.

(2 marks)

14. The volumes of a model and its actual figure are 72 cm3 and 9000 cm

3 respectively. Find the surface

area of the actual figure it its model was a surface area of 108 cm2. (3 marks)


15. Point P(300N,73

0E) and R(30

0N, 107

0W) are on the surface of the earth. Calculate the shortest

distance between the two points. (Radius of earth = 6370km). (3 marks)

16. Chords AB and CD intersects externally at Q. If AB = 5 cm, BQ = 6 cm and DQ = 4 cm. Find the length CQ. (2 marks)

A B

Q

D

C


SECTION II: (50 MARKS) Answer any FIVE question from this section

17. A business woman deals in two types of flour P and Q. Type P costs Kshs.400 per bag and type Q costs Ksh.350 per bag.

(a) This business woman mixes 30 bags of type P with 50 bags of type Q. If she sells the mixture at a profit of 20%, calculate the selling price of one bag of the mixture. (4 marks)

(b) She now mixes type P with type Q in the ratio x:y respectively. If the cost of the mixture is Kshs.383.50 per bag, find the ratio x:y. (4 marks)

(c) She now mixes one bag of the mixture in part (a) with one bag of the mixture in part „b‟ above. Calculate the ratio of type P to type Q flour in this mixture. (2 marks)


18. (a) Determine the interquartile range for the following set of data

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

(b) The table below shows a distribution of marks scored in a test by standard 8 pupils in Masingo Primary School.

Marks 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 71-75 76-80

No. of

pupils 1 5 10 10 19 20 20 8 4 3

Using 57 as the assumed mean mark, calculate;

(i) the actual mean for the grouped marks. (3 marks)

(ii) the standard deviation of the marks. (4 marks)


19. The table below shows the rates of taxation in a certain year.

Income in K p.a Rate of taxation in shs.per K

1 – 3900 3901 – 7800

7801 – 11700 11701 – 15600

15601 – 19,500 Above 19500

2 3

4 5

7 9

In that period, Kabwebwe was earning a basic salary of Kshs.21,000 per month. In addition, he was entitled to a house allowance of Ksh.9000 p.m and a personal relief of Kshs.1056 p.m.

(a) Calculate how much income tax Kabwebwe paid per month. (7 marks)


(b) Kabwebwe‟s other deductions per month were;

● Co-operative society contributions = shs.2000 ● Loan repayment = shs.25000

Calculate his net salary per month. (3 marks)


20. In a triangle OAB, M and N are points on OA and OB respectively such that OM:MA = 2:3 and ON:NB is 2:1, AN and BM intersect at X. Given that OA = a and OB = b

(a) Express, in terms of a and b; the vectors:

(i) BM (1 mark)

(ii) AN (1 mark)

(b) taking BX = tBM and AX = hAN where t and h are scalars, find two expressions for OX. (4 marks)

(c) find the values of t and h (4 marks)


21. (a) Using a ruler and a pair of compasses only, construct triangle ABC in which AB = 9 cm,

BC = 8.5 cm and BAC = 600. (3 marks)

(b) On the same side of AB as C,

(i) Determine the locus of a point P such that BAC = 600 (3

marks)

(ii) Construct the locus of R, inside ΔABC such that AR 4 cm. (2 marks)

(iii) Shade the region T, inside triangle ABC such that ACT BCT (2 marks)


22. A quadrilateral ABCD has vertices A(4,-4), B(2,-4), C(6,-6) and D(4,-2).

(a) On the grid provided, draw the quadrilateral ABCD. (1 mark)


(b) A1B

1C

1D

1 is the image of ABCD under a positive quarter turn about the origin. On the same grid,

draw the image of A1B

1C

1D

1 (3 marks)

(c) A11

B11

C11

D11

is the image of A1B

1C

1D

1 under a transformation given by the matrix

(i) determine the co-ordinates of A11

B11

C11

D11

(2 marks)


(ii) on the same grid, draw the quadrilateral A11

B11

C11

D11

(1 mark)

(d) Determine a single matrix that maps ABCD onto A11

B11

C11

D11

(3 marks)

23. In a game of darts, three players i.e. Masimbakosi, Avulamusi and Omariati have the following probabilities of hitting the bull‟s eye:

Masimbakosi - 0.2 Avulamusi – 0.3

Omariati – 0.15

(a) Draw a tree diagram to show all the possible outcomes. (2 marks)


(b) Find the probability that;

(i) all hit the bull‟s eye (2 marks)

(ii) only one hits the bull‟s eye (2 marks) (iii) none of them hits the bull‟s eye. (2 marks)


(iv) at most one misses the bull‟s eye (2 marks)

24. (a) The first term of an Arithmetic Progression (AP) is 2. The sum of the first terms of the AP is 156.

(i) Find the common difference of the AP. (2 marks)


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

(b) The 3rd

, 5th and 8

th terms of another AP form the first three terms of a G.P if the common

difference of the AP is 3, find; (i) the first term of the G.P (3 marks)

(ii) the sum of the first 9 terms of the G.P, to 4 s.f. (2 marks)


ANSWERS:

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KAKAMEGA SOUTH SUB-COUNTY EXAMINATIONS

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