Bondo-Rarieda Districts Mocks Examination - 2008

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121/2

MATHEMATICS

Paper 2

July / August 2008

2 ½ hours

BONDO-RARIEDA DISTRICTS MOCKS EXAMINATION - 2008

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

121/2

MATHEMATICS

Paper 2

July / August 2008

2 ½ hours

INSTRUCTIONS TO CANDIDATES:

· Write your name and index number in the spaces provided at the top of this page.

· The paper contains Two sections: Section I and Section II.

· Answer ALL the questions in Section 1 and any FIVE questions from Section II

· All working and answers must be written on the question paper in the spaces provided below each question.

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

· Non-programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.

For Examiner's use only

Section I

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

Section II

17 / 18 / 19 / 20 / 21 / 22 / 23 / 24 / Total

Grand Total

This paper consists of 16 printed pages

Candidates should check the question paper to ensure that all the printed pages are printed as indicated and no questions are missing.

SECTION 1(50 MARKS)

1. Use logarithms to evaluate (4mks)

2. Factorize completely the expression

8x2 – 2y2 + 12y – 18 (2mks)

3. The matrices A, B and M are such that , B = and MA = B.

a) Determine matrix M. (2mks)

b) Given that n is the smallest positive integer such that Mn= k determine n and k. (2mks)

4. Given that a = 7.6cm, b=2.4cm and c=4.0cm find the maximum value of . (3mks)

5. The data below shows marks scored by 8 form four students in Siaya-Bondo-Rarienda Joint Mathematics contest.

44, 32, 67, 52, 64, 28, 39, 46

Calculate the mean absolute deviation. (4mks)

6. Make L2 the subject of the formula. (3mks)

7. Write down the first five terms of the expansion of . Using the first three terms of the expansion find the value of (1.01)5 to four decimal places. (4mks)

8. The figure below shows a circle centre O with a quadrilateral ABCD drawn in it, AC is the diameter.

Determine the size of (3mks)

a) ÐBOC

b) ÐBCO

c) ÐBCD

9. A bag contains 5 white balls. 3 black balls and 2 green balls. A ball is picked at random from the bag and not replaced. In three draws find the probability of obtaining white, Black and Green in that order. (2mks)

10. Christine deposited Ksh.50,000 in a financial institution in which interest is compounded quarterly. If at the end of the second year she received a total amount of Ksh.79,692.40, calculate the rate of interest per annum. (3mks)

11. The coordinates of two points on the Earth’s surface are P(600N, 400E) and Q (600N, 200W). Calculate, in nautical miles, the distance from P to Q along latitude 600N. (3mks)

12. a particle moves in a straight line such that its distance from a fixed point O is given by

S= at2 + bt + 3(a , b are constants). If the particle is accelerating uniformly at 10m/s2 and attains a velocity of 20m/s in 4 seconds determine the values of a and b. (3mks)

13. Given a line segment AB of length 6cm, construct the locus of a variable point N such that

Ð ANB = 1200. (3mks)

14. A quantity Y is partly constant and partly varies inversely as X. Given that Y=10 when X=1.5 and Y=20 when X = 1.25 find the value of Y when X=0.5. (3mks)

15. Two perpendicular lines meet at the point (4,5). If one of the lines passes through the point

(-2,1), determine the equation of the second line in the form ax + by + c = 0. (3mks)

16. Determine the turning point of the curve y=4x3 – 12x + 1. State whether the turning point is a maximum or a minimum point. (3mks)

SECTION II 50 MARKS

ANSWER ANY FIVE (5) QUESTIONS

17. a) The mth term of a sequence is given as 3m+1 – 2m. Find the 5th term of the sequence. (2mks)

b) Atieno was employed by an NGO on contract for a certain number of years. Her basic annual salary for the first year was Ksh.580,000 and her last basic annual salary was Ksh.630,400. By the end of the contract she had earned a total basic salary of Ksh.4,841,600. If the annual increment was constant, calculate ;

i) the period of the contract. (4mks)

ii) the annual increment. (2mks)

iii) the annual basic salary in the third year of the contract. (2mks)

18. a) Complete the table below for the function y= -x3 + 2x2 – 4x + 2.

x / -3 / -2 / -1 / 0 / 1 / 2 / 3 / 4
-x3 / 27 / 8 / - / 0 / - / -8 / - / -
2x2 / 18 / 8 / 2 / 0
-4x / - / 8 / 0 / -16
2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2
y / 26 / 2 / -6 / -46

Draw the graph of y= -x3 + 2x2 – 4x + 2 for -3 x 4. (3mks)

c) Use the graph to solve the equation -x3 + 2x2 – 4x + 2 = 0. (1mk)

d) By drawing a suitable line on the graph solve the equation -x3 + 2x2 – 5x + 3 = 0. (3mks)

19. A company employee earns a monthly basic salary of Ksh.25,000 and is also given a taxable allowances amounting to Ksh.10,480. Using the table of taxation below.

Monthly taxable income / Rate in Ksh / Pound
1 – 4350
4351 – 8900
8901 – 13455
13451 – 18005
18006 and above / 2
3
4
5
6

a) Calculate the employee’s taxable income. (2mks)

b) If the employee is entitled to a personal tax relief of Ksh. 800 per month, determine the net tax. (5mks)

c) If the employee was given 40% increase in his income, calculate the percentage increase in his income tax. (3mks)

20. The figure below shows a cuboid ABCDEFGH. Given that AB = 12cm, BC=8cm and BF = 4cm.

a) State the projection of AG on the plane EFGH. (1mk)

b) Determine the angle between the line AG and the plane EFGH. (3mks)

c) Given that M is the mid-point of FG, determine the angle between the planes AMD and ABCD. (3mks)

d) Find the angle between the skew lines AG and BC. (3mks)

21. In the figure below E is the mid-point of BC. AD : DC = 3:2 and F is the meeting point of BD and AE.

If AB = and AC = .

(i) Express BD and AE in terms of and . (3mks)

(ii) If BF = tBD and AF = nAE find the values of t and n. (5mks)

(iii) State the rations in which F divides BD and AE. (2mks)

2. ABC is a triangle with vertices A( 2, -1) B (4, -1) and C(3,2).

a) A1B1C1 is the image of ABC under the transformation represented by the matrix , determine the coordinates of A1B1C1. (2mks)

b) On the grid provided draw triangle ABC and its image A1B1C1 and describe the transformation fully. (3mks)

c) A11B11C11 is the image of A1B1C1 under reflection along the line y=0. State the co-ordinates of A11B11C11 and draw it on the same axes. (2mks)

d) Determine the matrix representing a single transformation that maps DABC onto DA11B11C11. (3mks)

23. Part of a farm is to be planted with sugar cane and another part with beans, observing the following restrictions.

Sugarcane / Beans / Maximum available
Labour per hectare (days) / 4 / 3 / 32
Cost of labour per hectare(Shs) / 10 / 20 / 180
Cost of fertilizer per hectare (shs) / 40 / 10 / 240

a) Assuming that sugar cane is on x hectares and beans on y hectares, write down all the inequalities that will satisfy the restrictions given on the table above. (4mks)

b) Plot the inequalities obtained above on the grid provided. From your graph; find;

i) the greatest numbers of hectares of sugar cane and beans that can be planted. (4mks)

(ii) The area of each crop that should be planted to give a maximum profit if sugar cane gives a profit of sh. 80 per hectare and beans sh. 40 per hectare. (1mk)

c) State the maximum profit. (1mk)

24. A bus left Nairobi at 8.00a.m and traveled towards Kisumu at an average speed of 80km/h. At 8.30a.m a car left Kisumu towards Nairobi at an average speed of 120km/h. Given that the distance between Nairobi and Kisumu is 400km. Calculate

a) The time the car arrived in Nairobi. (2mks)

b) The time the two vehicles met. (4mks)

c) The distance from Nairobi to the meeting point. (2mks)

d) The distance of the bus from Kisumu when the car arrived in Nairobi. (2mks)