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©Borabu/Masaba North Academic Committee Mathematics 121/2 Turn Over

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Name………………………………………………………. Index No……………………………

School……………………………………………………… Signature……………………………

Date…………………………………

121/2

MATHEMATICS

PAPER 2

July/August 2010

2 ½ hrs

BORABU /MASABA NORTH DISTRICTS JOINT EVALUATION TEST – 2010

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

MATHEMATICS

PAPER 2

July/August 2010

2 ½ hrs

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.

3. The paper contains two sections: Section I and II.

4. Answer all questions in section I and strictly five questions from section II.

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

question.

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

each question.

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

8. Non- programmable silent electronic calculators and KNEC mathematical tables may be used.

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

GRAND

TOTAL

This paper consists of 16 printed pages. Candidates should check carefully

to ascertain that all the pages are printed as indicated and no questions are missing.

17 18 19 20 21 22 23 24 Total


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SECTION I

Answer all the questions in this section.

1. Solve for x in log(2x-11) – log 2 = log 3 – log x. (3mks)

2. Given that kjia 532~

and b = i – 5j + 7k. Calculate |2a + b| (3mks)

3. Find the inverse of the matrix

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52. Hence solve the equations. (3mks)

2x + 5y = 9

3x + 4y = 6

4. Find the gradient of the curve. Y = x5 + 3x2 + 5x at the point (1, 3) (3mks)


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5. Determine the two possible values of a for which.

a

dxx

x

0

2

121

1 (3mks)

6. In the figure below, O is the centre of the circle PQRS. PQ = QR and angle PSQ = 350. Calculate

the size of angle POR and PQR. (4mks)

7. A flower garden is in the form of a trapezium as shown below. Find the area of the garden in

hectares. (4mks)


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8. In the diagram below, X is the point of intersection of the chords AC and BD of the circle such

that AX = 8cm, XC = 4cm and XD = 6cm.

(a) Find the length of XB. (2mks)

(b) Given that the area of triangle AXD = 6cm2. Find the area of triangle BXC. (2mks)

9. Two grades of Kenyan coffee costing sh. 200 and sh. 250 per kg respectively are mixed in the

ratio 3:5 by weight. The mixture is then sold at ksh. 240 per kg. Find the percentage profit on the

cost. (3mks)

10. Find the area under the graph y = 3x2 + 4 between x = 0 and x = 2 using 4 strips and the mid-

ordinate rule. (4mks)


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11. Make P the subject of the formula. PxP QXy (3mks)

12. Expand (1 + x)5

Hence use the first 4 terms of the expansion to estimate (1.04)5 correct to 4 decimal places.(2mks)

13. The nth term of a sequence is given by the general term 3n - 1

(a) Write down the first four terms of the sequence. (1mk)

(b) Find the value of the 20th term. (2mks)

14. An arc of a circle 9.42cm substends an angle of 107.930 at the centre of the circle. Calculate the

diameter of the circle to the nearest 1cm. (Take = 3.142) (3mks)


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15. A town P is 200km west of Q, town R is at a distance of 80km on a bearing of 0490 from P. Town

S is due East of R and due North of Q. Determine the bearing of S from P. (3mks)

16. A business man borrowed a certain amount of money from a bank which charged simple interest

at the rate of 18% per annum. At the end of 7 months, he had to pay sh. 5460 as interest. Find how

much money he had borrowed. (2mks)


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SECTION II

Answer only five questions in this section in the spaces provided.

17. In the year 2004, a farmer took a sample of 50 maize cobs to the A.C.K show. The lengths of the

maize cobs were measured and recorded as shown in the table below.

Length in CM Number of cobs.

8 -10 4

11 – 13 7

14 – 16 11

17 – 19 15

20 – 22 8

23 – 25 5

Taking an assumed mean (A) to be 15, calculate

(a) The mean (4mks)

(b) (i) The varience (4mks)

(ii) The standard deviation (2mks)


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18. Two towns A and B lie on the same parallel of latitude 600N if the longitude of A and B are 420W

and 290E respectively.

(a) Find the distance between A and B in nautical miles along the parallel of latitude. (2mks)

(b) Find the local time at A if at B is 1.00pm. (2mks)

(c) Find the shortest distance between A and B along the earth’s surface in km. (Take = 22/7

and R = 6370km) (3mks)

(d) If C is another town due south of A and 10010km away from A, find the coordinate of C.

(3mks)


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19. In the figure below PQR is a tangent at Q and RST is a straight line, angle QTU = 500, angle

UTW = 330 and angle TRQ = 250.

(i) Calculate angle TSQ (3mks)

(ii) Calculate the value of angle TSW (3mks)

(iii) Calculate angle TUQ (2mks)

(iv) Calculate angle PQW (2mks)


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20. In chemistry form 4 class, 1/3 of the class are girls and the rest boys. 4/5 of the boys and 9/10 of

the girls are right handed while the rest are left handed. The probability that a right – handed

student breaks a conical flask in any practical session is 3/10 and the corresponding probability

for a left – handed student 4/10. The probabilities are independent of the student’s sex.

(a) Represent the above information on a tree diagram with independent probabilities. (2mks)

(b) Determine the probability that student chosen at random from the class is left handed and does

not break a conical flask in simplest form. (3mks)

(c) Determine the probability that a conical flask is broken in any chemistry practical session in

simplest form. (3mks)

(d) Determine the probability that a conical flask is not broken by a right handed student in

simplest form. (2mks)


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21. A farmer has 50 acres of land. He has a capital of shs 2400 to grow carrot and potatoes as cash

crops. The cost of growing carrots is shs 40 per acre and that of growing potatoes is shs. 60 per

acre. He estimates that the respective profits per acre are shs. 30 (on carrots) and shs 40 (on

potatoes). He plants x acres of carrot and y acres of potatoes.

(a) Form suitable inequalities to represent this information. (3mks)

(b) By representing this information on a graph determine how many acres he should grow each

crop for maximum profit. (5mks)


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(c) Find the maximum profit. (2mks)

22. A particle P moves in a straight line so that its velocity, V m/s. at time t 0 seconds, V is given

V = 28 + t – 2t2. Find

(a) The time when P is momentarily at rest. (3mks)

(b) The speed of P at the instant when the acceleration of the particle is zero. (4mks)

(c) Given that P passes through the point O on the line when t = 0, find the distance of P from O

when P is momentarily at rest. (3mks)


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23. X, Y and Z are three quantities such that x varies directly as the square of Y and inversely as the

square root of Z.

(a) Given that X = 12 and Y = 24 and Z = 36, find X when y = 27 and z = 121. (3mks)

(b) If Y increases by 5% and Z decreases by 19%, find the percentage increase in x. (5mks)

(c) If y is inversely proportional to the square root of X and X = 4 when y = 3. Calculate the value

of X when y = 8. (2mks)


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24. (a) Complete the following table for the equation y = 2x2 + x – 6 (2mks)

X -3 -2 -1 0 -1 2 3

2x2 8 2 2 18

X -2 -1 1 3

-6 -6 -6 -6 -6

y = 2x2+x-6 0 -5 -3 15

(b) On the grid provided draw the graph y = 2x2 + x – 6 for -3x3.

Take the scale: 2cm for 1unit on the x-axis and 1cm for 1unit on the y-axis. (4mks)


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(c) (i) Use your graph to solve the equation 2x2 + 3x – 4 = 0 (2mks)

(ii) Find the range of values of X for which y -4. (2mks)


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END

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121/2 MATHEMATICS PAPER 2 BORABU /MASABA …magerezaacademy.sc.ke/wp-content/uploads/2017/03/MATHS-Q... · 2017-03-29 · 4. 5Find the gradient of the curve. ... In the figure below,