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121/2

MATHEMATICS

Paper 2

March/April 2014

Time: 21/2 Hours

Keny

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

MATHEMATICS Paper 2

March/April 2014 Time: 2

1/2 Hours

INSTRUCTIONS TO THE CANDIDATES

▪ Write your name and index number in the spaces provided above

▪ This paper contains two sections; Section 1 and Section 11.

▪ Answer all the questions in section 1 and only five questions from Section 11

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

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

▪ Calculations and KNEC Mathematical tables may be used EXCEPT where stated otherwise.

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

▪ This paper consist of 24 questions

FOR EXAMINERS’S USE ONLY

Section 1

Questio

n

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

l

Marks

Section 1I GRAND TOTAL

Questio

n

17 18 19 20 21 22 13 24 Total

Marks


This paper consists of 16 printed pages. Candidates should check to ascertain that all pages are printed as indicated and that no questions are

missing.

1. Given that 4x2 + 25x +k is a perfect square, determine the value of k. (3mrks)

2. A student scored the following marks in an exams: 43,55,40,48,60,54,48,60,56 and 74.

Determine the quartile deviation. (3mrks)

3. Make x the subject of the formula in the equation. (3mrks)

y = bx

√


4. Solve the equation

2logx-log (x-2) =2log3 (3mrks)

5. Simplify the expression √ leaving your answer in the √ where a,b, and c

are integers. √ + √

6. (a) Expand (1-x)5 (1mrk)

(b) Use the expression in (a) up to the term x2 to approximate the value of (0.98)

5. (2mrks)

7. Find the value of y in the figure below. (2mrks)


8. A customer deposited sh. 20,000 in a saving account. Find the accumulated amount after two

years if the interest was paid at 16% per annum compounded semi –annually. (3mrks)

9. The equation of a circle is given by x2 + 4x +y

2 – 2y -4=0. Determine the center and radius of

the circle. (3mrks)

10. (a) Find the inverse of the matrix 2 2 (2mrks)

3 2


(b) Hence solve the simultaneous equations below. (2mrks)

2x + y =21

3x + 2y=34

11. Two taps A and B can each fill an empty tank in 3 hours and 2 hours respectively. A drainage

tap R can empty the full tank in 6hours. Tap A and R are opened for 5hours then closed

(a) Determine the fraction of the tank that is still empty. (2mrks)

(b) Find how long it would take to fill the remaining fraction of the tank if all the three taps

are opened. (2mrks)

12. From the top of a cliff the angle of depression of a toy is 24o. The raft sails 50m towards the

cliff and the angle of depression is now 83o. Find the height of the cliff to 3 significant

figures. (3mrks)


13. A quantity T is partly constant and partly varies as the square root of S.

(a) Using constant a and b write down the equation connecting T and S. (1mrk)

(b) If S = 16 when T =24 and S =36 and T =32, find the values of the constants a and b.

(2mrks)

14. The third term of geometric sequence is 144 and the sixth term 486. Find the value of:

(a) The common ratio (3mrks)

(b) The first term (1mrk)

15. A point P divides AB in the ratio 7:-5 where A (2 , -3,4) and B (-4, 7, -2). Find the

coordinates of P. (3mrk)


16. The three sides of a triangle are given as 6.4cm, 4.6cm and 6.8 cm . Determine the

percentage error in estimating the perimeter of the triangle. (3mrks)

SECTION B

Answer only five questions

17. The table below shows the rate at which income tax is charged for all income earned in a

month in 2007.

Taxable Income p.m (Kє) Rate in % per Kє

1 -236 10%

237 -472 15%

473 -708 20%

709 – 944 25%

945 and over 30%


A total of Ksh. 12,000 is deducted from Mr. Rono’s monthly salary . He is entitled to a hous

allowance of Ksh. 6,000 and a person relief of Ksh. 1064 month. Every month he pays the

following.

(i) Electricity bill shs.680

(ii) Water bill shs. 460

(iii) Co-operative shares shs. 1280

(iv) Loan repayment Ksh. 5000

(a) Calculate his P.A.Y.E (2mrks)

(b)Calculate his monthly taxable income . (6mrks)

(c) Calculate his basic salary per month (2mrks)

18. The table below shows the masses in kilograms of 50 form 4 students in a school.

Mass 25-34 35-44 45-54 55-64 65-74 75-84 85-94

No. of students 3 6 16 12 8 4 1

(a) State the modal frequency. (1mrk)


(b) Draw a cumulative frequency curve of the data. (2mrks)

(c) Use your graph to estimate

(i) The median (1mrk)

(ii) The quartile deviation (3mrks)

(iii) The 9th

decile (1mrk)

19. Triangle PQR on the grid has vertisces P( 5,5) Q(10,10) R (10,5)

(a) Find the co-ordinates of the points P’ Q’ and R the images PQR under transformation m

whose matrix is (2mrks)

-0.6 0.8

0.8 0.6


(b) Given that M is a reflection

(i) Draw the triangle P’Q’R’ and the mirror line of the reflection. (2mrks)

(ii) Determine the equation of the morrior line of the reflection (1mrk)

(c)Triangle P’’ Q’’ R’’ is the image of triangle P’ Q’ R’ under reflection N where is a reflection in

the y-axis.

(i) Draw triangle P’’ Q’’ R’’ (1mrk)

(ii) Determine a 2x2 matrix equivalent to the transformation NM. (2mrks)

(iii) Describe fully a sinlge transformation that maps triangle PQR onto triangle P’’ Q’’ R’’.

(2mrks)

20. 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=b and AC=c


(a) Express the following in terms of b and c

(i) BD (2mrks)

(ii) AE (2mrks)

(b) If BF =t BD =AF=n AE, find the value of t and n (5mrks)

(c) State the ration BD:BF (1mrk)

21. Two variables x and y are related by the y=Kax where a and k are constants . The values of x

and y are given in the table below.

X 2 0 7 12 4 9 5

Y 286 256 385 525 316 437 339

(a) Write the linear equation showing the linear relationship between x and y. (1mrk)

(b) By drawing a suitable straight line graph ,find the values of k and a. (7mrks)


(c) Establish the relationship between x and y. (2mrks)

22. (a) Complete the table below, giving the values correct to 2 decimal places. (2mrks)

xo 0

o 30

o 60

o 90

o 120

o 150

o 180

o 210

o 240

o 270

o 300

o 330

o 360

o

Sin2xo 0 0.87 -0.87 0 0.81 0.87 0

3cosc-2 1.00 0.60 -2.00 -3.5 -4.60 -.05 1

(b) On the grid provided draw graphs of y=sin2x and y =3cos x-2for 0o ≤ x≤ 360

o on the

same axes. Use scale of 1cm to represent 30o on the x-axis and 2cm to represent 1 unit on

the y-axis. (5mrks)


(c) Use the graph in (b) to solve the equation 3 cos x-sin2x=2 (2mrks)

(d) State the amplitude of y=3cosx -2 (1mrk)

23. For this equation, use a ruler and a pair of compasses only

(a) In triangle ABC, AB =10cm, BC =6.4cm BAC=30o and angle ABC is obtuse.

Construct the triangle ABC. (2mrks)

(b) On the same diagram above, show the locus of point R such that R lies on the AC and is

equidistant from C and B. Measure RB. (2mrks)


(c) Drop a perpendicular from R to line AB. Mark x, the point intersection. Measure Ax

(2mrks)

(d) A variable point T lies within the triangle ABC and satisfies the following conditions

● RAT ≤ BAT

● CT≥TB

● The area of triangle BTC 6.4cm2

By shading the unwanted regions, show the location of T. (2mrks)

24. A box contains 3 brown, 9 pink and 15 white clothes pegs. The pegs are identical except t for

the colour

(a) Find the probability of picking

(i) A brown peg. (1mrk)

(ii) A pink or white peg (2mrks)


(B) Two pegs are picked at random, one at atime without replacement. Find the probability

that:

(i) A white peg and a brown peg are picked. (3mrks)

(ii) (ii) Both pegs are of the same coluor (4mrks)


ANSWERS:

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