Nyando District Joint Evaluation Test - 2008

Name: . …………………………………………………School:…………………………

Index No. ………………………………………………

NYANDO DISTRICT JOINT EVALUATION TEST - 2008

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

121/1

MATHEMATICS

Paper 1

July / August 2008

2 ½ Hours

INSTRUCTIONS TO CANDIDATES

1. Write your name and index number in the space provided at the top of this page.

2. The paper contains TWO sections; section I and section II

3. Answer all the questions in section I and ANY FIVE questions from section II

4. Show all the steps in your calculations; giving your answers at each stage in the spaces provided below each question.

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

6. Non-programmable silent electronic calculators and KNEC mathematical tables maybe used.

For Examiners use only

Section 1

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 12 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 I ( 50 MARKS)

Answer all the questions in this section

1.Use tables of cubes, cube roots and reciprocals to find the value of

(3mks)

2.Two translations T1 and T2 are represented by the vectors and respectively. Triangle ABC whose vertices are at A(2,3) B(4,6) and C(3,5) is mapped onto triangle A1B1C1 under the combined translationT2T1. Determine the co-ordinates of A1B1C1. (3mks)

3.The cost of five pineapples is the cost of ten mangoes. Three pineapples and two mangoes cost shs. 86. How much will one pay for buying seven pineapples and eight mangoes. (3mks)

4.Susan can do some piece of work in six hours. Atieno can do the same job in 10 hours while Jane can do it in 12 hours. If the three girls work together for two hours then the remaining work is left for Susan to complete, determine how long it would take Susan to complete the work. (3mks)

5.The diagram below shows a simple tent in the shape of a cube with a right pyramid top.

(a) Draw the net of the tent.(2mks)

(b) Determine the surface area of the material required to make the net.(2mks)

6.Simplify leaving your answer in the form p/q where p and q are integers. (3mks)

7.(a) Solve for x

.(2mks)

b) Illustrate your solution in (a) above on a number line.(1mk)

8.In the diagram below, ABCD is a parallelogram. AD is produced to E and BE and CD meet at F.

If angle DEF=250 and angle BFD=700, find the size of angle ABF.(3mks)

9.Solve for x in the equation.

Log3(x + 23) – log3(log264) + 1 = log3( 9 – x)(4mks)

10.In the figure below, ADC is a chord of a circle centre O passing through A,B and C. BD is a perpendicular bisector of AC. AD=3cm and BD = 1cm.

Find the perimeter of the figure to 1 decimal place.(4mks)

11.A salesman earns a basic salary of shs.10,800 per month. In addition she is also paid a commission of 15% for sales above 85,000. In a certain month, she sold goods worth shs.215,000 at a discount of 5 ½ %. Calculate his total earnings that month. (3mks)

12.Simplify(3mks)

13.Train A and B, moving in the same direction, are 10 metres apart. Train A is 3 metres long and moves at 100km/h while Train B is 10 metres long and moves at 50km/h. Find how long it will take train A to overtake train B. (3mks)

14.Find the value of  in the equation.(3mks)

for 0 360.

15.Given that 0.3 x 0.5, 80y 100 and 4.4 Z 12.4, find the maximum value of (2mks)

16.Evaluate(3mks)

3 – 2 ¼ + 1 5/8 – ( 3 ½ - 1 ¾ )

SECTION B

Answer any FIVE questions only.

17.The diagram below shows a circle centre O and of radius 2.1cm. The lines AB and DB are tangent to the circle at points A and D respectively and intersect at point B. The line OB cuts the circle at C and angle AOB = 450

Calculate

(a) The area of the minor sector OACD.(3mks)

b) The area of quadrilateral OABD.(4mks)

c) The area of the shaded region correct to two significant figures.(3mks)

18.a) Complete the table for y = 2x3 +x2 – 5x + 2 for the interval -3 x 3.(2mks)

x / -3 / -2 / -1 / 0 / 1 / 2 / 3
2x3 / -16 / -2 / 0 / 2 / 16
x2 / 9 / 4 / 1 / 0 / 1 / 4 / 9
-5x / 10 / 5 / 0 / -5 / -10
2 / 2 / 2 / 2 / 2 / 2 / 2 / 2
y / -28 / 0 / 50

b) (i) Draw the graph of y = 2x3 +x2 – 5x + 2 for the interval -3 x 3.(3mks)

(ii) Use your graph to solve the equation

2x3 + x2 – 5x + 2 = 0.(2mks)

(iii) By drawing a suitable straight line on the same axes, solve the equation.

2x3 + x2 + 11x – 10=0.(3mks)

19.a) Quadrilateral ABDC has its vertices at A(-5,4), B(-3,4) C(-5,3) and D(-4,3). The quadrilateral is mapped onto A1B1C1D1 by reflection along the line y=0. Determine the co-ordinates of A1B1C1D1 and draw the two quadrilaterals on the same Cartesian plane. (3mks)

b) A1B1C1D1 is mapped onto A11B11C11D11 by positive half turn about the origin. Draw A11 B11C11D11 on the same Cartesian plane and give its co-ordinates. (2mks)

c) On the same Cartesian plane, draw quadrilateral A111B111C111D111, the image of quadrilateral A11B11C11D11 under enlargement scale factor -2 centre (4,0) (2mks)

d) Name the quadrilateral that are

(i) Directly congruent

(ii) Oppositely congruent.(3mks)

20.In the triangle OAB below, OA=aOB =b AND OC = 3/2OA. M divides OB in the ratio 3:2

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

(i) AB.(1mk)

(ii) MC(1mk)

b) Given that MN = hMC and BN = KBA, express vector MN in two ways and hence, find the value of h and k. (6mks)

c) Show that the points M,N and C are collinear.(2mks)

21.a) In a safari rally, drivers are to follow route ABCDA. B is 250km from A on a bearing of 0750. C is on a bearing of 1100 from A and 280km from B. The bearing of C from D is 0400 and a distance of 300km. By scale drawing, show the position of the points A,B,C and D.

(4mks)

b) Determine

(i) The distance of A and C.(2mks)

(ii) the bearing of B from C.(1mk)

(iii) the distance and bearing of A from B.(3mks)

22.The graph below shows a semi-circle of radius 3cm.

a) Determine the equation of the circle writing it in the form y=; where a,b and c are constants. (3mks)

b) Estimate the area of the shaded region using Trapezium rule with 4 trapezia, giving your answer in 2d.p (5mks)

c) Find the area of the unshaded region. (Take  = 3.142)(2mks)

23.The diagram below shows a histogram representing marks obtained in a certain test.

a) Develop a frequency distribution table for the data.3mks

b) Estimate the quartile deviation.4mks

c) Calculate the mean.3mks

24.Use a ruler and a pair of compasses only in this question.

a) Construct a line AB of length 8cm. On both sides of line AB, construct the locus of point P such that APB = 750.

b) On one side of AB only, construct the locus of a point P1 such that the area of triangle AP1B=17.6cm2. Describe the locus of P1.

c) Let the locus of P1 meet the locus of P at M and N respectively. Name the quadrilateral ABNM.