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Name…………………………………………………… Index Number……………../……

Candidate’s Signature………………

Date…………………………………

121/2

MATHEMATICS

Paper 1

MARCH /APRIL 2012

2 ½ hours

THE LAINAKU 2012 JOINT ASSESSMENT TEST Kenya Certificate of Secondary Education MATHEMATICS

Paper 1

2 ½ hours

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 above.

3. This paper consists of TWO sections: Section I and Section II.

4. Answer ALL the questions in Section I and only 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 except

where stated otherwise.

9. This paper consists of 13 printed pages.

10. Candidates should check the question paper to ascertain that all the pages are printed as indicated

and that no questions are missing.

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



SECTION 1 (ANSWER ALL QUESTIONS)

1. Without using mathematical tables or calculators, evaluate:

3/8÷ (½-

1/3) of ¾ -

1/10 (3mks)

2. The distance between P and Q on a section of a straight road is 12km. Mwai and Muiru left points P and

Q respectively at the same time and moved towards each other at 1m/sec and 1.5m/s respectively.

Calculate a) their relative speed. (1mk)

b) The time they will take before meeting. (2mks)

3 (a)Find the value of P given that the lines 2y+x=3 and are perpendicular to each other.

(2mks)

(b) Find the angle the line makes with a positive x axis. (2mks)



4. A British tourist changes 120 sterling pounds to Kenya shillings at the rate of Kshs. 112 per

Sterling pound. Of the amount he received, he spent Ksh. 1,800 on accommodation and two

third of the reminder on entertainment. The remaining amount was converted to sterling

Pounds at a rate of 114.20 per sterling pound. How many sterling pounds did he get? (3mks)

5. Using a pair of compasses and a ruler only.

(a) Construct a triangle ABC such that AB=6cm, BC=8cm and ∠ABC=135o (2mks)

(b) Construct the height of triangle ABC in (a) above taking BC as the base and measure the height.

(2mks)

6. Simplify. (3mks)



7 Given that , find without using tables tan 15 in the form while p, q and

m are integers. (3mks)

8. Study the histogram below and use the histogram to complete the frequency table below.

(3mks)

Class boundary Frequency

0.5-2.5 2

2.5 – 4.5 6

4.5 - 6.5

6.5 - 9.5

9.5 – 13.5

13.5 – 14.5

9. Find the surface area of a sphere whose volume is 736cm3. (3mks)



10 Find the range of values of x which satisfy the following inequalities simultaneously

4x – 9 < 6 + x

8 – 3x ≤ x + 4

and represent them on a number line. (3mks)

11. The area of a rectangle with the two shorter side measuring 3cm by 4cm is changed in the ratio 2:1.

Find the area of the new rectangle. (3mks)

12. Find a quadratic equation whose roots are and , expressing it in the form ,

where a, b, and c are integers. (3mks)

13. The points A’ (3,-8) and B’ (-5,4) are the images of A and B under a transformation whose matrix is

Find the coordinates of A and B. (3mks)



14. The coordinates of P and Q are P (5,1) and Q (11,4) point M divides line PQ in the ratio 2:1 Find the

Magnitude of vector OM. (3mks)

15 Find correct to 3s.f the value of;

+ - without using a calculator. (3mks)

16. Solve for x and y (3mks)

and



SECTION II (50 Marks)

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

17. The taxation rates for income earned in a certain year were as follows:

Income Tax Rate

K£ p.a Kshs. Per £

1 – 4512 2

4513 – 9024 3

9025 – 13536 4

13537 – 18048 5

18049 – 22560 6

Over 22560 6.5

After a personal relief of Kshs.1056 per month, Mrs. Wanjau paid tax amounting to Kshs.18,152 that year.

a) How much tax would she have paid if she did not have the personal relief (2 mks)

b) Find her taxable income in K£ that year (5 mks)

c) If Mrs. Wanjau receives allowances amounting to 18% of the taxable income. Calculate his

monthly basic salary in Kshs. (3 mks)



18. A ship leaves port P for port R through port Q. Q is 200km on a bearing of 220° from P. R is 420km

on bearing of 140° from Q. Another ship leaves for S which is on a bearing of 12o and 220km from P.

a. Using the scale 1:4,000,000, draw a diagram showing the relative positions of the four ports P,

Q, Rand S (4mks)

b. By further drawing on the same diagram determine how far R is to the west of P (2mks)

c. Determine distance and bearing of R from S (2mks)

d. If the ship had sailed directly from P to R at an average speed of 74km/h, find how long it would

take to arrive at R (2mks)



19. OPQR is a trapezium in which and is parallel to with 2 T is a point

on extended so that =2:1. PT and QR intersect at x so that and

P Q

X

O R T

a. Find in terms of (2mks)

b. Express in terms of , (1mk)

c. Express in terms of , (1mk)

d. From (b) and (c) calculate the values of h and k (4mks)



e. In what ratio does T divide (2mks)

20. Complete the table below for in

a. The interval (2mks)

x -3 -2 -1 0 0.5 1 2 3

2x3 -54 -2 0.25 16

X2 9 4 0.25 1

-5x 5 0 -2.5 -5 -10

+2 2 2 2 2 2 2 2 2

y 6 0 50

b. Draw the graph of for the interval (2mks)



c. Use your graph to solve the equation (2mks)

d. Use your graph to solve equation (2mks)

e. Find the gradient of the curve at x=2 (2mk)



21. The figure below shows a solid frustrum with a rectangular base measuring 18cm by 24cm and the top

measuring 6 cm by 8cm. The slant edges are each 26cm long.

Determine:

a) Height of the original pyramid. (4mks)

b) Volume of the frustrum. (3mks)

c) Density in g/cm3 if the ssolid has a mass of 7.488kg (3mks)

22. A triangle has vertices A(-4,-1), B(-1, -3) and c(-2,-1)

a. Draw triangle ABC on the Cartesian plane (1mk)



b. Construct the image of triangle A’B’C’ of ∆ABC under reflection in the line y=-x (3mks)

c. Construct the image A”B”C” of under rotation of +90 about the origin (3mks)

d. Construct the image A”’B”’C’” of A”B”C” under enlargement scale factor -1 centre (-1,0)

(3mks)



23. A car moving at a speed of 20m/s decelerates at a uniform rate of 2m/s for 3 seconds. It then

accelerates at a rate of 2.5m/s2 for 4 seconds and finally it is brought to rest by applying brakes in

2seconds.

a. Draw a velocity time graph to represent this motion (use the space below) (5mks)

b. Use your graph to determine the distance covered in the 9 seconds (2mks)

c. Two trains travelling at 15km/h and 25km/h respectively in the same direction are such that, the

faster train passes the other in 10.8s. Find the length of each if the faster train is twice as long.

(3mks)



24. (a) Find the derivative of

y = (3x – 2x2) (5 + 4x) (3mks)

(b) A diver leaps from a diving board 32m above the surface of a swimming pool. At time t second,

his position h, above the surface of the swimming pool is given by h = 32 + 16t – 16t2.

Find:

(i) The time he took to hit the water surface. (4mks)

(ii) The velocity at which he hit the water surface. (3mks)

Documents

THE LAINAKU 2012 JOINT ASSESSMENT TEST - KCSE PAST PAPERS | KCSE … KCSE LAINAKU MOC… · · 2012-05-06 Mathematics 121/1 Turnover Page 1 of 15 Name ... SECTION 1 (ANSWER ALL