THE LAINAKU JOINT ASSESSMENT

Name…………………………………………………… 

Index Number……………../…… 

Candidate’s Signature……………… 

121/2 

MATHEMATICS 

Paper 2 

MARCH/APRIL 2012 

2 ½ hours 

Date………………………………… 

THE LAINAKU JOINT ASSESSMENT 

Kenya Certificate of Secondary Education 

MATHEMATICS 

Paper 2 

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 15 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 

© The Lainaku Joint Assessment www.kcse-online.info 

Mathematics 121/2 Turnover Page 1 of 15

SECTION I 

50 MARKS 

1. Use logarithm to four decimal places to evaluate:- ( 4 marks ) 

2. Expand upto the term with . Hence find the value of correct to 3s.f. (4mks) 

2 2 3 

3. Given that − = a + b c . Find the values of a, b and c. (3mks) 

1+ 3 1− 

3 



4. Make Q the subject of the formula below . ( 3 marks ) 

5. Find the radius and the 

centre of a circle whose equation is 2x 2 + 2y 2 – 6x + 10y + 9 = 0 

(3marks) 

6. Two integers are selected at random from a set of integers numbered 1 to 6 and another set of 

integers numbered 7 to 9, and the outcome noted down as ordered pair. Draw a probability space 

showing the possible outcome 

(1 mks) 

hence 

a. Find the probability of getting an outcome which has 

i. Two odd numbers 

ii. Two even numbers 



iii. An odd and an even number 

(3 mks) 

7. Given below are three points A, B and C. Locate point D 

such that AD=BD =CD. Construct the locus of a point P whose distance from D is always =AD 

(3mks) 

. C 

.B 

.A 

8. A rectangle measures 10cm by 15cm to the nearest centimeter. Find the percentage error in its area. (3 mks) 

9. Shown below are two intersecting chord at point N of a circle with Centre O and a radius of 5cm. Find the 

length ON. 

(3 mks) 



10. The cost of maize flour and millet flour is Ksh.45 and Khs.56 respectively per kilogram.. Calculate the ratio in 

which they were mixed if a profit of 20% was made by selling the mixture at Ksh.66 per kilogram. (3mks) 

11. Two places A and B are at and respectively. Calculate the shortest distance in 

nautical miles between A and B. 

(2mks) 

12. Solve for in (3mks) 



13. Find the inequalities that define the region R in the diagram below. ( 3 marks ) 

14. Three bells P, Q and R are programmed to ring after an interval of 15 minutes, 25 minutes and 50 

minutes respectively. If they all rang together at 6.45 am, how many times will they have rang 

together by 4.45 pm? (3 Mks) 

15. A customer deposited sh. 20,000 in a savings account. Find the accumulated amount after two years. 

If the interest was paid at 16% per annum compounded semi-annually. 

(3mks) 



16. The following is a section of a figure which has a rotation order four. Complete the figure. ( 3 

marks ) 

17. In the figure below,PQR is a tangent to the circle at Q. 

Find the following angles, giving reasons for each answer. 



(a) SVT: (2mks) 

(b) SQR: (2mks) 

(c) VQT: (3mks) 

(d) QSR: (3mks) 

18. The fourth ,eighth and sixteenth terms of an arithmetic progression (A.P) are the second , third and 

fourth terms of a geometric progression (G.P). If the common difference of the A.P is 3, find 

(a) The common ratio of the G.P. ( 5 marks ) 



(b) The last term of the A.P given that there are twenty terms. ( 2 marks ) 

(c ) The sum of the first ten terms of the G.P. (3 marks ) 

19. A triangle has vertices of A (2, 3) B (2, 1) and C(6, 1). It is mapped onto triangle 

A 1 B 1 C 1 by a transformation matrix 

(a) Plot the object ABC and the image triangle a A 1 B 1 C 1 on the Cartesian plane below. ( 3 marks ) 

(b) On the same axis plot triangle A 11 B 11 C 11 is the image of triangle A 1 B 1 C 1 under a reflection in the 

line x = 0. Plot the image triangle A 11 B 11 C 11 . ( 2 marks ) 

(c )Triangle A 11 B 11 C 11 is transformed by matrix onto triangle A 111 B 111 C 111 .Plot the 

image triangle A 111 B 111 C 111 hence or otherwise find the area of image triangle A 111 B 111 C 111 . 

( 3 marks ) 



(d) What single transformation matrix maps triangle ABC onto A 111 B 111 C 111 ? ( 2 marks ) 

20. ABCDEFGH is a cuboid with AB = BC = 16cm and CH = 20cm. M, N and O are the midpoints 

of DE, BC and AC respectively. 

E 

H 

F 

M • 

G 

20cm 

D 

C 

• • 

O 

N 

A 

16cm 

B 



Calculate 

(a) the length EN. (2mks) 

(b) the length BM. (2mks) 

(c) the angle between the line EN and the plane ABCD. (3mks) 

(d) the angle between the plane AMC and the plane ABCD. (3mks) 

21. On some day, Mr. Makori bought some oranges worth ksh. 45. On another day of the same week, Mrs 

Makori spent the same amount of money but bought the oranges at a discount of 75 cents per orange. 

(a)If Mr. Makori bought an orange at sh x, write down a simplified expression for the total number of 

oranges bought by the two in the week. 

(3mks) 



(b If Mrs. Makori bought 2 oranges more than her husband, find how much each spent on an orange. 

(5mks) 

(c) Find the number of oranges bought for the family that week. 

(2mks) 

22. The table below shows marks scored by 50 students in a Mathematics class. 

Marks 01-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 

Number of 

students 

1 3 4 5 8 10 10 6 2 1 

(b) Draw a cumulative frequency curve (ogive curve). (4mks) 



From your graph:- 

(i) Estimate the median mark. 1mk) 

(ii) Find the quartile deviation. (3mks) 

(iii) If 60% of the students are to pass, estimate the pass mark. (2mk) 

23. A varies directly as the square of B and inversely as the square root of C. 

a. Find A in terms of B and C. (2 marks) 



. Find A when (2 marks) 

c. If B is increased by 30% and C decreased by 36% find the percentage change in A (6 marks) 

24. (a) Using a scale of 1cm represents on the x-axis and 4cm represents I unit on the y-axis draw the 

graphs of y = ½ sin 2x and y = sin x for 0 ≤ x ≤ 360 on the same set of axes 

(7mks) 

x 

½ sin 2x 0.00 0.43 0.00 -0.43 0.43 0.00 -0.43 

sin x 0.00 0.5 0.87 0.00 -0.87 -0.87 0.00 



(b) Use your graph to solve the equation 

Sin 2x = 2 sin x. 

(3 marks)

THE LAINAKU JOINT ASSESSMENT

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