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121/2 Mathematics Question Paper
121/2 Mathematics
Course:Mathematics
Institution: Form 4 Mock question papers
Exam Year:2010
NAME………………………………………………INDEX NO………………….….DATE…………..….….
SCHOOL:…………………………………………..……SIGNATURE………………..………………………
121/2
MATHEMATICS
PAPER 2
JULY / AUGUST, 2010
2½ HOURS
LAICOMET
Kenya Certificate of Secondary Education 2010
121/2
MATHEMATICS
PAPER 2
JULY / AUGUST 2010
INSTRUCTIONS TO CANDIDATES
1. Write your name and index number in the spaces provided at the top of this page.
2. This paper consists of two sections: Section I and Section II.
3. Answer all 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 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 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
17 18 19 20 21 22 23 24 Total
Grand
Total
This paper consists of 16 pages. Candidates should check the question paper to ensure that all the pages are printed as indicated and no questions are missing.
SECTIONI (50 Marks):
Answer all questions in this section
1. Use logarithm tables to evaluate the following correct to 4 s .f (3mrks)
2. is a right – angled triangle
The ratio of Sin ? to tan ? is . Find the value of y. (3mks)
3. If State the values of the rational numbers a and b. (3mks)
4. Wanjiku can plough a piece of land in 3 days while Chebet can plough the same piece in 5 days. Find how long they’d take working together. (2mrks)
5. Find the number of terms that will give a sum of 800 in the series
(2mks)
6. A flower garden is in the form of a trapezium shown below. Find the area of garden in m2 (4mks)
7. In an examination taken by 50 candidates , the following results were obtained
Marks
No. of candidates
Calculate the mean mark (3mks)
8. In this figure and and EF= 18cm
Calculate the lengths
a) ( 2mks)
b) ( 2mks)
9. a) Expand ( (2mks)
b) Use the first four terms of your expansion to find the value of 0.994 (2mks)
10. Given cos 2? = 1 – 2sin2?, solve simultaneous equation
y = cos 2?
y = sin ? for 00 < ? < 3600 (4mks)
11. In the figure below, the area bounded by the curve, the lines x = -3, x = 2 and the x- axis is 35 square units.
Find the area of shaded region (2mks)
12. In the figure below , AB is a tangent to the circle IS a straight line. Angle ABC=300,
and . Calculate , hence the area of the triangle . (4mks)
13. Find the area of a regular hexagon of side . (4mks)
14. Find the radius and the co-ordinates of the centre of a circle whose equation is given as
(3mks)
15. A quantity T is partly constant and partly varies as the square root of S.
a) Using constants a and b, write down an equation connecting T and S (1mk)
b) If when , and ,when , find the values of the constants a and b
(2mks)
16. A particle moves in a straight line such that the distance S metres , travelled after time , t seconds is given by ;
Find the acceleration of the particle at (3mks)
SECTION II (50 Marks)
Answer only FIVE questions from this section
17. VABCD below is a square based right pyramid whose edges are all equal to 10 cm . M and N are the mid points of BC and CD respectively
c) Calculate
i) Volume of the pyramid (4mks)
ii) Angle (4mks)
d) Sketch the net of the pyramid (2mks)
18. In the figure below , and are tangents to the circle whose centre is 0.
Given that and
Find, giving reasons the sizes of the angles
a) (2mks)
b) (2mks)
c) (2mks)
d) (2mks)
e) (2mks)
19. a) The probability that a student is left – handed is 0.35. Calculate the probability that
i) a student chosen at random is right –handed. (1mk)
ii) Two students chosen at random are both left handed. (2mks)
b) A family of three children could get a girl first, followed by a boy then another boy. this
could be denoted by . Given that getting a boy or a girl at any stage is equally likely;
(i) Use the letters B and G to show the possibility space for all families with three children (1mk)
(ii) Using the possibility space calculate the probability that a family of three children has
at least one girl. (2mks)
(iii) The family has two girl. (2mks)
(iv) The oldest and the youngest are of the same sex. (2mks)
20. (a) Complete the table below for (2mks)
(b) On the grid provided draw the graph of and on the same axes for
values of in the domain Using the scale 1 cm for 1 unit on x axis and 1cm for 2
units on y – axis. (4mks)
Grid
(i) State the equation of the line of symmetry of the curve (1mk)
(ii) Use your graph to solve the equation (2mks)
(iii) State the range of values of x for which (1mk)
21. A businessman wants to buy machines that make plastic chairs. There are two types of machines that can make these chairs, type A and type B. Type A makes chairs a day, occupies of space and is operated by 5 men. Type B makes chairs a day, occupies of space and is operated by 3men.The businessman has 200m2 of space and 40 men.
a) List all inequalities representing the above information given that the business man buys x machines of type A and y machines of type B. (3mks)
b) Represent the inequalities above a graph. (3mks)
Grid
c) Using your graph find the number of machines of type A and those of type B that the business man should buy to maximize the daily chair production. (2mks)
d) Given that the price of a chair is , determine the maximum daily sales the businessman can make. (2mks)
22. In the figure below S is the mid- point of line . Is a point on the line such that = and is the point of intersection of the lines and
a) Given that and , express in terms of c and d the vectors;
(i) (1mk)
(ii) (1mk)
b) Given further that and ,
i. Express OX in terms of w,c and d (2mks)
ii. Express OX in terms of t, c and d (2mks)
c) Hence find the values of t and w (4mks)
23. A trader deals in maize, beans and peas and mixes them for selling at different prices. The cost of maize per kg is that of beans and peas is sh. 60 and sh. 80 per kg respectively.
a) In making a certain brand of githeri regular he mixed maize and beans in the ratio Calculate his selling price if he has to make a profit of 25 % on a kilogram of ‘Githeri Regular’ (3mks)
b) In making ‘Githeri super ‘he mixed maize and beans in the ratio x:y. If the total cost per kg was 49.20 find the ratio x:y (3mks)
c) Another special brand, ‘Githeri Royal’, has the ratio of maize, beans and peas as 2:2:1. Find his percentage profit if he sells this brand at sh. 71 per kilogram. (4mks)
24. The velocity V metre per second of a vehicle is related to the time t seconds by
t 1 2 3 4 5 6 7 8 9 10 11 12 13
v 2 6 18 27 51 83 123
a) Complete the table below
b) Use the trapezium rule to determine the total distance traveled by the vehicle from to seconds, using 6 strips. (3mks)
c) Use calculus to determine;
(i) The exact distance traveled by the vehicle from to seconds. (3mks)
(ii) Find the percentage error in determining the distance by trapezium rule. (2mks)
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