121/2 Mathematics Question Paper
121/2 Mathematics
Course:Mathematics
Institution: Form 4 Mock question papers
Exam Year:2010
Name……………………………………………………………. Index No……………………………..
School…………………………………………………………… Candidate’s sign…………………….
Date………………………………….
121/2
MATHEMATICS
PAPER 2
July/August 2010
2 ½ hrs
BUTERE DISTRICT JOINT EVALUATION TEST – 2010
Kenya Certificate of Secondary Education (K.C.S.E)
121/2
MATHEMATICS
PAPER 2
July/August 2010
2 ½ hrs
INSTRUCTION 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.
3. The paper contains two sections: Section I and II.
4. Answer all questions in section I and strictly 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.
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 printed pages. Candidates should check carefully
to ascertain that all the pages are printed as indicated and no questions are missing.
SECTION I (50 MARKS)
Answer all the questions in this section in the spaces provided.
1. Evaluate without using mathematical tables or calculators,
2 log10 5 – ½ log10 64 + 2 log10 40. (3mks)
2. Evaluate without using a calculator. (3mks)
3. In the figure below, AB is parallel to DE. Find the value of x and y. (3mks)
4. Given that and is an acute angle, find without using tables or calculators, Sin (90 - ), leaving your answer in simplified surd form. (2mks)
5. (a) Expand and simplify the binomial expression (2 + x)5 upto the term in x3. (2mks)
(b) Use your expression to estimate (1.97)5 correct to 4 s.f. (2mks)
6. The sketch below represents the graph of y = x2 – x – 6. Use the curve and five trapezia to estimate the area bounded by the x – axis, y – axis and the line x = 5. (3mks)
7. Find all integral values that satisfy the inequality 2x + 3 ? 5x – 3 > -8. (3mks)
8. Use matrix method to solve the (3mks)
3y + 2x = 13
2y – 3x = 0
9. A man invests Ksh 10000 in an account which pays 16% interest p.a. The interest is compounded quarterly. Find the interest earned after 1 ½ years to the nearest shilling. (4mks)
10. Given the points P(-6, -3), Q(-2, -1) and R(6, 3) express PQ and QR as column vectors. Hence show that the points P, Q and R are collinear. (3mks)
11. A quantity V is partly constant and partly varies inversely as the square of W. If W = 2 when V = 14 and W = 3 when V = 9. write an equation connecting V and W and hence find V when W = 6. (4mks)
12. In the triangle XYZ below, find the angle ZXY. (3mks)
13. An arithmetic progression whose first term is 2 and whose nth term is 32 has the sum of its first n terms equal to 557. Find n. (3mks)
14. Given that express y in terms of T and X. (3mks)
15. Solve the equation (3mks)
16. The figure below shows a solid regular tetrapack of sides 4cm.
(a) Draw a labelled net of the solid. (1mk)
(b) Find the surface area of the solid. (2mks)
SECTION B
Answer any five questions in this section.
17. A cylindrical water tank is of diameter 14 metres and height 3.5 metres.
(a) Find the capacity of the water tank in litre. (3mks)
(b) Six members of a family use 20 litres each per day. Each day 80 litre are used for cooking and washing. A further 50 litres is wasted daily. Find the number of complete days a full tank would last the family. (3mks)
(c) Two members of the family were absent for 90 days. During this time, wasting was reduced by 20% as cooking and washing remained the same. Calculate the number of days a full tank would now last the family. (4mks)
18. On the grid provided, draw triangle PQR with P(2,3), Q(1,2) and R(4,1). On the same axes draw triangle P11Q11R11 with vertices P11(-2,3), Q11(-1,2) and R11(-4,1). (2mks)
(a) Describe fully a single transformation which will map triangle PQR onto triangle P11Q11R11. (1mk)
(b) On the same plane, draw triangle P1Q1R1 the image of triangle PQR under reflection in the line y = -x. (2mks)
(c) Describe fully a single transformation which maps triangle P1Q1R1 onto triangle P11Q11R11. (2mks)
(d) Draw triangle P111Q111R111 such that it can be mapped onto triangle PQR by a position quarter about (0,0) (2mks)
(e) State all pairs of triangles that are oppositely congruent. (1mk)
19. The figure below is a squre based pyramid ABCD with AB = BC = 6cm and height VO = 10cm.
(a) State the projection of VA on the base ABCD. (1mk)
(b) Find the length VA. (3mks)
(c) Calculate angle between VA and plane ABCD. (2mks)
(d) Find angle between VCD and ABCD. (2mks)
(e) Calculate the volume of the solid (2mks)
20. Two identical baskets A and B contain white and red balls. Basket A contains 7 white balls and 3 red balls while basket B contains 5 white balls and 5 red balls. A bag is chosen at random and 2 balls picked from it one after another without replacement.
(a) Illustrate this information using a tree diagram. (2mks)
(b) Find the probability that:-
(i) The 2 balls picked are of the same colour. (2mks)
(ii) The two balls picked are of different colours. (2mks)
(iii) Only one of the balls picked is red. (2mks)
(iv) At least one white ball is picked. (2mks)
21. Complete the table below by filling in the blank spaces.
X0 00 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300 3600
Cos x 1.00 0.50 -0.87 -0.87
2cos½x 2.00 1.93 0.50
(2mks)
On the grid provided, using a scale of 1 cm to represent 300 on the horizontal axis and 4cm to represent 1 unit on the vertical axis draw the graph of y = cos x0 and y = 2 cos ½ x0. (4mks)
(a) State the period and amplitude of y = 2 cos ½ x0 (2mks)
(b) Use your graph to solve the equation 2 cos ½ x – cos x = 0. (2mks)
22. Points P(300N, 200W), Q(300N, 400E), R(600N, a0E) and S(b0N, c0W) are four points on the surface of the earth. R is due North of Q ands is due West of R and due North of P.
(a) State the values of a, b and c. (3mks)
(b) Given that all distances are measured along parallels of latitudes or along meridians, and in nautical miles, find the distance of R from P using two alternative routes via Q and S. (4mks)
(c) Two pilots start flying from P to R one along the route PQR at 400 knots and the other along PSR at 300 knots which one reaches R earlier and by how long? (3mks)
23. A tailoring business makes two types of garments A and B. Garment A requires 3 metres of material while garment B requires 2 ½ metres of material. The business uses not more than 600 metres of material daily in making both garments. It must make not more than 100 garments of type A and not less than 80 of type B each day.
(a) Write down four inequalities from this information. (3mks)
(b) Graph these inequalities. (3mks)
(c) If the business makes a profit of shs 80 on garment A and a profit of shs 60 on garment B, how many garments of each type must it make in order to maximize the total profit? (4mks)
24. A body moves in a straight line in such a way that at any time, t seconds, its distance S metres from the starting point is given by S = 8t – t2.
(a) How fast is the body moving at (3mks)
(i) t = 1 second
(ii) t = 3 seconds.
(b) What is the maximum displacement from the starting point that the body achieves. (4mks)
(c) Find the acceleration of the body. (1mk)
(d) After how long will the body be back to the starting point? (2mks)
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