Sample Mathematics Problem Type Examination (Math Problem Sample)

NAME:________________________________________________________
ADM NO:_______________________________CLASS:__________
121/2
MATHEMATICS
PAPER2
MARCH, 2020
TIME: 2½ HOURS
ANESTAR SCHOOLS FORM 4 MID TERM EXAM
.
INSTRUCTIONS TO CANDIDATES
* This paper contains two sections: section A and section B
* Show all the steps in your calculations, giving your answers at each stage in the spaces below each question.
* Marks may be given for correct working even if the answer is wrong.
* Non programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.
For Examiner’s Use only
Section A
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Section B
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Grand Total
This paper consists of 15 printed pages. Candidates should check the question paper to ensure that all the pages are printed as indicated and no questions are missing.
SECTION A (50 MARKS)
1. Using logarithms, evaluate correct to 4d.p.(4mks)
0.8
25.48 X 0.0212
6.159
2. Solve the equation below.
72x – 8 X 7x + 7 = 0 (3mks)
3.Given that x2 – 4x + y2 – 6y + 4 = 0 is an equation of a circle, determine the centre and radius of the circle. (3 marks)
4.Y varies partly as x and partly as the square of X. When X = 2, Y = 14 and when X = 4,Y = 44. Find Y when X = 6.(4 marks)
5.a)Expand in ascending powers of x.(2 marks)
b)Use the first three terms of the expansion above to approximate the value of (3.025)4 to 3 decimal places.(2 marks)
6.A student recorded the length of a copper wire as 20.66 cm. If the actual length was 20.6 cm, calculate the fractional error committed. (3 marks)
7.If, find the value of a and b where a and b are rational numbers.(3marks)
8. Given the matrix 5-x23x4 has no inverse, find the value of x.(2 marks)
1 Find the percentage area in calculating the perimeter of a triangle whose dimensions are 5cm, 6.3cm and 7.0cm. (3mks)
10.A coffee trader buys two grades of coffee at sh.80 and sh.100 per packet. Find the ratio at which she should mix them so that by selling the mixture at sh.120, a profits of 25% is realized. (3mks)
11.Without using a calculator or mathematical tables rationalize and simplify.
(3mks)
QUOTE - QUOTE
12.(a) The consecutive terms in a G.P are 3x+1/2, 9x and34. Calculate the value ofx. (2mks)
(b) Given that the 5th and 7th terms of the G.P. in (a) above form the first two consecutive terms of an AP. Calculate the sum of the first 10 terms. (2mks)
13.Determine the ratio in which P(11,0) divides AB, where A and B are the point (2,-3) and (17, 2) respectively (2mks)
14. Make x the subject in the formula:(3mks)
M=X-PP1-PX
15.Solve for x: (log3 x)2 - ½ 1og3 x = 3/2 (3mks)
16. Find the longest side of the right-angled triangle whose other sides are; (2 + l)cm and (2 - l)cm long, leaving your answer in surd form. (3mks)
SECTION B ( 50 MARKS) ANSWER ANY 5 QUESTIONS
17.In the figure angle CBD = 37o, angle BCD = 20o, CDE is a straight line and ABC is a tangent to the circle at B.
BAEDC
a)Find with reasons
i)Angle BED.(2 marks)
ii)Angle ABE(2 marks)
iii)Angle BDC(2 marks)
b)With reasons state whether triangle BDC is similar to triangle CBE.2 marks)
c)Given that the radius of the circle is 2.5 cm find the length of B(2 marks)
18.a)A plane flew from airport X (600S, 300E) due North to airport Y (300N, 300E) at 180knots. After 20 minutes stop over for fuelling at Y, the plane flew due West to an airport Z (300N, 150E) at the same speed.
(i)Calculate the total distance covered by the plane in nautical miles4 marks)
(ii)Calculate the total time taken to complete the journey from X through Y to Z. (4marks)
b)P and Q are two towns on the surface of the earth. Their local times differ by hours. If the longitude of P is 150E, find two possible longitudes of Q.(2marks)
ABDOC19.The diagram given below shows a triangle OAB. OA = a andOB = b. A point C divides OA in the ratio 2:3, D divides OB in the ratio 3:4 and the lines AD and BC meet at E.
a)Find in terms of a and b the vectors
i)OC(1 mark)
(ii)CB(1 mark)
(b)Given that CE = mCB and DE = nDA where m and n are scalars
(i)Write down two distinct expressions for OE (3 marks)
(ii)Hence find the values of m and n(4 marks)
~(iii) Find OE in terms of a and b only(1 mk)
20. a)ABCD is a quadrilateral with vertices as follows: A (3, 1), B (2, 4),C (4, 3)
and D (5, 1)
(i)A'B'C'D'is the image ofABCDunder a transformation whose matrix is. On the grid provided draw the quadrilateralABCD and its image A'B'C'D'