Name: . …………………………………………………School:…………………………
Index No. ………………………………………………
121/2
MATHEMATICS
Paper 2
July / August 2008
2 ½ Hours
NYANDO DISTRICT JOINT MOCK EXAMINATION - 2008
Kenya Certificate of Secondary Education (K.C.S.E)
121/2
MATHEMATICS
Paper 2
July / August 2008
2 ½ Hours
INSTRUCTIONS TO CANDIDATES
1. Write your name and index number in the space provided at the top of this page.
2. The paper contains TWO sections; section I and section II
3. Answer all the 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 provided 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 maybe used.
For Examiners use only
Section 1
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / TotalSection II
17 / 18 / 19 / 20 / 21 / 22 / 23 / 24 / Total / Grand TotalThis paper consists of 16 printed pages
Candidates should check the question paper to ensure that all
the printed pages are printed as indicated and no questions are missing.
SECTION I ( 50 MARKS)
Answer all the questions in this section
1.Use logarithm table only to evaluate.(4mks)
2.The length and breadth of a rectangular floor were measured and found to be 5.2metres and 3.3 metres respectively. If a possible error of one centimeter was made in each of the measurements, find the;
a) Maximum and minimum possible area of the floor.(2mks)
b) Maximum possible wastage in a carpet ordered to cover the whole floor.(1mk)
3.Given that A = ; B = and that C = (AB)-1, Determine the matrix C. (3mks)
4.Two brands of tea P and Q costs sh. 30 and sh. 36 per kilogram respectively. A shopkeeper decides to sell one kilogram of the mixture at a price of sh.42 and makes a profit of 20% on the cost price. Find the ratio in which he mixes the two brands. (3mks)
5.A statue is made up of a pyramid top with a square base resting on a cube block. The cube measures 8cm. Calculate the total surface area if the vertical height of the pyramid is 3cm. (4mks)
6.In the diagram below, determine the equation of line XY in the form y = mx + c.(3mks)
7.a) Expand (1 + 2x)7 in ascending powers of x.(2mks)
b) Hence, use the first five terms in the expansion to estimate the value of (1.02)7. state your answer to 4 decimal places. (2mks)
8.A coloured television set was valued at sh.45,000. The value depreciated at a constant rate of 4% per annum. What will be the value of the set after a period of 3 years? Leave your answer to the nearest shilling. (3mks)
9.If P = , express q in term of P.(3mks)
10.Show that 3x2 + 3y2 + 6x– 12y – 12 = 0 is an equation of a circle, hence, state the radius and centre of the circle. (3mks)
11.a quantity P is partly constant and partly varies inversely as a quantity q. Given that P=10, when q=1.5 and P=20 when q=1.25. Find the value of P when q=0.5. (4mks)
12.Find the coordinates of the turning point of the curve whose equation is y = 6 + 4x – 8x2.
(3mks)
13.Given that tan 650 = 3 + , without using a table or a calculator, determine tan 250, leaving your answer in the form a + b. (3mks)
14.Five students, Anita, Beth, Charity and Daphin and Eder obtained the marks 54, 42, 61, 81 and 57 respectively. The table below shows part of the work to find the standard deviation.
Student / Mark (x) / /Anita
Beth
Charity
Daphin
Eder / 54
42
61
81
57 / -5
-17
2
22
-2
(a) Complete the table(1mk)
b) Determine the standard deviation (Give your answer to 1 d.p)(2mks)
15.In the figure below, O is the centre of the circle. SQ and SR are tangents to the circle at Q and R respectively. Given that angle QPR=600. Determine the size of angle QSR. (2mks)
16.In the diagram below, determine vector OW in terms of i, j and k. Given that W divides AB in the ratio 2:3. (3mks)
SECTION II ( 50 MARKS)
Answer any FIVE questions from this question
17.On the grid provided, plot the quadrilateral whose vertices are A(2,0), B(6,0), C(6,5) and D(2,2)
a) Name the quadrilateral.(1mk)
b) ABCD is mapped onto A1B1C1D1 by a positive quarter turn about the origin. Draw the quadrilateral A1B1C1D1. (3mks)
c) A transformation maps A1B1C1D1 onto A11B11C11D11. Obtain the co-ordinates of A11B11C11D11 and plot it on the grid. (4mks)
d) Determine a single matrix that maps A11B11C11D11 onto ABCD.(2mks)
18.a) Complete the table below for y=tan x and y=2 sin 2x. State the values to 2 decimal places. (2mks)
x / 00 / 150 / 300 / 450 / 600 / 750 / 900Tan x / 0 / 0.27 / 0.58 / 3.73
2 sin 2x / 0 / 1.00 / 1.73 / 1.00
b) On the grid provided, draw the graphs of y=tan x and y=2 sin2x for 00 x 900.
Use a scale of;
2cm to represent 150 on the x-axis
2cm to represent 1 unit on the y-axis.(5mks)
c) Use your graph to;
(i) Solve the equation;
Tan x – 2sin 2x = 0.(1mk)
(ii) State the range of values that satisfy the inequality
2sin 2x > tan x(2mks)
19.A particle moves in a straight line. It passes through point O at t=0 with a velocity v=5mls. The acceleration a mls2 of the particle at time t, seconds after passing through O is given by a=6t + 4.
a) Express the velocity v, of the particle at time t seconds in terms of t.(4mks)
b) Calculate;
(i) the velocity of the particle when t=3 seconds.(3mks)
(ii) the distance covered by the particle between t=2 and t=4 seconds.(3mks)
20.An aircraft leaves town P(300S, 170E) and moves directly northwards to Q(600N, 170E). It then moved at an average speed of 300 knots for 8 hours westwards to town R. Determine;
a) the distance PQ in nautical miles.(3mks)
b) the position of town R.(3mks)
c) the local time at R if local time at Q is 3.12p.m.(2mks)
d) the total distance moved from P to R in kilometers. Take 1 nautical = 1.853 kilometers. (2mks)
21.The figure below is a triangular pyramid such that AB=BD=BC=AC=AD=6cm. M is the mid point of BC.
Determine;
(a) Height of the pyramid.(6mks)
(b) The angle AD makes with the base ABC.(2mks)
(c ) The volume of the pyramid.(2mks)
22.One day during inspection, in a certain secondary school, it was discovered that there was a probability of 2/5 that a student had shaggy hair. If a student had shaggy hair, there was a probability of ½ that he had torn uniform. But if he had properly combed hair, there was a probability of ¼ that he had a torn uniform. If a student had torn uniform, there was a probability of 4/5 that he had unpolished shoes, otherwise there was a probability of 3/5, that he had published shoes.
a) Represent this information in a probability tree diagram.(2mks)
b) Find the probability that;
(i) A student had all the three faults.(2mks)
(ii) A student had exactly two faults.(4mks)
(iii) A student had no fault at all.(2mks)
23.The table shows the tax rates.
Income in Kshs per annum / Rate in percentage1 -84,000
84,001 – 168,000
168,001 – 240,000
240,001 – 300,000
300,001 – 420,000
420,000 and above / 10%
15%
20%
25%
30%
35%
Janet earns a monthly salary of Kshs.21,000. She gets a house allowance of Kshs.7200 monthly . She is also entitled to a non-taxable medical allowance of Kshs.6,000 per month. Her family relief is Kshs.1056p.m. Her monthly deductions are NHIF of Kshs 360, cooperative loan of Kshs.3600 and cooperative share contribution of Kshs.2000.
Determine ;
a) Her annual taxable income in Kshs.(1mk)
b) Her net tax in Kshs. Per month.(5mks)
c) Her total deductions per month.(2mks)
d) Her net earnings per month in Kshs.(2mks)
24.A tailor is required to make two types of skirts. Type A and type B. The total number of skirts must not exceed 500. Skirts of type B must not be less than skirts of type A. The tailor must make atleast 200 skirts of type A. Let x represent the number of skirts of type A and y represent the number of skirts of type B.
a) Write down the inequalities that describe the given conditions above.(3mks)
b) On the grid provided, draw the three inequalities and shade the unwanted regions.
(3mks)
(c ) Profits were as follows:
Type A, Kshs. 900 per skirt
Type B, Kshs. 700 per skirt
Determine the maximum possible profit.(4mks)
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© The Nyando Districts Joint Examination Panel Mathematics 121/2 Turn Over