SECTION 1
- Use logarithms to 4 decimal places to evaluate: (4 marks)
- The sides of a rectangle are given as 4.5 cm and 2.5 cm. Calculate the percentage error in its area. (3 marks)
- Rationalize the denominator in the following (3mks)
- Solve for in the simultaneous equations using matrices method. (4mks)
2x + 3y = 7
y - x = 2 - Solve the equation below by completing the square. 5 - 9x - 2x2 = 0 (2 mks)
- The distance from a point X to the centre of a circle is 12 cm. If the diameter of the circle is 12cm, Calculate the length of the tangent from X to the point of contact with circle hence calculate the area that lies outside the circle to four significant figures. (3mks)
- Make r the subject of the formula (3marks)
- Expand (1 + 1/2x)8 up to the term x3. Use your expansion to find the approximate value of correct to 2 decimal places. (3 mks)
- The sum of the first ten terms of an arithmetic Progression is 400.If the sum of the first 6 terms of the same series is 120, find the 15th term . (3mks)
- Solve for x (3marks)
52x - 5x - 12 = 0 - The position vectors of points X and Y are X = 2i + j - k and Y = 3i + 2j - 2k respectively. Find XY. (3 marks)
- The equation of a circle is x2 - 8x + y2 + 12y + 16 = 0. Determine the coordinates of the centre of the circle and its radius. (3mks)
- A vendor mixed grade 1 rice and grade 2 rice in the ratio 1:3 to form a mixture which she sold at sh.105 making a profit of 40%.Given that the cost price of grade 2 rice is sh.80 per kg. Find the cost price of 1kg grade 1 rice. (3marks)
- If ½Sin(2x + 30) = 0.4216, find x for -180o ≤ x ≤ 180o. (3 marks)
- The volume V of a cylinder of base radius r and height h varies jointly as h and r2. If V=352cm3, when h=7cm and r=4cm, find r to 1 decimal place, when V=905.1428cm3 and h=8cm (3mks)
- Calculate the variance of the following distribution (4marks)
x 5 7 9 11 13 f 2 4 8 6 4
SECTION II
Answer any five questions in this section
- The table below shows monthly income tax rates.
Monthly taxable pay (K£) Rate of tax ksh. Per £ 1 – 342 2 343 – 684 3 685 – 1026 4 1027 – 1368 5 1369 – 1710 6 1710 and above 7
Mr. Onyando who is a civil servant earns a monthly basic salary of ksh. 20,000 and is provided with a house at a nominal rent of kshs. 700 per month.- Taxable pay is the employee’s salary plus 15% of basic salary less nominal rent. Calculate Mr Onyando’s taxable pay in K£. (3 marks)
- Calculate the total tax Mr. Onyando pays. (4 marks)
- If Mr. Onyando is entitled to a personal tax relief of ksh. 600 per month, what is the payable tax? (1 mark)
- Mr Onyando has the following deductions on his pay; loan repayment of ksh. 2100 per month, salary processing ksh. 200 and service charge at 2% of his basic salary. Calculate Onyando’s net pay. (2 marks)
- A trader wishes to buy some goats. A she-goat cost sh.900, while a he-goat cost sh.1500. He has to buy atleast 9 she-goats. He also has a space to hold atmost 20 goats and sh.21,000 to spend. Taking the number of he-goats bought to be x and the number of she-goats bought to be y.
- Form all inequalities from the above information. (4mks)
- Plot the inequalities above in the graph provided below. (3mks)
- If he makes a profit of sh.200 on each she-goat and sh.280 on each he-goat. How many goats of each type should he buy to maximize his profit. (3mks)
- The acceleration a m/s2 of an object moving in a straight line after t sec of motion is given by a = 48t - 6.
- Given that the initial velocity was 5m/s;
- Find the velocity of the object after 2sec of motion. (3marks)
- Find the displacement of the object after 3sec of motion. 3marks
- A particle moving in a straight line is such that its distance from a fixed point 0 is given by s = 1/2t2 - 7/2t2 + 6t + 5 where t is the time in sec after the particle passes 0.Find the time when the particle is at rest. (4marks).
- Given that the initial velocity was 5m/s;
- There are two examiners A and B marking a mathematics examination. After marking 10 scripts, examiner A marks 6 scripts accurately but deviates in the rest. Examiner B marks 7 scripts accurately out of 10 but deviates in the rest. Determine the probability that;
- Both will mark with deviations a given set of scripts. (2 marks)
- Only one will mark accurately. (2 marks)
- Both of the examiners will mark accurately a given set of scripts. (2 marks)
- At least one will mark accurately. (2 marks)
- At most one will mark accurately. (2 mark)
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- Complete the table below for the function y = 2sin(x + 20o) and y = cos(x - 10o) (2mks)
xo 0 30 60 90 120 150 180 210 240 270 300 330 360 y = 2sin(x + 20o) 0.68 1.53 -1.53 -1.88 0.68 y=cos(x - 10o) 0.98 0.17 0.34 - Draw the graphs of y = 2 sin(x + 20o) and y = cos(x - 10o) on the same axes (5mks)
- Find the values of x for which cos(x - 10o) = 2 sin(x + 20o) (1mk)
- Find the Amplitude and period of each wave (2mks)
- Complete the table below for the function y = 2sin(x + 20o) and y = cos(x - 10o) (2mks)
- The figure below represents a cuboid in which PQ=18cm,QR=14cm and RU=7cm.
- Name the projection of the line PU on the plane UVWT. (1mark)
- Calculate correct to 1d.p
- The size of the angle between PS and QU (2marks)
- The angle between the line QT and the plane PQRS (3marks)
- The angle between planes QWTR and QRUV (2marks)
- Point A is the midpoint of TU. Calculate the length QA, correct to 2d.p (2marks)
- Two aircrafts A and B are at T (200N, 380E). Aircraft A flies 1800nm due South, then 1800nm due West to airport X. Aircraft B flies 1800nm due East then 1800nm due South to airport Y.
- Determine the position of airport X and Y. (5 marks)
- Find the distance between X and Y in nautical miles. (3 marks)
- If the local time at T was 2 pm on Monday when the aircrafts left T. What was the local time at X? (2 marks)
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- Draw a regular pentagon PQRST of sides 7cm. On it draw a line AR such that it is a line of symmetry to the figure. (4mks)
- Locate a point M on AR such that M is equidistant from P and Q, hence measure the shortest distance of M from TS. (2mks)
- Shade the region within the figure such that a variable X must lie, given that X satisfies the following conditions: (4mks)
- X is nearer to PT than to PQ.
- RX is not more than 7.5cm.
- Angle PXT is greater than 900.
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