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(a) Two towns on latitude 30oS are 3000km apart. Find the longitude different of the two towns
(Take 
and the radius of the earth to be 6370km)
(b) The positions of airport P and Q are (60oN,45oN) and Q(60oN,KoE). It takes a plane 5 hrs to travel due east from P to Q at an average speed of 600 knots
(i) Calculate the value of K
(ii) The local time at P is 10.45am, what is the local time at Q when the plane reaches where?
(c) Calculate the shortest distance between (30oS,36oE) and (30oS,144oW) in nautical miles
Date posted:
November 8, 2019
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The cash price of a camera is Sh.42,200. Joseph bought the camera on hire purchase (H.P) term by paying a deposit of Sh.7,200 and cleared the balance in 24 equal monthly installments each of Sh.2,250
(a) Find the amount of interest paid under hire purchase plan
(b) Ken took a loan from a financial institution and bought the camera with cash. He repaid the loan in two years at 18% interest compound semi-annualy. Find the total interest paid by Ken
(c) The cash price is taken as the value of the Camera. If the camera depreciated at a rate of 15% in the first year after buying and at P% p.a for rest of the time, calculate the value of p if the value of the camera after 5 years was Sh.23,534
Date posted:
November 8, 2019
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(a) A sequence is formed by adding corresponding terms of an A.P and a G.P. The first, second and third terms of the sequence formed after adding the first three terms of the sequences are 14,34 and 78 respectively. Given that the first term of the A.P is a and the first term of the G.P is b, and that the common ratio of the G.P is 3; Find the first term of the AP and G.P and the common difference of the A.P
(b)The second and third terms of a geometric progression are 24 and 12(x+1) respectively. Given that the sum of the first three terms of the progression is 76, find the whole number value of x and hence the first term
Date posted:
November 8, 2019
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(a) The points A1B1 and C1 are the images of A(4,1), B(0,-2) and C(-2,4) respectively under transformation represented by the matrix M= 
write down the coordinates of A1B1C1
(b) A11B11C11 are the images of A1B1C1 under another transformation whose matrix is 
write down the coordinates of A11B11C11
(c) Transformation m followed by N can be represented by a single transformation P. Determine the
matrix for P
(d) Another transformation has the matrix T = 
Determine the matrix for transformation m followed by N and T in that order
Date posted:
November 8, 2019
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The diagram below shows a square based pyramid V vertices above the middle of the base. PQ=10cm and VR=13cm M is the midpoint of VR
Find
(a)(i) the length PR
(ii) the height of the pyramid
(b)(i) the angle between VR and the base PQRS
(ii) the angle between PM and the base PQRS
(iii) the angle between the planes QVR and PQRS
Date posted:
November 8, 2019
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Given that OA= -i +j, OB=3i+5j and OC= 11i+13j. Show that A, B and C are collinear.
Date posted:
November 8, 2019
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Three towns X,Y and Z are such that Y is 50km South of X and Z is on a bearing of 300o from Y. Calculate the angle XZY given that XZ is 70km.
Date posted:
November 8, 2019
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A transformation matrix 
maps an object of area 21cm2 to an image of area 42cm2. Determine the value of p.
Date posted:
November 8, 2019
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The points P and Q are 7.4cm apart. By construction locate the locus R such that PR=2.5cm and angle PRQ=90o.
Date posted:
November 8, 2019
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Find the radius and the coordinates of the centre of the circle whose equation is
2x2 + 2y2 – 3x +2y + 1/2 = 0
Date posted:
November 8, 2019
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A bag contains 2 white balls and 3 black balls. A second bag contained 3 white balls and 2 black balls. The balls are identical except for the colours. Two balls are drawn at random, one after the other from the first bag and placed in the second bag. Calculate the probability that the two balls are both white.
Date posted:
November 8, 2019
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A circle whose equation is x2+y2+4x-10y+4=0 touches a straight line (-7,3). Find the equation of the line
Date posted:
November 8, 2019
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Find the value of x given that the matrix is a singular matrix.
Date posted:
November 8, 2019
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If, 
,find the values of a and b where a and b are irrational numbers
Date posted:
November 8, 2019
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The dimensions of a rectangle are 40cm and 45cm. If there is an error of 5% in the length and 8% in the width. Find the percentage error I calculating the area of the rectangle.
Date posted:
November 8, 2019
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Use logarithms correct to 4 decimal places to evaluate.
Date posted:
November 8, 2019
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Given that x=2i+j-2k, y=-3i+4j-k, and z=-5i+3j+2k and p=3x-y+2z, calculate the magnitude of p correct to 3 significant figures
Date posted:
November 8, 2019
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a) Using the trapezium rule with seven ordinates estimate the area of the region bounded by the
curve y= - x2 + 6x +1, the line x=0,y=0 and x=6.
b) Calculate:
i) The area of the region in (a) above by integration.
ii) The percentage error of the estimated area to the actual area of the region, correct to 2d.p.
Date posted:
November 8, 2019
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Find the relative error in the area of a parallelogram whose base is 8cm and height 5.0cm
Date posted:
November 8, 2019
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The figure below shows a solid structure in the shape of a frustum of a cone with a hemispherical bottom. The radius of the hemispherical part is 28cm and is equal to the radius of the bottom of the frustum. The frustum has a top radius of 16cm and a height of 12cm. (Use Π=22/7.)
a) Calculate to 2d.p.
i) The volume of the frustum.
ii) The volume of the solid.
b) Given that the solid has a mass of 20kg. Find its density in g/cm3.
Date posted:
November 8, 2019
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(i) Expand 
to the term in x3
(ii) Use your expansion to estimate the value of 
correct to one decimal place
Date posted:
November 8, 2019
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The football team in school decided to raise ksh.3, 600 for a party. Each student was to contribute the same amount. However, before the contributions were made, five members of the football team decided to transfer to other schools. This meant that the remaining contributors had to pay more to meet the same target.
If the increase in contributor per student was ksh.24. Taking the original number of footballers to be x.
i) Give an expression for the initial amount that each student should have contributed.
ii) Give an expression for the contribution by each student after the transfer.
iii) Form an equation hence find the number of members in the football team originally.
iv) Calculate the percentage increase in the contribution per student caused by the transfer.
Date posted:
November 8, 2019
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Karanja and Kamau decided to start a business. Karanja contributed ksh.400, 000 and Kamau ksh.640, 000. The two men agreed that in any year 15% of the profit shall be divided equally between them and 20% of the profit will be used to meet the cost of the business and the rest to be shared in the ratio of their contributions. The profit made after the first year was ksh.432, 000.
a) How much did they set aside towards the cost of running the business for the 2nd year?
b) How much did Kamau receive at the end of the first year?
c) Karanja bought Samsung T.V sets with his share of the profit. If each T.V set cost ksh.18, 000, how many sets did he buy?
Date posted:
November 8, 2019
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Solve for 
in the equation sin 
Date posted:
November 8, 2019
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Given that b = 
,make h the subject of the formula
Date posted:
November 8, 2019
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Use logarithms tables to evaluate
Date posted:
November 8, 2019
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Work out 3210-1910 in 8-bit binary notation;
(i) As a signed magnitude representation using ones complements.
(ii) Using two’s complement
Date posted:
November 7, 2019
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The following Trial balance was extracted from PEMUR STORES on 31st Dec 2009.
Additional information;-
Closing stock was valued at sh. 22,000
Prepare PEMUR STORES; Trading, profit and loss accounts for year ending 31/12/2009.
Date posted:
November 7, 2019
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Convert each of the following numbers;
(i) 126810 to hexadecimal
(ii) 51C3D16 to its binary equivalent
(iii) 84C16 to octal
(iv) 1768 to hexadecimal.
Date posted:
November 7, 2019
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Pemba is an Island within the Indian Ocean. She had registered an improvement in her national income. Explain five factors that may have contributed to this trend.
Date posted:
November 7, 2019