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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...
(Solved)
(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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Answers (1)
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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
(Solved)
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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Answers (1)
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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...
(Solved)
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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Answers (1)
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A transformation matrix maps an object of area 21cm2 to an image of area 42cm2. Determine the value of p.
(Solved)
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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Answers (1)
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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...
(Solved)
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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Answers (1)
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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...
(Solved)
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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Answers (1)
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Use logarithms correct to 4 decimal places to evaluate.
(Solved)
Use logarithms correct to 4 decimal places to evaluate.

Date posted:
November 8, 2019
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Answers (1)
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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
(Solved)
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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Answers (1)
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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...
(Solved)
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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Answers (1)
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Find the relative error in the area of a parallelogram whose base is 8cm and height 5.0cm
(Solved)
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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Answers (1)
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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%...
(Solved)
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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Answers (1)
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Make h the subject of the formula
(Solved)
Given that b =
,make h the subject of the formula
Date posted:
November 8, 2019
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Answers (1)
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The figure below (Not drawn to scale) shows the cross-section of a metal bar of length 3metres. The ends are equal semi-circles. (use ?=3.142)
Determine the...
(Solved)
The figure below (Not drawn to scale) shows the cross-section of a metal bar of length 3metres. The ends are equal semi-circles. (use Π=3.142)

Determine the mass of the metal bar in kg if the density of the metal is 2.35g/cm3. (Give your answer to two 2dp).
Date posted:
November 7, 2019
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Answers (1)
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The figure below shows frustrum ABCDEFH of a right pyramid. AB = 24cm, BC = 10cm, FG = 18cm, GH=7.5cm and AF = BG =...
(Solved)
The figure below shows frustrum ABCDEFH of a right pyramid. AB = 24cm, BC = 10cm, FG = 18cm, GH=7.5cm and AF = BG = CH = DE = 15cm.

Determine.
a) The altitude of the pyramid.
b) The angle between:
i) AF and the base ABCD
ii) FE and GB
c) The distance AG
Date posted:
November 7, 2019
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Answers (1)
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A number 0.7 is truncated to 3.sf. Calculate the percentage error due to the truncation.
(Solved)
A number 0.7 is truncated to 3.sf. Calculate the percentage error due to the truncation.
Date posted:
November 7, 2019
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Answers (1)
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Expand (1 + 1/2x)5 upto the term on x³, use the expansion to estimate the value of (1.05)5 correct to 4 significant figures.
(Solved)
Expand (1 + 1/2x)5 upto the term on x³, use the expansion to estimate the value of (1.05)5 correct to 4 significant figures.
Date posted:
November 7, 2019
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Answers (1)
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The equation of a circle is x² + 4x + y² - 5 = 0. Find the centre and the radius of the circle.
(Solved)
The equation of a circle is x² + 4x + y² - 5 = 0. Find the centre and the radius of the circle.
Date posted:
November 7, 2019
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Answers (1)
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In the figure below, P, Q, R and S are points on the circumference of the circle centre O. TP and TR are tangents to...
(Solved)
In the figure below, P, Q, R and S are points on the circumference of the circle centre O. TP and TR are tangents to the circle at P and R respectively. POQ is a diameter of the circle and angle PQR = 64°

Giving reasons in each case, find the size of
a) b) c) d) e)
Date posted:
November 6, 2019
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Answers (1)
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A pirate boat sails from port A on a bearing of 050° at a speed of 112km/h, for 2½ hours to port B. From port...
(Solved)
A pirate boat sails from port A on a bearing of 050° at a speed of 112km/h, for 2½ hours to port B. From port B it changes its course and travelled on a bearing of 170° at a speed of 75km/h for 2 2/3 hours toward part C. From C it travelled to port D. D is on a bearing of 130° and 160km from A.
a) Using a scale of 1cm to represent 40km, Draw a diagram showing the positions of the ports A, B, C and D.
b) Use your drawing to find.
i) The distance CD
ii) The bearing of C from D
c) A marine police patrol leaves port A to intercept the pirate boat at M as it moves from B to C in the shortest time possible.
i) How far from A will the two boats meet at M.
ii) If the boats meets after 2 hours, what is the speed of the marine police boat.
Date posted:
November 6, 2019
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Answers (1)
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A closed cylindrical metal tin has radius r and height h. The capacity of the tin is 250 p litres
a) Express in term of r.
i)...
(Solved)
A closed cylindrical metal tin has radius r and height h. The capacity of the tin is 250 π litres
a) Express in term of r.
i) the height h of the tin.
ii) the total surface area of the tin.
b) i) Find the value of r for which the surface are of the metal used is to be minimum
ii) The minimum area of the metal used to make the cylinder.
Date posted:
November 6, 2019
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Answers (1)