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- OAB is a triangle with OA = a , OB = b. R is a point of AB. 2AR = RB. P is on OB...(Solved)
OAB is a triangle with OA = a , OB = b. R is a point of AB. 2AR = RB. P is on OB such that 3OP = 2PB. OR and AP intersect at Y, OY = m OR and AY = nAP. Where m and n are scalars. Express in terms of a and b.
(i) OR
(ii)AP
(b) Find the ratio in which Y divides AP
Date posted: March 29, 2019. Answers (1)
- The following was Kenya`s income tax table in 1988.
Income in K£ P.a Rate (Ksh) £
1 - 2100 ...(Solved)
The following was Kenya`s income tax table in 1988.
Income in K£ P.a Rate (Ksh) £
1 - 2100 2
2101 - 4200 3
4201 - 6303 5
6301 - 8400 7
(a) Maina earns £ 1800 P.a. How much tax does he pay?
(b) Okoth is housed by his employer and therefore 15% is added to salary to make taxable income. He
pays nominal rent of Sh.100 p.m His total tax relief is Shs.450. If he earns K£3600 P.a, how much
tax does he pay?
Date posted: March 29, 2019. Answers (1)
- A rectangular tennis court is 10.5m long and 6m wide. Square tiles of 30cm are fitted on the floor.
(a) Calculate the number of tiles needed....(Solved)
A rectangular tennis court is 10.5m long and 6m wide. Square tiles of 30cm are fitted on the floor.
(a) Calculate the number of tiles needed.
(b) Tiles needed for 15 such rooms are packed in cartons containing 20 tiles. How many cartons are
there in total?
(c) Each carton costs shs. 800. He spends shs. 100 to transport each 5 cartons. How much would one
sell each carton to make 20% profit ?
Date posted: March 29, 2019. Answers (1)
- Members of a youth club decided to contribute shs 180,000 to start a company. Two members withdrew their membership and each of the remaining member...(Solved)
Members of a youth club decided to contribute shs 180,000 to start a company. Two members withdrew their membership and each of the remaining member had to pay shs. 24,000 more to meet the same expense. How many members remained?
Date posted: March 29, 2019. Answers (1)
- A right cone with slant height of 15cm and base radius 9cm has a smaller cone of height 6cm chopped off to form a frustum....(Solved)
A right cone with slant height of 15cm and base radius 9cm has a smaller cone of height 6cm chopped off to form a frustum. Find the volume of the frustum formed
Date posted: March 29, 2019. Answers (1)
- A solid sphere of radius 18cm is to be made from a melted copper wire of radius 0.4mm . Calculate the length of wire in...(Solved)
A solid sphere of radius 18cm is to be made from a melted copper wire of radius 0.4mm . Calculate the length of wire in metres required to make the sphere. (5mks)
(b) If the density of the wire is 5g/cm3. Calculate the mass of the sphere in kg.
Date posted: March 29, 2019. Answers (1)
- A building contractor has to move 150 tonnes of cement to a site 30km away. He has at his disposal 5 lorries. Two of the...(Solved)
A building contractor has to move 150 tonnes of cement to a site 30km away. He has at his disposal 5 lorries. Two of the lorries have a carrying capacity of 12 tonnes each while each of the remaining can carry 7 tonnes. The cost of operating a 7 tonne lorry is sh. 15 per km and that of operating a 12 tonne lorry is sh. 25 per km. The number of trips by the bigger lorries should be more than twice that made by smaller lorries.
(a) Represent all the information above as inequalities.
(b) How should the contractor deploy his fleet in order to minimise the cost of moving the cement?
Date posted: March 29, 2019. Answers (1)
- Given a circle of radius 3 units as shown in the diagram below with its centre at O(-1, 6). If BE and DE are tangents...(Solved)
Given a circle of radius 3 units as shown in the diagram below with its centre at O(-1, 6). If BE and DE are tangents to the circle where E (8,2). Given further that angle DAB = 800.
(a) Write down the equation of the circle in the form ax2 + bx + cy2 + dy + e = 0 where a, b, c, d, e are constants.
(b) Calculate the length DE.
(c) Calculate the value of angle BED.
(d) Calculate the value of angle DCB.
Date posted: March 29, 2019. Answers (1)
- Find the distance between points A(500 S, 250 E) and B(500 S, 1400 E) in:
(i) Km ...(Solved)
Find the distance between points A(500 S, 250 E) and B(500 S, 1400 E) in:
(i) Km (ii) nm
(take radius of earth to be 6400km, π = 3.14)
Date posted: March 29, 2019. Answers (1)
- A bag contains x red balls and y yellow balls. Four times the number of red balls is equal to nine times the number of...(Solved)
A bag contains x red balls and y yellow balls. Four times the number of red balls is equal to nine times the number of yellow balls and twice the total number of balls exceeds the number of yellow balls by 44.
(a) How many balls of each colour are three in the bag?
(b) If two balls are drawn out of the bag at random one at a time with replacement what is the probability that the two balls are red?
Date posted: March 29, 2019. Answers (1)
- The diagram below represents a bucket that has been placed upside down. The radius of the top surface is 15cm and that of the bottom...(Solved)
The diagram below represents a bucket that has been placed upside down. The radius of the top surface is 15cm and that of the bottom is 40cm. The vertical height of the bucket is 50cm.
Determine:-
(a) The volume of the bucket.
(b) The curved surface area of the bucket. (leave your answers in terms of π)
Date posted: March 29, 2019. Answers (1)
- Find the co-ordinates of the turning point on the curve of y = x3 – 3x2 and distinguish between them.(Solved)
Find the co-ordinates of the turning point on the curve of y = x3 – 3x2 and distinguish between them.
Date posted: March 29, 2019. Answers (1)
- Calculate the Area of each of the two segments of y = x(x+1)(x-2) cut off by the x axis.(Solved)
Calculate the Area of each of the two segments of y = x(x+1)(x-2) cut off by the x axis.
Date posted: March 29, 2019. Answers (1)
- The Probabilities that it will either rain or not in 30days from now are 0.5 and 0.6 respectively. Find the probability that in 30 days...(Solved)
The Probabilities that it will either rain or not in 30days from now are 0.5 and 0.6 respectively. Find the probability that in 30 days time.
a) it will either rain and not.
b) Neither will not take place.
c) One Event will take place.
Date posted: March 29, 2019. Answers (1)
- Two towns T and S are 300km apart. Two buses A and B started from T at the same time travelling towards S. Bus B...(Solved)
Two towns T and S are 300km apart. Two buses A and B started from T at the same time travelling towards S. Bus B travelled at an average speed of 10km/hr greater than that of A and reached S 1 ¼ hrs earlier.
(a) Find the average speed of A.
(b) How far was A from T when B reached S.
Date posted: March 29, 2019. Answers (1)
- In the figure below, a and b are the position vectors of points A and B respectively. K is a point on
AB such that the...(Solved)
In the figure below, a and b are the position vectors of points A and B respectively. K is a point on
AB such that the AK:KB = 1:1. The point R divides line OB in the ratio 3:2 and point S divides OK in
the ratio 3:1.
(a) Express in terms of a and b
(i) OK (iii) RS
(iii) OS (iv) RA
(b) Hence show that R,S and A are collinear.
Date posted: March 29, 2019. Answers (1)
- The marks obtained by Form 4 students in Examination were as follows:
Using 74.5 as the Assumed mean, calculate:
(i) The mean mark
(ii) The standard deviation(Solved)
The marks obtained by Form 4 students in Examination were as follows:
Using 74.5 as the Assumed mean, calculate:
(i) The mean mark
(ii) The standard deviation
Date posted: March 29, 2019. Answers (1)
- The depth of the water in a rectangular swimming pool increases uniformly from 1M at the shallow
end to 3.5m at the deep end. The pool...(Solved)
The depth of the water in a rectangular swimming pool increases uniformly from 1M at the shallow
end to 3.5m at the deep end. The pool is 25m long and 12m wide. Calculate the volume of the pool
in cubic meters.
The pool is emptied by a cylindrical pipe of internal radius 9cm. The water flows through the pipe at speed of 3 metres per second. Calculate the number of litres emptied from the pool in two minutes to the nearest 10 litres. (Take π = 3.142)
Date posted: March 29, 2019. Answers (1)
- V A B C D is a right pyramid with a square base A B C D of side 5 cm. Each of its four...(Solved)
V A B C D is a right pyramid with a square base A B C D of side 5 cm. Each of its four triangular
faces is inclined at 750 to the base. Calculate
a. The perpendicular height of the pyramid
b. The length of the slant edge VA
c. The angle between edge VA and base A B C D
d. The area of the face VAB
Date posted: March 29, 2019. Answers (1)
- Two unbiased dice are thrown. Find the probability of obtaining
i. A product of 6
ii. A sum of 8
iii. The same number showing(Solved)
Two unbiased dice are thrown. Find the probability of obtaining
i. A product of 6
ii. A sum of 8
iii. The same number showing
Date posted: March 29, 2019. Answers (1)