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A cattle dip is 150cm wide and 12m long. The depth of the water increases uniformly from a shallow end of 60cm to a maximum...
(Solved)
A cattle dip is 150cm wide and 12m long. The depth of the water increases uniformly from a shallow end of 60cm to a maximum of 6m.
(a)Find the volume of water that can be held by the full dip in litres
(b)If the dip is drained by a pipe of radius 15cm at the rate of 6m/l, how long will it take to drain a full dip?
Date posted:
September 16, 2019
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Answers (1)
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The position vector of A and B are a=4i+4j-6k and b =10i+4j+12k.D is a point on AB such that AD:DB is 2:1.Find the co-ordinates...
(Solved)
The position vector of A and B are a=4i+4j-6k and b =10i+4j+12k.D is a point on AB such that AD:DB is 2:1.
Find the co-ordinates of D.
Date posted:
September 16, 2019
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Answers (1)
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Find the percentage error in calculating the volume of a sphere radius 4.9cm.
(Solved)
Find the percentage error in calculating the volume of a sphere radius 4.9cm.
Date posted:
September 16, 2019
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Answers (1)
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Complete the table below for the functions y = 2 sin (x – 300) and y = Cos 2x
(Solved)
Complete the table below for the functions y = 2 sin (x – 300) and y = Cos 2x.

(a) On the same set of axes, draw the graphs of y = 2 Sin (x - 30) and y = cos 2x in
The range 00 < 3600
(b) Use your graph to solve the equation 2 sin (x - 300) = cos 2x
(c) State the,
(i) phase angle for the wave y = 2 Sin (x -30°)
(ii) period for the wave y = cos 2x.
Date posted:
September 13, 2019
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Answers (1)
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The table below shows monthly income tax rates.
(Solved)
The table below shows monthly income tax rates.

A civil servant earns a salary of Sh.42000 and is provided with a house at a nominal rent of Sh. 1500 per month.
(a) Taxable pay is the employee’s salary plus 15% of salary less nominal rent. Calculate the civil servant’s taxable income in K£ p.m.
(b) If the employee is entitled to a personal relief of Sh.900 p.m., what is his PAYE?
(c,) The following deductions are made from his gross monthly pay; NHIF - Sh 630, WCPS - Sh 540, Union dues - Sh 330, SACCO loan recovery - Sh.7000 and Co - operative shares Sh.2500 Calculate his net monthly pay.
Date posted:
September 13, 2019
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Answers (1)
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A student misread the number 0.4 07 for 0.407 . Calculate the percentage error incurred in using the wrong number
(Solved)
A student misread the number 0.4 07 for 0.407 . Calculate the percentage error incurred in using the wrong number
Date posted:
September 13, 2019
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Answers (1)
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From a point P a boy notices that the angle of elevation of the top of a tall building is 45°.
(Solved)
From a point P a boy notices that the angle of elevation of the top of a tall building is 45°. He moves 270m from P to Q and realizes that the new angle of depression is 30°. Given that Q is on the same side of the building as P, find the height of the building.
Date posted:
September 13, 2019
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Answers (1)
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A farmer has three containers of capacity 12, 15 and 21 litres.
(Solved)
A farmer has three containers of capacity 12, 15 and 21 litres. Calculate the capacity of the largest. container which can fill each one of them an exact number of times.
Date posted:
September 13, 2019
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Answers (1)
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A small scale farmer wishes to buy some sheep and goats for rearing. A sheep costs sh.400 and a goat costs sh.300.
(Solved)
A small scale farmer wishes to buy some sheep and goats for rearing. A sheep costs sh.400 and a goat costs sh.300. The farmer has enough space for only 20 animals and may spend at most sh.6800. The number of goats should not exceed twice the number of sheep.
a) By letting x and y to represent the number of sheep and goats he can buy respectively, write down all inequalities from the above information.
b) Represent the inequalities on the grid provided.
c) From your graph; find the maximum number of animals he can buy at the lowest cost.
Date posted:
September 13, 2019
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Answers (1)
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The probability that it will rain on a certain morning is 1/3.
(Solved)
The probability that it will rain on a certain morning is 1/3. If it rains, the probability that Sagero misses the bus is 3/4. If it does not rain, the probability that he catches the bus is 5/6.
a) Represent the above information in a tree diagram.
b) Calculate the probability that on a given morning
i) it rains and he catches the bus.
ii) it rains and he misses the bus.
iii) he misses the bus.
iv) it does not rain and he misses the bus.
Date posted:
September 13, 2019
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Answers (1)
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A particle P moves in a straight line so that its velocity Vm/s at time t seconds where
(Solved)
A particle P moves in a straight line so that its velocity Vm/s at time t seconds where t> or equal to 0 is given by V=28+t-2t2
Find;
a) The time when P is instantaneously at rest.
b) The speed of P at the instant when the acceleration of P is zero
c) Given that P passes through point O of the line when t=0
i) Find the distance of P from O when P is instantaneously at rest
ii) Find the distance covered by the particle during the 3rd second
Date posted:
September 13, 2019
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Answers (1)
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In the figure below, E is the midpoint of BC,AD:DC=3:2 and AE intersect with BD at F.
(Solved)
In the figure below, E is the midpoint of BC,AD:DC=3:2 and AE intersect with BD at F.

a) Given that AB=b and AC=c, express in terms of b and c
(i)AE
(ii)BD
b) If BF= t BD and AF= sAE , where t and s are scalars, find the values of t and s.
c) What is the ratio in which F divides AE
Date posted:
September 13, 2019
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Answers (1)
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The table below shows income tax rates.
(Solved)
The table below shows income tax rates.

Agnes earns a monthly salary of Ksh. 20,000 per month, Her house allowance is Ksh. 15000P.M. She is entitled to a personal relief of Ksh. 1260P.M. Her deductions are NHIF sh.960, cooperative loan sh. 3500 and service charge of Ksh.400 per month.
Calculate
a) the taxable income.
b) the tax charged on Agnes earning.
c) the tax paid.
d) the net salary.
Date posted:
September 13, 2019
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Answers (1)
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Simplify without using mathematical tables or calculator.
(Solved)
Simplify without using mathematical tables or calculator.

Date posted:
September 13, 2019
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Answers (1)
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Mrs. Ondiek invested Ksh. 63560 in a bank where the interest was compounded quarterly at the rate of 12% per month.
(Solved)
Mrs. Ondiek invested Ksh. 63560 in a bank where the interest was compounded quarterly at the rate of 12% per month. Determine the amount of money she had after 2 ½ years.
Date posted:
September 13, 2019
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Answers (1)
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Calculate the relative error in 7.9 ÷ 4.3
(Solved)
Calculate the relative error in 7.9 ÷ 4.3
Date posted:
September 13, 2019
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Answers (1)
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Two towns A and B lie on the same latitude in the northern hemisphere. When it is 8:00 am At A, the time at B...
(Solved)
Two towns A and B lie on the same latitude in the northern hemisphere. When it is 8:00 am At A, the time at B is 11:00 a.m.
a) Given that the longitude of A is 150 E, find the longitude of B.
b) A plane leaves A for B and takes 3 ½ hours to arrive at B traveling along a parallel of latitude at 850 km/h. Find:
i) The radius of the circle of latitude on which town A and B lie.
ii) The latitude of the two towns. ( Take radius of the earth to be 6371km).
Date posted:
September 12, 2019
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Answers (1)
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In the figure below PQ = Q and PR = r QM: MR = 1:2. The point S is the midpoint of PQ.
(Solved)
In the figure below PQ = Q and PR = r QM: MR = 1:2. The point S is the midpoint of PQ. X is the intersection of PM and SR. SX = hSR, pX = kPM where k and h are constants.

Find:
a) QR in terms of q and r.
b) PM in terms of q and r
c) SR in terms of q and r
d) Express SX in two ways in terms of h,r and q and in terms of k,r and q, hence determine the ratio in which x divides SR.
Date posted:
September 12, 2019
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Answers (1)
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A cupboard has 7 white cups and 5 brown cups all identical in size and shape.
(Solved)
A cupboard has 7 white cups and 5 brown cups all identical in size and shape. There is a blackout in the town and Mrs. Wafula has to select three cups one after the other without replacing the previous ones.
a) Draw a tree diagram for the information.
b) Calculate the probability that she chooses.
i) Two white cups and one brown cup
ii) Two brown cups and one white cup.
iii) At least one white cup.
iv) Three cups of the same colour
Date posted:
September 12, 2019
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Answers (1)
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Two grades of tea, costing sh 100 and 150 per kg respectively are mixed in the ratio 3:5 by weight.
(Solved)
Two grades of tea, costing sh 100 and 150 per kg respectively are mixed in the ratio 3:5 by weight. The mixture is then sold at sh. 160 per kg. Find the percentage profit on the cost price.
Date posted:
September 12, 2019
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Answers (1)