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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)
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A translation maps a point P(3,2) onto P` ( 5,-4)
(Solved)
A translation maps a point P(3,2) onto P` ( 5,-4).
a) Determine the translation vector.
b) A point Q` is the image of the point Q ( 2,5) under the same translation. Find the length of P` Q` leaving the answers in surd form.
Date posted:
September 12, 2019
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Answers (1)
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A circle of radius 7 units has it’s centre at the point of intersection between the lines x +2y + 1 = 0 and 2x...
(Solved)
A circle of radius 7 units has it’s centre at the point of intersection between the lines x +2y + 1 = 0 and 2x + 3y – 3 = 0
Find the equation of the circle expressing it in the form x2 + y2+ gx +fy +c =0
Date posted:
September 12, 2019
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Answers (1)
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A school bus was valued at sh 6,000,000 in January 2000. Each year, its value decreased by 12.5% of its value at the beginning of...
(Solved)
A school bus was valued at sh 6,000,000 in January 2000. Each year, its value decreased by 12.5% of its value at the beginning of the year. Find the value of the bus in January 2005, giving your answer correct to 4.s.f
Date posted:
September 12, 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:
September 12, 2019
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Answers (1)
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The table below shows the marks scored by eighty Form 4 students in a mathematics test.
(Solved)
The table below shows the marks scored by eighty Form 4 students in a mathematics test.

a) Calculate
i) Mean mark.
ii) Lower quartile
b) On the grid provided draw the cumulative frequency curve to represent the above
distribution
c) From the graph estimate the
i) 4th decile
ii) Range of marks of the middle 70% of the students.
Date posted:
September 12, 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

Faith earns a monthly basic salary of Ksh 45,000 and she is also given taxable allowances amounting to Ksh 20480 per month.
a) Calculate Faiths’ gross income tax per month.
b) Faith is entitled to a personal tax relief of Ksh 1162. Determine her net income per month.
c) Faith received 50% increase in her total income; calculate the corresponding percentage increase on the net income tax.
Date posted:
September 12, 2019
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Answers (1)
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Make Q the subject of the formula
(Solved)
Make Q the subject of the formula

Date posted:
September 12, 2019
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Answers (1)
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A point P divides AB in the ratio 7: -5 where A (2,-3, 4) and B (-4, 7,-2). Find the coordinates of P.
(Solved)
A point P divides AB in the ratio 7: -5 where A (2,-3, 4) and B (-4, 7,-2). Find the coordinates of P.
Date posted:
September 12, 2019
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Answers (1)
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The diagram below shows a straight line intersecting the curve y = (x – 1)2 + 4
(Solved)
The diagram below shows a straight line intersecting the curve y = (x – 1)2 + 4 at the points P and Q. The line also cuts the x – axis at (7, 0) and y – axis at (0, 7)

(a) Find the equation of the straight line in the form y = mx + c.
(b) Find the co-ordinates of P and Q
(c) Calculate the area of the shaded region.
Date posted:
September 11, 2019
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Answers (1)
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Three towns are located on the earth’s surface at the co-ordinates P(150N, 450E)
(Solved)
Three towns are located on the earth’s surface at the co-ordinates P(150N, 450E), Q(300S, 450E) and R(150N, 900E). A plane A flies from P to Q in 6 hours 40 minutes using the shortest route between the two towns. Another plane B takes off from town P at the same time as A and flies to town R along the parallel of latitude.
(a) Calculate the shortest distance between towns P and Q in km.
(b) Find the distance in km traveled by plane B between P and R to the nearest km
(c) If the two planes fly at the same speed determine to the nearest minute, which plane Reaches its destination earlier and by how long.
(Take pi=22/7 and radius of earth R = 6370km)
Date posted:
September 11, 2019
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Answers (1)