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A particle P moves in a straight line so that its velocity, V m/s at time t = 0 seconds t is given by V...
(Solved)
A particle P moves in a straight line so that its velocity, V m/s at time t ≥ 0 seconds t is given by V = 28 + t – 2t2. Find.
a) The time when p is momentarily at rest.
b) The speed of P at the instant when the acceleration of the particles is zero.
c) Given that P passes through the point O of the line when t = 0, find the distance of P from O when P is momentarily
at rest.
Date posted:
April 30, 2019
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Answers (1)
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Every evening before the end of preps, Eunice either reads a novel or solves a mathematical problem. The probability
that she reads a novel is 4/5.If...
(Solved)
Every evening before the end of preps, Eunice either reads a novel or solves a mathematical problem. The probability
that she reads a novel is 4/5.If she read a novel, there is a probability of 3/4 that she will fall asleep. If he solves a mathematical problem, there is a probability of 1/4 that she will fall asleep. Sometimes the teacher on duty enters Eunice’s classroom. When Eunice is asked whether she had been asleep, there is a probability of only 1/5 that she will
admit that she had been asleep and a probability of 3/5 that she will claim to have been asleep when she had not been asleep
By use of a tree diagram, find the probability that
a) She sleeps and admits
b) She sleeps and does not admit
c). She does not sleep but claims that she had been asleep
d). She does not sleep and says that she has not been asleep
Date posted:
April 30, 2019
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Answers (1)
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A man sold a plot of land for sh. 160,000 and invested the money in a bank which pays 12% p.a. compounded semiannually.
After 2 years,...
(Solved)
A man sold a plot of land for sh. 160,000 and invested the money in a bank which pays 12% p.a. compounded semiannually.
After 2 years, he withdrew sh. 100,000 and the left the rest for a further 3 years.
a) How much did she leave in the bank at the end of 2 years?
b) How much did he have in the bank at the end of 5 years?
c) Calculate the total interest made for the whole period.
Date posted:
April 30, 2019
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Answers (1)
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The first three terms of a geometric series are 2x,x- 8 and 2x+ 5 respectively.
(Solved)
The first three terms of a geometric series are 2x,x− 8 and 2x+ 5 respectively.
a) Find the possible values of x.
b) For the value of x being an integer, find:
i) The value of the eleventh term
ii) The sum of the first 15 terms
Date posted:
April 30, 2019
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Answers (1)
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Two tanks of equal volume are connected in such a way that one tank can be filled by pipe A in 1 hour 20 minutes....
(Solved)
Two tanks of equal volume are connected in such a way that one tank can be filled by pipe A in 1 hour 20 minutes. Pipe
B can drain one tank in 3hours 36 minutes but pipe C alone can drain both tanks in 9 hours. Calculate:
(a) The fraction of one tank that can be filled by pipe A in one hour.
(b) The fraction of one tank that can be drained by both pipes B and C in one hour.
(c) Pipe A closes automatically once both tanks are filled. Assuming that initially both tanks are empty and all pipes
opened at once, calculate how long it takes before pipe A closes.
Date posted:
April 30, 2019
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Answers (1)
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A shear parallel to the x-axis maps point (1,2) onto a point (5, 2) .Determine the shear factors and hence state the shear matrix (invariant...
(Solved)
A shear parallel to the x-axis maps point (1,2) onto a point (5, 2) .Determine the shear factors and hence state the shear matrix (invariant line is y = 0)
Date posted:
April 30, 2019
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Answers (1)
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An enlargement with centre (-2,3) maps (1,0) onto (4,-3). What is the image of (-3,-6) with the same centre of enlargement
(Solved)
An enlargement with centre (-2,3) maps (1,0) onto (4,-3). What is the image of (-3,-6) with the same centre of enlargement
Date posted:
April 30, 2019
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Answers (1)
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A car uses 1 litre of petrol for every 8 kilometres. The car was to travel 480 kilometres and had 15 litre of petrol at...
(Solved)
A car uses 1 litre of petrol for every 8 kilometres. The car was to travel 480 kilometres and had 15 litre of petrol at the beginning of the journey. Each litre of petrol cost sh. 112.00. How much did it cost for the extra petrol added?
Date posted:
April 30, 2019
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Answers (1)
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If x:y = 9:11, find the ratio of (5x - 3y):(2x + 3y)
(Solved)
If x:y = 9:11, find the ratio of (5x - 3y):(2x + 3y).
Date posted:
April 30, 2019
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Answers (1)
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A straight line through the points A (2,1) and B (4,m) is perpendicular to the line whose equation is 3y = 5-2x.
Determine the value of...
(Solved)
A straight line through the points A (2,1) and B (4,m) is perpendicular to the line whose equation is 3y = 5-2x.
Determine the value of m and it's equation.
Date posted:
April 30, 2019
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Answers (1)
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Solve 4x -3 = 6x -1< 3x + 16 and list all the integral values of x.
(Solved)
Solve 4x -3 ≤ 6x -1< 3x + 16 and list all the integral values of x.
Date posted:
April 30, 2019
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Answers (1)
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The product of the first three terms of a geometric progression is 64. If the first term is a and the common ratio is r,
(Solved)
The product of the first three terms of a geometric progression is 64. If the first term is a and the common ratio is r,
a) Express r in terms of a
b) Given that the sum of the three terms is 14;
i) Calculate the values of a and r and hence write down two possible sequences each up to the 4th term
ii) Find the product of the 50th terms of the two sequences
Date posted:
April 29, 2019
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Answers (1)
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The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136m2.
(Solved)
The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136m2.
(i) Calculate the perimeter of the floor
(ii) A rectangular carpet is placed on the hall leaving an area of 64cm2. If the length of the carpet is twice its width,determine the width of the carpet
Date posted:
April 29, 2019
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Answers (1)
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Three quantities R, S, T are such that R varies directly as S and inversely as the square of T.
(Solved)
Three quantities R, S, T are such that R varies directly as S and inversely as the square of T.
(a) Given that R = 480 when S = 150 and T = 5, write an equation connecting R, S and T
(b) (i) Find the value of R when S = 360 and T = 1.5
(ii) Find the percentage change in R if S increases by 5% and T decreases by 20%
Date posted:
April 29, 2019
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Answers (1)
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The table below shows income tax rates for a certain year.
(Solved)
The table below shows income tax rates for a certain year.

A tax relief of Kshs. 1162 per month was allowed. In a certain month of the year, an employee’s taxable income in the
fifth band was Kshs. 2108.
a) Calculate:
i) Employees total taxable income in that month
ii) The tax payable by the employee in that month
b) The employees income includes a house allowance of Kshs. 15,000 per month. The employees contributed 5% basic
salary to a cooperative society. Calculate the employees net pay for that month.
Date posted:
April 29, 2019
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Answers (1)
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Point T is the mid-point of a straight line AB. Given that the position vectors of A and T are i-j+k and 2i + 1½...
(Solved)
Point T is the mid-point of a straight line AB. Given that the position vectors of A and T are i-j+k and 2i + 1½ k
respectively, find the position vector of B in terms of i , j and k.
Date posted:
April 29, 2019
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Answers (1)
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The image of P(0,2), under an enlargement with a scale factor 3 is P’ (4,6). Find the centre of enlargement.
(Solved)
The image of P(0,2), under an enlargement with a scale factor 3 is P’ (4,6). Find the centre of enlargement.
Date posted:
April 29, 2019
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Answers (1)
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Solve the inequality 2x + 3> 5x – 3> - 8 and represent your answer on the number line
(Solved)
Solve the inequality 2x + 3> 5x – 3> - 8 and represent your answer on the number line
Date posted:
April 29, 2019
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Answers (1)
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Tap P can fill a tank in 2 hours and tap Q can fill the same tank in 4 hours. Tap R can empty the...
(Solved)
Tap P can fill a tank in 2 hours and tap Q can fill the same tank in 4 hours. Tap R can empty the tank is 3 hours.
a) If tap R is closed, how long would it take taps P and Q to fill the tank?
b) Calculate how long it would take to fill the tank when the three taps P, Q and R are left running.
Date posted:
April 29, 2019
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Answers (1)
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In the figure below OY = 20B, OX = 5/2 OA, OA = a and OB = b
(Solved)
In the figure below OY = 20B, OX = 5/2 OA, OA = a and OB = b

a) Express the following in terms of a and b
(i) AB
(ii) XY
(b) Given that AC = 6AB, express OC & XC interms of a and b
(c) Show the points X, Y and C are collinear
(d) State the ratio in which C divides XY
Date posted:
April 29, 2019
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Answers (1)