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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)
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The displacement, S metres, of a moving particle after t seconds is given by
S = 40t3 – t2 + 3t + 3. Determine:
(Solved)
The displacement, S metres, of a moving particle after t seconds is given by
S = 40t3 – t2 + 3t + 3. Determine:
(a) The velocity of the particle when t= 3 seconds
(b) The value of t when the velocity of the particle is 4M/S
(c) The displacement when the particle velocity is 4M/S
(d) The acceleration of the particle when t = 3 seconds
Date posted:
April 29, 2019
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Answers (1)
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The diagram below shows a cross-section of a bottle. The lower part ABC is a hemisphere of radius 5.2cm and the
upper part is a frustrum...
(Solved)
The diagram below shows a cross-section of a bottle. The lower part ABC is a hemisphere of radius 5.2cm and the upper part is a frustrum of a cone. The top radius of the frustrum is one third of the radius of the hemisphere. The hemisphere part is completely filled with water as shown in the diagram.
(a) Determine the height of the frustrum part.
(b) Find the surface area of the frustrum part of the bottle.
Date posted:
April 29, 2019
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Answers (1)
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The distance between towns M and N is 280km. A car and a lorry travel from M to N.
The average speed of the lorry is...
(Solved)
The distance between towns M and N is 280km. A car and a lorry travel from M to N.
The average speed of the lorry is 20km/h less than that of the car. The lorry takes 1h 10min more than the car to
travel from M to N.
a) If the speed of the lorry is xkm/h, find x
b) The lorry left town M at 8.15am. The car left town M later and overtook the lorry at 12.15pm. Calculate the time the car left town M.
Date posted:
April 29, 2019
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Answers (1)
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On the diagram below, the line whose equation is 7y – 3x + 30 = 0 passes through the points A and B. Point A...
(Solved)
On the diagram below, the line whose equation is 7y – 3x + 30 = 0 passes through the points A and B. Point A is on
the x-axis while point B is equidistant from x- and y-axes.
Calculate the co-ordinates of the point A and B
Date posted:
April 29, 2019
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Answers (1)