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Rationalize the denominator and simplify
(Solved)
Rationalize the denominator and simplify
Date posted:
April 26, 2019
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Answers (1)
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The table below show tax rates on a certain year.
(Solved)
The table below show tax rates on a certain year.
Robi earns a basic salary of KSh. 20,000 per month, she is given allowances amounting to KSh. 5000. She is housed by
her employer therefore pays a nominal rent of Sh. 700 per month and is entitled to a personal relief of Sh. 1200 per month. Calculate;
(i) Her taxable income in Kenya pounds per year.
(ii) Her gross tax per month.
Date posted:
April 26, 2019
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Answers (1)
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OA = 3i + 4j – 6k and OB = 2i + 3j + k are two position vectors. P divides a line AB in...
(Solved)
OA = 3i + 4j – 6k and OB = 2i + 3j + k are two position vectors. P divides a line AB in the ratio 3:-2. Write down the
coordinates of P.
Date posted:
April 26, 2019
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Answers (1)
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In the figure below XY = 8cm and O is the centre of the circle.
(Solved)
In the figure below XY = 8cm and O is the centre of the circle.
Determine the area of the circle if angle AOX = 150.
Date posted:
April 26, 2019
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Answers (1)
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The cost of maize floor and millet flour is KSh. 40 and KShs. 52 respectively. Calculate the ratio in which they were mixed if a...
(Solved)
The cost of maize floor and millet flour is KSh. 40 and KShs. 52 respectively. Calculate the ratio in which they were mixed if a profit of 15% was made by selling the mixture at 52.90 per kilogram.
Date posted:
April 26, 2019
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Answers (1)
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A bus moving at a speed of 80km/h is being overtaken by a car moving at 100km/h in a clear section of a road. Given
that...
(Solved)
A bus moving at a speed of 80km/h is being overtaken by a car moving at 100km/h in a clear section of a road. Given
that the bus is 21m long and the car is 4m long.
(a) How much time (in seconds) will elapse before the car can completely overtake the bus?
(b) How much distance (in metres) will the car travel before it can completely overtake the bus?
(c) Given that as soon as the car completed overtaking the trailer, a bus heading towards the trailer and the car and
moving at a speed of 90km/h became visible to the car driver. It took exactly 18 seconds for the car and the bus to
completely by pass each other from the moment they first saw each other.
(i) How far was the tail of the bus from tail of the car at the instance they first saw each other giventhat the bus is 12 metres long?
(ii) How far a part was the trailer and the bus just immediately after the car and the bus had passed each other?
Date posted:
April 26, 2019
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Answers (1)
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The displacement h metres of a particle moving along a straight line after t seconds is given by;
(Solved)
The displacement h metres of a particle moving along a straight line after t seconds is given by
(a) Find its initial acceleration
(b) Calculate;
(i) The time when the object was momentarily at rest
(ii) Its displacement by the time it comes to rest
(c) Calculate the maximum speed attained
Date posted:
April 26, 2019
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Answers (1)
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In the figure below, O is the centre of the circle. PQ is a tangent to the circle at N. Angle NCD is 100 and...
(Solved)
In the figure below, O is the centre of the circle. PQ is a tangent to the circle at N. Angle NCD is 100 and angle ANP is 300.
Giving reasons;
(i) Angle DON
(ii) Angle DNQ
(iii) Angle DBA
(iv) Angle ONA
(v) Angle ODN
Date posted:
April 26, 2019
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Answers (1)
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In the figure below, O is the centre of the circle. PQ is a tangent to the circle at N. Angle NCD is 100 and...
(Solved)
In the figure below, O is the centre of the circle. PQ is a tangent to the circle at N. Angle NCD is 100 and angle ANP is 300.
Giving reasons;
(a) Angle DON
(b) Angle DNQ
(c) Angle DBA
(d) Angle ONA
(e) Angle ODN
Date posted:
April 26, 2019
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Answers (1)
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A solid is made up of a conical frustum and a hemispherical top. The slant height of the frustum is 8cm and its base radius...
(Solved)
A solid is made up of a conical frustum and a hemispherical top. The slant height of the frustum is 8cm and its base radius is 4.2cm. If the radius of the hemispherical top is 3.5cm.
(a) Find the area of:
(i) the circular base.
(ii) the curved surface of the frustum
(iii) the hemispherical surface
(b) A similar solid has a total surface area of 81.51cm2. Determine the radius of its base.
Date posted:
April 26, 2019
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Answers (1)
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(a) A rectangular tank of base 2.4m by 2.8m and a height of 3m contains 3600 litres of water initially.Water flows into the tank at...
(Solved)
(a) A rectangular tank of base 2.4m by 2.8m and a height of 3m contains 3600 litres of water initially.Water flows into the tank at the rate of 0.5 litres per second. Calculate:
(i) The amount needed to fill the tank
(ii) The time in hours and minutes required to fill
(b) Pipe A can fill an empty tank in 3 hours while pipe B can fill the same tank in 6 hours. When the
tank is full, it can be emptied by pipe C in 8 hours. Pipes A and B are opened at the same time when the tank is
empty. If one hour later pipe C is also opened, find the total time taken to fill the tank.
Date posted:
April 26, 2019
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Answers (1)
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Three warships A, B and C are at sea such that ship B is 500km on a bearing N300E from ship A. Ship C is...
(Solved)
Three warships A, B and C are at sea such that ship B is 500km on a bearing N300E from ship A. Ship C is 700km from
ship B on a bearing of 1200. An enemy ship D is sighted 800km due south of ship B.
(a) Taking a scale of 1cm to represent 100km, locate the positions of ships A,B, C and D. (4 Marks)
(b) Find the bearing of:
(i) Ship A from D
(ii) Ship D from C
(c) Use scale drawing to determine the distance between
(i) D and A
(ii) C and D
(d) Measure angle DAC and angle BCD
Date posted:
April 26, 2019
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Answers (1)
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An ant moved from Y to X the midpoint of RS through P in the right pyramid below.
(Solved)
An ant moved from Y to X the midpoint of RS through P in the right pyramid below.
Draw the net of the pyramid showing the path of the ant hence find the distance it moved.
Date posted:
April 26, 2019
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Answers (1)
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The G.C.D. and L.C.M of three numbers are 3 and 1008 respectively. If two of the numbers are 48 and 72, find the least
possible value...
(Solved)
The G.C.D. and L.C.M of three numbers are 3 and 1008 respectively. If two of the numbers are 48 and 72, find the least
possible value of the third number.
Date posted:
April 26, 2019
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Answers (1)
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A woman walks directly from point A towards the foot of a tall building 240m away. After covering 180m, he observes
that the angle of elevation...
(Solved)
A woman walks directly from point A towards the foot of a tall building 240m away. After covering 180m, he observes
that the angle of elevation of the top of the building is 450. Determine the angle of elevation of the top of the building
from A.
Date posted:
April 26, 2019
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Answers (1)
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ABCD is a rhombus. A is the point(2,1) and C is the point (4,7). Find the equation of the diagonal BD in the form ax...
(Solved)
ABCD is a rhombus. A is the point(2,1) and C is the point (4,7). Find the equation of the diagonal BD in the form ax + by = c
Date posted:
April 26, 2019
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Answers (1)
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The ratio of the lengths of the corresponding sides of two similar rectangular petrol tanks is 3:5. The volume of the
smaller tank is 8.1m3. Calculate...
(Solved)
The ratio of the lengths of the corresponding sides of two similar rectangular petrol tanks is 3:5. The volume of the
smaller tank is 8.1m3. Calculate the volume of the larger tank.
Date posted:
April 26, 2019
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Answers (1)
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A regular n-sided polygon has its interior angle equal to 4 times its exterior. Find n.
(Solved)
A regular n-sided polygon has its interior angle equal to 4 times its exterior. Find n.
Date posted:
April 26, 2019
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Answers (1)
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During a certain month, the exchange rates in a bank were as follows;
(Solved)
During a certain month, the exchange rates in a bank were as follows;
A tourist left Kenya to the United States with KSh. 1,000,000.At the airport he exchanged all the money to dollars and
spent 190 dollars on air ticket. While in US he spent 4500 dollars for upkeep and proceeded to Europe. While in Europe he spent a total of 2000 Euros. How many Euros did he remain with?
Date posted:
April 26, 2019
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Answers (1)
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Without using calculator, evaluate.
(Solved)
Without using calculator, evaluate.
leaving the answer as a mixed fraction.
Date posted:
April 26, 2019
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Answers (1)