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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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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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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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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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A two digit number is such that the one’s digit is four more than the tens digit, and the sum of the digits is 14....
(Solved)
A two digit number is such that the one’s digit is four more than the tens digit, and the sum of the digits is 14. Find the
number.
Date posted:
April 26, 2019
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Answers (1)
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All prime numbers less than ten are arranged in ascending order to form a number.
(Solved)
All prime numbers less than ten are arranged in ascending order to form a number.
(a) Write down the number formed.
(b) Express the number in (a) above in expanded form.
Date posted:
April 26, 2019
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Answers (1)
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The first term of an Arithmetic Progression (AP) is 200. The sum of the first 10 terms of AP is 24500.
(Solved)
The first term of an Arithmetic Progression (AP) is 200. The sum of the first 10 terms of AP is 24500.
(a) (i) Find the common difference.
(ii) Given that the sum of the first n terms of the AP is 80100, find n.
(b) The 3rd, 5th and 8th terms of another AP, form the first three terms of a Geometric Progression (GP). If the common
difference of AP is 5, find:-
(i) The first term of the GP.
(ii) The sum of the first 12 terms of the GP, to four significant figures.
Date posted:
April 26, 2019
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Answers (1)
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In the figure below, QT = a and QP = b.
(Solved)
In the figure below, QT = a and QP = b.
(a) Express the vector PT in terms of a and b.
(b) If PX = kPT, express QX in terms of a, b and k, where k is a scalar.
(c) If QR = 3a and RS = 2b, write down an expression for QS in terms of a and b.
(d) If QX = tQS, use your result in (b) and (c) to find the value of k and t.
(e) Find the ratio PX : XT.
Date posted:
April 26, 2019
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Answers (1)
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The figure below shows a circle centre O in which QOT is a diameter.
(Solved)
The figure below shows a circle centre O in which QOT is a diameter. RSU are straight lines.
Calculate the following angles giving a reason in each case.
(a) (b) (c) (d) Obtuse (e)
Date posted:
April 26, 2019
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Answers (1)
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In what ratio must “Murang’a” coffee costing sh. 25g per 100g be mixed with “Kisii” coffee costing sh. 17.50 per 100g,
so that by selling the...
(Solved)
In what ratio must “Murang’a” coffee costing sh. 25g per 100g be mixed with “Kisii” coffee costing sh. 17.50 per 100g,
so that by selling the mixture at sh. 25 per 100g, a profit of 25% is made?
Date posted:
April 26, 2019
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Answers (1)
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QRST is a rhombus. The equations of QR, RS and TS are 2x + y = 7, x = 1 and 2x + y =...
(Solved)
QRST is a rhombus. The equations of QR, RS and TS are 2x + y = 7, x = 1 and 2x + y = -1 respectively. Determine:-
(a) The co-ordinates of Q and S.
(b) The co-ordinates of m, the point of intersection of the diagonals.
(c) The co-ordinates of R and T.
Date posted:
April 26, 2019
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Answers (1)
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a) Solve the equation:
(Solved)
(a) Solve the equation:
(b) A rectangular room is 4m longer than its width. If its area is 12m2, find its dimensions and hence the perimeter of the
room.
Date posted:
April 26, 2019
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Answers (1)
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(a) A bus travelling at 99km/hr passes a check-point at 10.00a.m. and a matatu travelling at 132km/h in the same
direction passes through the check point...
(Solved)
(a) A bus travelling at 99km/hr passes a check-point at 10.00a.m. and a matatu travelling at 132km/h in the same
direction passes through the check point at 10.15a.m. If the bus and the matatu continue at their uniform speeds, find
the time the matatu will overtake the bus.
(b) Two passenger trains A and B which are 240m apart and travelling in opposite directions at 164km/h and 88km/h
respectively approach one another on a straight railway line. Train A is 150 metres long and train B is 100 metres
long. Determine time in seconds that elapses before the two trains completely pass each other.
Date posted:
April 26, 2019
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Answers (1)
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A pail is in the shape of a container frustrum with base radius 6cm and top radius 8cm. The slant height of the pail is
30cm...
(Solved)
A pail is in the shape of a container frustrum with base radius 6cm and top radius 8cm. The slant height of the pail is
30cm as shown below. The pail is full of water.
(a) Calculate the volume of water.
(b) All the water is poured into a cylindrical container of circular radius 7cm, if the cylinder has the height of 35cm;
calculate the surface area of the cylinder which is not in contact with water.
Date posted:
April 26, 2019
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Answers (1)
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Every Sunday Barmao drives a distance of 80km on a bearing of 0740 to pick up her sister Afandi to go to church. The
church is...
(Solved)
Every Sunday Barmao drives a distance of 80km on a bearing of 0740 to pick up her sister Afandi to go to church. The
church is 75km from Afandi’s home on bearing of S500E. After church they drive a distance of 100km on a bearing of
2600 to check on their friend Akoth before Barmao drives to Afandi’s home to drop her off then proceed to her house.
(a) Using a scale of 1cm to represent 10km, show the relative positions of these places.
(b) Use your diagram to determine:
(i) The true bearing of Barmao’s home from Akoth’s house.
(ii) The compass bearing of the Akoth’s home from Afandi’s home.
(c) (i) The distance between Afandi’s home and Akoth’s home.
(ii) The total distance Barmao travel every Sunday.
Date posted:
April 26, 2019
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Answers (1)