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The figure below shows a rectangular sheet of metal whose length is twice its width.
An open rectangular tank is made by cutting equal squares of...
(Solved)
The figure below shows a rectangular sheet of metal whose length is twice its width.

An open rectangular tank is made by cutting equal squares of length 60 cm from each of its four corners and folding along the dotted lines shown in the figure above. Given that the capacity of the tank so formed is 1920 litres and the width of the metal sheet used was x cm;
a) (i) Express the volume of the tank formed in terms of x cm.
(ii) Hence or otherwise obtain the length and width of the sheet of metal that was used.
b) If the cost of the metal sheet per m2 is Kshs 1000 and labour cost for making the tank is 300 per hour.
Find the selling price of the tank in order to make a 30% profit if it took 6 hours to make the tank.
Date posted:
November 13, 2019
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Answers (1)
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A village Q is 7 km from village P on a bearing of 0450. Village R is 5 km from village Q on a bearing...
(Solved)
A village Q is 7 km from village P on a bearing of 0450. Village R is 5 km from village Q on a bearing of 1200 and village S is 4 km from village R on a bearing of 2700.
a) Taking a scale of 1 m to represent 1 Km, locate the three villages.
b) Use the scale drawing to find the:
i. Distance and bearing of the village R from village P.
ii. Distance and bearing of village P from village S.
iii. Area of the polygon PQRS to the nearest 4 significant figures.
Date posted:
November 13, 2019
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Answers (1)
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A sector of angle 1080 is cut from a circle of radius 20 cm. It is folded to form a cone.
Calculate:
(a) The curved surface area...
(Solved)
A sector of angle 1080 is cut from a circle of radius 20 cm. It is folded to form a cone.
Calculate:
(a) The curved surface area of the cone.
(b) The base radius of the cone.
(c) The vertical height of the cone.
(d) If 12 cm of the cone is chopped off to form a frustrum as shown below.

Calculate the volume of the frustum formed.
Date posted:
November 13, 2019
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Answers (1)
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Nyongesa is a sales executive earning a salary of Kshs. 120,000 and a commission of 8% for the sales in excess of Kshs. 1,000,000. If...
(Solved)
Nyongesa is a sales executive earning a salary of Kshs. 120,000 and a commission of 8% for the sales in excess of Kshs. 1,000,000. If in January he earned a total of Kshs. 480,000 in salaries and commission.
(a) Determine the amount of sales he made in the month of January.
(b) If the total sales in the month of February increased by 18% and in the month of March dropped by 30% respectively;
Calculate:-
(i) Nyongesa’s commission in the month of February.
(ii) His total earning in the month of March.
Date posted:
November 13, 2019
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Answers (1)
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The figure below shows two sectors in which AB and CD are arcs of concentric circles centre O.
Angle AOB = 2/5 radians and AD =...
(Solved)
The figure below shows two sectors in which AB and CD are arcs of concentric circles centre O.
Angle AOB = 2/5 radians and AD = BC = 5 cm.

Given that the perimeter of the shape ABCD is 24 cm, calculate the length of OA.
Date posted:
November 13, 2019
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Answers (1)
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A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 12 cm and the slanting height...
(Solved)
A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 12 cm and the slanting height of the cone is 10 cm. Calculate correct to two decimal places, the surface area of the solid.
Date posted:
November 13, 2019
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Answers (1)
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Solve for y given that y is acute and sin (3y – 500) – cos (2y + 100) = 0
(Solved)
Solve for y given that y is acute and sin (3y – 500) – cos (2y + 100) = 0
Date posted:
November 13, 2019
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Answers (1)
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Janice, a fruit vendor obtained a total of Kshs. 6144 from her sales of oranges on Saturday at Kshs. 8.00 each. She had bought 560...
(Solved)
Janice, a fruit vendor obtained a total of Kshs. 6144 from her sales of oranges on Saturday at Kshs. 8.00 each. She had bought 560 more oranges to add to what had remained on Friday where she had sold 240 more oranges than on Thursday. She had sold 750 oranges on Thursday. Calculate the total number of oranges Janice had bought on Thursday.
Date posted:
November 13, 2019
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Answers (1)
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Using a ruler and a pair of compasses only, construct a rhombus PQRS such that PQ = 6 cm and angle PQR = 1350 hence...
(Solved)
Using a ruler and a pair of compasses only, construct a rhombus PQRS such that PQ = 6 cm and angle PQR = 1350 hence measure the shortest diagonal.
Date posted:
November 13, 2019
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Answers (1)
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Complete the diagram below so as to make a net for a cuboid. Hence find the surface area of the cuboid.
(Solved)
Complete the diagram below so as to make a net for a cuboid. Hence find the surface area of the cuboid.

Date posted:
November 13, 2019
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Answers (1)
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Wanyama on arrival in Kenya to play for Harambee Stars against Uganda Cranes converted 6000 Euros into Kenyan Shillings. During his stay in Kenya he...
(Solved)
Wanyama on arrival in Kenya to play for Harambee Stars against Uganda Cranes converted 6000 Euros into Kenyan Shillings. During his stay in Kenya he spent Kshs. 260,000 and converted the remaining amount into US Dollars before travelling back to England. Using the exchange rates below, find how many US Dollars he got?
Currency Buying Selling
(Kshs.) (Kshs.)
1 US Dollar 96.20 96.90
1 Euro 112.32 112.83
Date posted:
November 13, 2019
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Answers (1)
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The sum of four consecutive odd integers is greater than 24. Determine the first four such integers.
(Solved)
The sum of four consecutive odd integers is greater than 24. Determine the first four such integers.
Date posted:
November 13, 2019
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Answers (1)
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Wafula uses 1/6 of his land for planting maize, 1/12 for beans and 4/9 of the remainder for grazing.
He still has 10 hectares of unused...
(Solved)
Wafula uses 1/6 of his land for planting maize, 1/12 for beans and 4/9 of the remainder for grazing.
He still has 10 hectares of unused land. Find the size of Wafula’s land.
Date posted:
November 13, 2019
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Answers (1)
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The table below shows the income tax ratesJuma is a salaried employee who is given an automatic house allowance of sh. 8000 monthly. He also gets...
(Solved)
The table below shows the income tax rates

Juma is a salaried employee who is given an automatic house allowance of sh. 8000 monthly. He also gets a single relief of Ksh1320. If his P.A.Y.E is Ksh 5420 a month,
(a) Find his total tax in shillings per annum
(b) How much does he earn per month?
Date posted:
November 12, 2019
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Answers (1)
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(a) Using trapezoidal rule estimate the area bounded by the curve y=3x2 - 2 and the lines x=-4 ,x=4 and x-axis.
(b) find the actual area...
(Solved)
(a) Using trapezoidal rule estimate the area bounded by the curve y=3x2 − 2 and the lines x=−4 ,x=4 and x−axis.
(b) find the actual area bounded by the curve y=3x2 − 2 and the lines x=−4 ,x=4 and x−axis.
(c) Calculate the percentage error when trapezoidal rule is used.
Date posted:
November 12, 2019
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Answers (1)
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The probability that a boy goes to school by bus is 1/3 and by matatu is ½. If he uses a bus the probability that...
(Solved)
The probability that a boy goes to school by bus is 1/3 and by matatu is ½. If he uses a bus the probability that he is late to school is 1/5 and if he uses a matatu the probability of being late is 3/10. If he uses other means of transport, the probability of being late is 1/20. What is he probability that;
(a) He will be late to school
(b) He will not be late to school
(c) He will be late to school if he does not use a matatu
(d) He neither uses a bus nor matatu but arrives to school early.
Date posted:
November 12, 2019
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Answers (1)
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The first term of A.P is 3.5, the common difference is d if the difference of 20th and 6th terms is 40.
(a) (i)find the common...
(Solved)
The first term of A.P is 3.5, the common difference is d if the difference of 20th and 6th terms is 40.
(a) (i)find the common difference, d
(ii) calculate the sum of the first 40 terms of the AP
(b) The progression is such that the 2nd , 14th and 85th terms of the AP forms the first 3 terms of a G.P. If the common difference of A.P is 2.5
Find
(i) 2nd term of the G.P
(ii) Sum of the two 10 terms of G.P
Date posted:
November 12, 2019
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Answers (1)
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An aeroplane that moves at a constant speed of 600 knots flies from town A (140N, 300W) southwards to town B (X0S, 300W) taking 3...
(Solved)
An aeroplane that moves at a constant speed of 600 knots flies from town A (140N, 300W) southwards to town B (X0S, 300W) taking 3 1/2 hrs. It then changes direction and flies along latitude to town C (X0S, 600E). Given π = 3.142 and radius of the earth R= 6370 km
(a) Calculate
(i) The value of X
(ii) The distance between town B and town C along the parallel of latitude in km.
(b) D is an airport situated at (50N, 1200W), calculate
(i) The time the aeroplane would take to fly from C to D following a great circle through the South Pole.
(ii) The local time at D when the local time at A is 12.20 pm
Date posted:
November 12, 2019
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Answers (1)
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The figure below shows a frustum of a square based pyramid (not drawn to scale). The base ABCD is a square of sides 10cm. The...
(Solved)
The figure below shows a frustum of a square based pyramid (not drawn to scale). The base ABCD is a square of sides 10cm. The top A’B’C’D’ is a square of side 4 cm and each slant edges of the frustum is 5cm long. Calculate the angle between AC’ and the line AC.

Date posted:
November 12, 2019
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Answers (1)
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Triangle ABC has vertices A(1,0), B(4,0) and C(1,4) is mapped onto A’B’C’ under a shear matrix, x axis invariant and C(1,4) is mapped onto C’(7,4)....
(Solved)
Triangle ABC has vertices A(1,0), B(4,0) and C(1,4) is mapped onto A’B’C’ under a shear matrix, x axis invariant and C(1,4) is mapped onto C’(7,4). Find the shear matrix hence find the coordinates of the image of P(2,-3) and Q(-2,-3).
Date posted:
November 12, 2019
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Answers (1)