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The mass of two similar solid are 324g and 768g. Find
(Solved)
The mass of two similar solid are 324g and 768g. Find
(a) height of the smaller solid if the height of the bigger solid is 20cm.
(b) the surface area of the smaller solid if the surface area of the bigger solid is 40cm².
Date posted:
April 25, 2019
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Answers (1)
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(a) Express 1050 in terms of its prime factors.
(b) Determine the smallest positive number such that 1050p is a perfect square.
(Solved)
(a) Express 1050 in terms of its prime factors.
(b) Determine the smallest positive number such that 1050p is a perfect square.
Date posted:
April 25, 2019
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Answers (1)
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Two variables A and B are connected by the equation.
A = kBn
(Solved)
Two variables A and B are connected by the equation.
A = kBn
Where k and n are constants.
The table below gives values of A and B
(b) On square paper draw a suitable straight line graph to represent the relation in (a) above (scale 1cm to represent 0.1 units on both axis)
(c) Use your graph to estimate the values of k and n in to one decimal place.
Date posted:
April 24, 2019
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Answers (1)
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In the figure above, OPQ is a triangle in which;
(Solved)
Date posted:
April 24, 2019
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Answers (1)
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Veterinary researchers were experimenting with a new drug on fowls in a research station. A sample of fowls which were known to have the disease...
(Solved)
Veterinary researchers were experimenting with a new drug on fowls in a research station. A sample of fowls which were known to have the disease was used. In this sample 30 fowls were treated with the drug and the remaining 18 fowls were not treated.
(a) Calculate the probability that a fowl selected at random from the sample is
(i) treated with the drug
(ii) not treated with the drug
(b) The probability that a fowl treated with the drug will die is 1/10
, while the probability that one which is not
treated will die is 7/10
Calculate the probability that a fowl picked at random from the sample is
(i) treated with the drug and will die
(ii) not treated with the drug and will die
(iii) treated with the drug and will not die
(iv) not treated with the drug and will not die
Date posted:
April 24, 2019
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Answers (1)
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Two towns on the earth’s surface are located at P (070N,300E) and Q (130S,300E). A pilot plans to fly from P to Q the shortest...
(Solved)
Two towns on the earth’s surface are located at P (070N,300E) and Q (130S,300E). A pilot plans to fly from P to Q the shortest route between the two towns.
(a) Calculate the shortest distance between P and Q in km.
(b) Find the distance in nautical miles (nm)
(c) The speed of the aircraft is 360 knots. Determine how long it takes to fly from P to Q.
Date posted:
April 24, 2019
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Answers (1)
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Under a transformation represented by a matrix m a point p (x, y) is mapped onto PI, (xI,yI) where
(Solved)
Under a transformation represented by a matrix m a point p (x, y) is mapped onto PI, (xI,yI) where
(a) Write down the matrix for m. (2 Marks)
(b) Find the inverse of m.
(c) The points AI (16,-2) BI (-8, 1), CI (8,-1) and DI (9,-8) are the images of A, B, C and D respectively under M.
Determine the coordinates of A, B, C and D.
Date posted:
April 24, 2019
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Answers (1)
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Kennedy bought three cows and twenty-five goats spending a total of Sh. 75000. If he had bought two cows and thirty three goats, he would...
(Solved)
Kennedy bought three cows and twenty-five goats spending a total of Sh. 75000. If he had bought two cows and thirty three goats, he would have saved Sh. 5400. Kennedy later sold all his animals at a profit of 40% per cow and 50% per goat.
Determine;
(a) the cost at which he bought each animal.
(b) the total amount of money Kennedy received after selling all the animals.
Date posted:
April 24, 2019
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Answers (1)
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Wambua invested Sh. 6400 at 15% per annum compound interest for 3 years. Muinde invested twice that amount at 12.5% per annum simple interest for...
(Solved)
Wambua invested Sh. 6400 at 15% per annum compound interest for 3 years. Muinde invested twice that amount at 12.5% per annum simple interest for the same period of time. Find whose investment earned more interest and by how much.
Date posted:
April 24, 2019
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Answers (1)
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Solve for x in the equation log (x – 1) = log 12 – log (x – 2)
(Solved)
Solve for x in the equation log (x – 1) = log 12 – log (x – 2)
Date posted:
April 24, 2019
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Answers (1)
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The equation of a circle is x2 – 8x + y2 + 12y + 16 = 0.Determine the coordinates of the centre of the circle...
(Solved)
The equation of a circle is x2 – 8x + y2 + 12y + 16 = 0.Determine the coordinates of the centre of the circle and its radius.
Date posted:
April 24, 2019
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Answers (1)
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The length and breadth of a metal sheet are measured to the nearest centimetre and recorded as 25cm and 16cm
respectively.
(Solved)
The length and breadth of a metal sheet are measured to the nearest centimetre and recorded as 25cm and 16cm
respectively.
(a) Find the maximum possible error in the area of the sheet.
(b) Calculate to one decimal place the percentage error in the area of the sheet.
Date posted:
April 24, 2019
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Answers (1)
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Triangle PQR has vertices at P (2,3), Q(1,2) and R(4,1), while triangle PIQIRI has vertices PI(-2,3),QI(-1,2), RI(-4,1)
(Solved)
Triangle PQR has vertices at P (2,3), Q(1,2) and R(4,1), while triangle PIQIRI has vertices PI(-2,3),QI(-1,2), RI(-4,1)
(a) (i) Draw triangle PQR and PIQIRI on the grid provided.
(ii) Describe fully a single transformation which maps triangle PQR onto triangle PIQIRI.
(b) (i) On the same grid, draw triangle PIIQIIRII the image of PQR under a reflection on the line y + x = 0.
(ii) Describe fully a single transformation which maps triangle PIIQIIRII onto triangle PIQIRI.
Date posted:
April 24, 2019
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Answers (1)
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P, Q and R are three villages such that PQ = 10km, QR = 8km and PR = 4km are connecting roads.
(Solved)
P, Q and R are three villages such that PQ = 10km, QR = 8km and PR = 4km are connecting roads.
(a) Using a scale of 1cm to represent 1km, locate the relative positions of the three villages.
(b) A water tank T is to be located at a point equidistant from the three villages. By construction locate water tank T and measure its distance from R.
(c) Determine the shortest distance from T to the road PQ by construction.
(d) Determine the area enclosed by the roads PQ, QR and PR by calculation.
Date posted:
April 24, 2019
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Answers (1)
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Triangle PQR is inscribed in the circle. PQ = 7.8cm, PR = 6.6cm and QR = 5.9cm.
(Solved)
Triangle PQR is inscribed in the circle. PQ = 7.8cm, PR = 6.6cm and QR = 5.9cm.
Find;
(a) size of angle QPR
(b) the radius of the circle.
(c) the area of the shaded region.
Date posted:
April 24, 2019
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Answers (1)
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John bought 3 brands of tea; A, B and C. The cost price of the three brands were Sh. 25, Sh. 30 and Sh. 45...
(Solved)
John bought 3 brands of tea; A, B and C. The cost price of the three brands were Sh. 25, Sh. 30 and Sh. 45 per kilogram
respectively. He mixed the three brands in the ratio 5:2:1 respectively. After selling the mixture, he made a profit of
20%.
(a) How much profit did he make per kilogram of the mixture?
(b) After one year the cost price of each brand was increased by 10%.
(i) For how much did he sell one kilogram of the mixture to make a profit of 15%?
(Give your answer to the nearest 5 cents)
(ii) What would have been his percentage profit if he sold one kilogram of the mixture at Sh. 45.
Date posted:
April 24, 2019
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Answers (1)
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The figure below is a velocity time graph for a car.
(Solved)
The figure below is a velocity time graph for a car.
(i) Find the total distance travelled by the car.
(ii) Calculate the deceleration of the car.
(b) A car left Nairobi towards Eldoret at 7.12 a.m. at an average speed of 90km/h. At 8.22 a.m, a bus left
Eldoret for Nairobi at an average speed of 72km/hr. The distance between the two towns is 348km. Calculate:
(i) the time when the two vehicles met.
(ii) the distance from Nairobi to the meeting place.
Date posted:
April 24, 2019
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Answers (1)
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The figure below shows a cone from which a frustum is made. A plane parallel to the base cuts the cone two thirds
way up the...
(Solved)
The figure below shows a cone from which a frustum is made. A plane parallel to the base cuts the cone two thirds
way up the vertical height of the cone to form frustum ABCD. The top surface radius of the frustum is labelled r and the
bottom radius R.
(a) Find the ratio r:R.
(b) Given that r = 7cm, find R.
(c) If the height VY of the original cone is 45cm. Calculate to the nearest whole number the volume of the
frustum. (Take 𝜋 =22/7)
(d) The frustum represents a bucket which is used to fill a rectangular tank measuring 1.5m long, 1.2m wide and
80cm high with water. How many full buckets of water are required to fill the tank.
Date posted:
April 24, 2019
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Answers (1)
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A group of people planned to contribute equally towards buying land at a price of Shs 180,000. However 3 members of
the group withdrew from the...
(Solved)
A group of people planned to contribute equally towards buying land at a price of Shs 180,000. However 3 members of
the group withdrew from the project. As a result, each of the remaining members were to contribute KShs. 3000 more.
(a) Find the original number of members in the group.
(b) How much would each person have contributed if the 3 people had not withdrawn.
(c) Calculate the percentage increase in the contribution per person caused by the withdrawal.
Date posted:
April 24, 2019
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Answers (1)
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The diagram below represents a right pyramid on a square base of side 3cm. The slant edge of the pyramid is 4cm.
(Solved)
The diagram below represents a right pyramid on a square base of side 3cm. The slant edge of the pyramid is 4cm.
(a) Draw a labelled net of the pyramid.
(b) On the net drawn, measure the height of a triangular face from the top of the pyramid.
Date posted:
April 24, 2019
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Answers (1)