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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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(a) Expand and simplify the binomial expression.
(Solved)
(a) Expand and simplify the binomial expression.
(b) Use the first four terms of the simplified expression in (a) above to evaluate to 5 significant figures.
(1.98)5.
Date posted:
April 24, 2019
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Answers (1)
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Under a transformation whose matrix
(Solved)
Under a transformation whose matrix
a figure whose area is 2.5cm2 is mapped onto a figure whose area is 10cm2. Find two possible values of a and hence write down two possible matrices for T.
Date posted:
April 24, 2019
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Answers (1)
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The table below shows the masses of 40 students in a form 4 class.
(Solved)
The table below shows the masses of 40 students in a form 4 class.
(a) State the modal class.
(b) Calculate the median mass
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 number of bacteria in a colony was originally 3 millions. This number doubled itself after every one hour.Calculate the number of bacteria generated in...
(Solved)
The number of bacteria in a colony was originally 3 millions. This number doubled itself after every one hour.Calculate the number of bacteria generated in the colony during the 7thhour.
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 following distribution shows the marks obtained by 82 students in a Mathematics test.
(Solved)
The following distribution shows the marks obtained by 82 students in a Mathematics test.
(a) State the modal class.
(b) Calculate to 2 decimal places:
(i) the mean mark.
(ii) the difference between the median and the mean marks.
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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Use reciprocal and square tables to evaluate, to 4 significant figures, the expression.
(Solved)
Use reciprocal and square tables to evaluate, to 4 significant figures, the expression.
Date posted:
April 24, 2019
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Answers (1)
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Using logarithms tables only, evaluate.
(Solved)
Using logarithms tables only, evaluate.
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)
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A Kenyan bank buys and sells foreign currencies at the exchange rates shown below.
(Solved)
A Kenyan bank buys and sells foreign currencies at the exchange rates shown below.
An American arrived in Kenya with 20 000 Euros. He converted all the Euros to Kenya shillings at the bank. He spent
KShs. 2,512,000 while in Kenya and converted the remaining Kenya shillings into US Dollars at the bank. Find the
amount in Dollars that he received.
Date posted:
April 24, 2019
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Answers (1)
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The line which joins the point A (3, k) and B (-2, 5) is parallel to the line whose equation is
5y + 2x – 7...
(Solved)
The line which joins the point A (3, k) and B (-2, 5) is parallel to the line whose equation is
5y + 2x – 7 = 0. Find the value of k.
Date posted:
April 24, 2019
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Answers (1)