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- Given a circle of radius 3 units as shown in the diagram below with its centre at O(-1, 6). If BE and DE are tangents...(Solved)
Given a circle of radius 3 units as shown in the diagram below with its centre at O(-1, 6). If BE and DE are tangents to the circle where E (8,2). Given further that angle DAB = 800.
(a) Write down the equation of the circle in the form ax2 + bx + cy2 + dy + e = 0 where a, b, c, d, e are constants.
(b) Calculate the length DE.
(c) Calculate the value of angle BED.
(d) Calculate the value of angle DCB.
Date posted: March 29, 2019. Answers (1)
- Find the distance between points A(500 S, 250 E) and B(500 S, 1400 E) in:
(i) Km ...(Solved)
Find the distance between points A(500 S, 250 E) and B(500 S, 1400 E) in:
(i) Km (ii) nm
(take radius of earth to be 6400km, π = 3.14)
Date posted: March 29, 2019. Answers (1)
- A bag contains x red balls and y yellow balls. Four times the number of red balls is equal to nine times the number of...(Solved)
A bag contains x red balls and y yellow balls. Four times the number of red balls is equal to nine times the number of yellow balls and twice the total number of balls exceeds the number of yellow balls by 44.
(a) How many balls of each colour are three in the bag?
(b) If two balls are drawn out of the bag at random one at a time with replacement what is the probability that the two balls are red?
Date posted: March 29, 2019. Answers (1)
- The diagram below represents a bucket that has been placed upside down. The radius of the top surface is 15cm and that of the bottom...(Solved)
The diagram below represents a bucket that has been placed upside down. The radius of the top surface is 15cm and that of the bottom is 40cm. The vertical height of the bucket is 50cm.
Determine:-
(a) The volume of the bucket.
(b) The curved surface area of the bucket. (leave your answers in terms of π)
Date posted: March 29, 2019. Answers (1)
- Find the co-ordinates of the turning point on the curve of y = x3 – 3x2 and distinguish between them.(Solved)
Find the co-ordinates of the turning point on the curve of y = x3 – 3x2 and distinguish between them.
Date posted: March 29, 2019. Answers (1)
- Calculate the Area of each of the two segments of y = x(x+1)(x-2) cut off by the x axis.(Solved)
Calculate the Area of each of the two segments of y = x(x+1)(x-2) cut off by the x axis.
Date posted: March 29, 2019. Answers (1)
- The Probabilities that it will either rain or not in 30days from now are 0.5 and 0.6 respectively. Find the probability that in 30 days...(Solved)
The Probabilities that it will either rain or not in 30days from now are 0.5 and 0.6 respectively. Find the probability that in 30 days time.
a) it will either rain and not.
b) Neither will not take place.
c) One Event will take place.
Date posted: March 29, 2019. Answers (1)
- Two towns T and S are 300km apart. Two buses A and B started from T at the same time travelling towards S. Bus B...(Solved)
Two towns T and S are 300km apart. Two buses A and B started from T at the same time travelling towards S. Bus B travelled at an average speed of 10km/hr greater than that of A and reached S 1 ¼ hrs earlier.
(a) Find the average speed of A.
(b) How far was A from T when B reached S.
Date posted: March 29, 2019. Answers (1)
- In the figure below, a and b are the position vectors of points A and B respectively. K is a point on
AB such that the...(Solved)
In the figure below, a and b are the position vectors of points A and B respectively. K is a point on
AB such that the AK:KB = 1:1. The point R divides line OB in the ratio 3:2 and point S divides OK in
the ratio 3:1.
(a) Express in terms of a and b
(i) OK (iii) RS
(iii) OS (iv) RA
(b) Hence show that R,S and A are collinear.
Date posted: March 29, 2019. Answers (1)
- The marks obtained by Form 4 students in Examination were as follows:
Using 74.5 as the Assumed mean, calculate:
(i) The mean mark
(ii) The standard deviation(Solved)
The marks obtained by Form 4 students in Examination were as follows:
Using 74.5 as the Assumed mean, calculate:
(i) The mean mark
(ii) The standard deviation
Date posted: March 29, 2019. Answers (1)
- The depth of the water in a rectangular swimming pool increases uniformly from 1M at the shallow
end to 3.5m at the deep end. The pool...(Solved)
The depth of the water in a rectangular swimming pool increases uniformly from 1M at the shallow
end to 3.5m at the deep end. The pool is 25m long and 12m wide. Calculate the volume of the pool
in cubic meters.
The pool is emptied by a cylindrical pipe of internal radius 9cm. The water flows through the pipe at speed of 3 metres per second. Calculate the number of litres emptied from the pool in two minutes to the nearest 10 litres. (Take π = 3.142)
Date posted: March 29, 2019. Answers (1)
- V A B C D is a right pyramid with a square base A B C D of side 5 cm. Each of its four...(Solved)
V A B C D is a right pyramid with a square base A B C D of side 5 cm. Each of its four triangular
faces is inclined at 750 to the base. Calculate
a. The perpendicular height of the pyramid
b. The length of the slant edge VA
c. The angle between edge VA and base A B C D
d. The area of the face VAB
Date posted: March 29, 2019. Answers (1)
- Two unbiased dice are thrown. Find the probability of obtaining
i. A product of 6
ii. A sum of 8
iii. The same number showing(Solved)
Two unbiased dice are thrown. Find the probability of obtaining
i. A product of 6
ii. A sum of 8
iii. The same number showing
Date posted: March 29, 2019. Answers (1)
- The table below gives the performance of students in a test in percentage score.
Using an assumed mean of 44.5, calculate
a. The mean
b. The standard deviation
c....(Solved)
The table below gives the performance of students in a test in percentage score.
Using an assumed mean of 44.5, calculate
a. The mean
b. The standard deviation
c. Find the median mark
Date posted: March 29, 2019. Answers (1)
- A racing cyclist completes the uphill section of a mountain course of 75 km at an average speed of v km/hr. He then returns downhill...(Solved)
A racing cyclist completes the uphill section of a mountain course of 75 km at an average speed of v km/hr. He then returns downhill along the same route at an average speed of (v + 20) km/hr. Given that the difference between the times is one hour, form and solve an equation in v.
Hence
a. Find the times taken to complete the uphill and downhill sections of the course.
b. Calculate the cyclists average speed over the 150km.
Date posted: March 29, 2019. Answers (1)
- A line pass through A (4,3) and B(8,13). Find
(i) Gradient of the line
(ii) The magnitude of AB
(iii) The equation of the perpendicular bisector of AB.(Solved)
A line pass through A (4,3) and B(8,13). Find
(i) Gradient of the line
(ii) The magnitude of AB
(iii) The equation of the perpendicular bisector of AB.
Date posted: March 29, 2019. Answers (1)
- A joint harambee was held for two schools that share a sponsor. School A needed Shs.15 million while
School B needed 24 million to complete their...(Solved)
A joint harambee was held for two schools that share a sponsor. School A needed Shs.15 million while
School B needed 24 million to complete their projects. The sponsor raised Shs.16.9 million while other
guest raised Shs.13.5 million.
(a) If it was decided that the sponsor's money be shared according to the needs of the school
with the rest equally, how much does each school get (5 mks)
(b) If the sponsor's money was shared according to the schools needs while the rest was in the ratio of students, how much does each school get if school A has 780 students and school B 220
students
Date posted: March 29, 2019. Answers (1)
- A cylindrical tank connected to a cylindrical pipe of diameter 3.5cm has water flowing at 150
cm per second. If the water flows for 10 hours...(Solved)
A cylindrical tank connected to a cylindrical pipe of diameter 3.5cm has water flowing at 150
cm per second. If the water flows for 10 hours a day
(a) Calculate the volume in M3 added in 2 days
(b) If the tank has a height of 8 m and it takes 15 days to fill the tank, calculate the base radius
of the tank
Date posted: March 29, 2019. Answers (1)
- A businessman bought pens at Shs.440. The following day he bought 3 pens at Shs.54. This
purchase reduced his average cost per pen by Sh.1.50. Calculate...(Solved)
A businessman bought pens at Shs.440. The following day he bought 3 pens at Shs.54. This
purchase reduced his average cost per pen by Sh.1.50. Calculate the number of pens bought earlier and the difference in cost of the total purchase at the two prices
Date posted: March 29, 2019. Answers (1)
- The income tax in 1995 was collected as follows:
Income in Kshs. p.a rate of tax %
1 - 39,600 ...(Solved)
The income tax in 1995 was collected as follows:
Income in Kshs. p.a rate of tax %
1 - 39,600 10
39,601 - 79,200 15
79,201 - 118,800 25
118,801 - 158,400 35
158,401 - 198,000 45
Mutua earns a salary of Kshs.8,000. He is housed by the employer and therefore 15% is added to his salary to arrive at its taxable income. He gets a tax relief of Shs.400 and pay Shs.130 service charge. Calculate his net income.
Date posted: March 29, 2019. Answers (1)