- 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)
- Maina bought a car at Kshs.650,000. The value depreciated annually at 15%
(a) After how long to the nearest 1 decimal place will the value of...(Solved)
Maina bought a car at Kshs.650,000. The value depreciated annually at 15%
(a) After how long to the nearest 1 decimal place will the value of the car be Kshs.130,000
(b) Calculate the rate of depreciation to the nearest one decimal place which would make the value of
the car be half of its original value in 5 years
Date posted: March 29, 2019. Answers (1)
- The table below shows the mass of 60 women working in hotels
(a) State (i) The modal class
...(Solved)
The table below shows the mass of 60 women working in hotels
(a) State (i) The modal class
(ii) The median class
(b) Estimate the mean mark
(c) Draw a histogram for the data
Date posted: March 29, 2019. Answers (1)
- The given Region below (unshaded R) is defined by a set of inequalities. Determine the inequalities(Solved)
The given Region below (unshaded R) is defined by a set of inequalities. Determine the inequalities
Date posted: March 29, 2019. Answers (1)
- Maina, Kamau and Omondi share Shs.180 such that for every one shilling Maina gets, Kamau gets 50
Cts and for every two shillings Kamau gets, Omondi...(Solved)
Maina, Kamau and Omondi share Shs.180 such that for every one shilling Maina gets, Kamau gets 50
Cts and for every two shillings Kamau gets, Omondi gets three shillings. By how much does Maina's
share exceed Omondi's
Date posted: March 28, 2019. Answers (1)
- In quadrilateral OABC, OA = 4i - 3j. OC = 2i + 7j
AB = 3OC. cm: mB = 2:3. Find in terms of i and...(Solved)
In quadrilateral OABC, OA = 4i - 3j. OC = 2i + 7j
AB = 3OC. cm: mB = 2:3. Find in terms of i and j
vector Om
Date posted: March 28, 2019. Answers (1)
- By matrix method, solve the equations
5x + 5y = 1
4y + 3x = 5(Solved)
By matrix method, solve the equations
5x + 5y = 1
4y + 3x = 5
Date posted: March 28, 2019. Answers (1)
- Six men take 14 days working 8 hours a day to pack 2240 parcels. How many more men working
5 hours a day will be required...(Solved)
Six men take 14 days working 8 hours a day to pack 2240 parcels. How many more men working
5 hours a day will be required to pack 2500 parcels in 2 days
Date posted: March 28, 2019. Answers (1)
- A 2 digit number is such that the tens digit exceeds the unit by two . If the digits are reversed, the number formed is smaller...(Solved)
A 2 digit number is such that the tens digit exceeds the unit by two . If the digits are reversed, the number formed is smaller than the original by 18. Find the original number.
Date posted: March 27, 2019. Answers (1)