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- Simplify the following expression as far as possible.(Solved)
Simplify the following expression as far as possible.
Hence or otherwise simplified
Date posted: May 3, 2019. Answers (1)
- The vectors a = (2x - 4)i + (x - 3)j + (x - 2)k and the length of /a/ = 7. Find two possible...(Solved)
The vectors a = (2x - 4)i + (x - 3)j + (x - 2)k and the length of /a/ = 7. Find two possible values of x.
Date posted: May 3, 2019. Answers (1)
- Given that (x - 2) is a factor of 3x2 + kx - 2 find the value of k and hence the other factor.(Solved)
Given that (x - 2) is a factor of 3x2 + kx - 2 find the value of k and hence the other factor.
Date posted: May 3, 2019. Answers (1)
- a) Expand and simplified the first four terms of the binomial expression (2 - 3x)6.(Solved)
a) Expand and simplified the first four terms of the binomial expression (2 - 3x)6.
b) Use the simplified expression in (a) above to estimate the value of (1.97)6 correct 5 decimal places.
Date posted: May 3, 2019. Answers (1)
- Two values X and Y are such that
3.5 < x < 4.9
0.03 < y < 0.27
What is the greatest possible value of x2/y(Solved)
Two values X and Y are such that
3.5 ≤ x ≤ 4.9
0.03 ≤ y ≤ 0.27
What is the greatest possible value of x2/y
Date posted: May 3, 2019. Answers (1)
- The equation of a circle is x2 - 8x + y2 + 12y = 12. Determine the centre and its radius of the circle.(Solved)
The equation of a circle is x2 - 8x + y2 + 12y = 12. Determine the centre and its radius of the circle.
Date posted: May 3, 2019. Answers (1)
- In the figure below XY is a tangent to a circle at YZ.VZ is a chord which produced to meet XY at Y. Given that...(Solved)
In the figure below XY is a tangent to a circle at YZ.VZ is a chord which produced to meet XY at Y. Given that XY = 9cm
and YZ = 6cm. Calculate the length of VZ.
Date posted: May 3, 2019. Answers (1)
- Without using mathematical tables evaluate,(Solved)
Without using mathematical tables evaluate,
Date posted: May 3, 2019. Answers (1)
- Make y the subject of the formula.(Solved)
Make y the subject of the formula.
Date posted: May 3, 2019. Answers (1)
- Use logarithms to evaluate.(Solved)
Use logarithms to evaluate.
Date posted: May 3, 2019. Answers (1)
- The distance S metres from a fixed point, covered by a particle t seconds is given by the equation.
s = t3 - 6t2 + 9t...(Solved)
The distance S metres from a fixed point, covered by a particle t seconds is given by the equation.
s = t3 - 6t2 + 9t + 5.
a) Calculate the gradient of the curve at t = 0.5 seconds.
b) Determine the value of s at the maximum turning point of the curve.
Date posted: May 3, 2019. Answers (1)
- A bus left town A at 11.45 a.m and travelled towards town B at average speed of 60km/h. A car left town B at 1.15p.m
on...(Solved)
A bus left town A at 11.45 a.m and travelled towards town B at average speed of 60km/h. A car left town B at 1.15p.m
on the same day and travelled towards town A along the same road at an average speed of 90km/h. The distance
between the two towns is 540km. Determine
a) The time of day when the two vehicles met.
b) How far from A they met.
c) How far outside town B the bus was when the car reached town A.
Date posted: May 3, 2019. Answers (1)
- The table below shows Kenya’s tax rates in a certain year.(Solved)
The table below shows Kenya’s tax rates in a certain year.
In that year Mr. Mwangi earned a basic salary of Kshs. 16000 per month. He is entitled to a house allowance of ksh.12000 per month and a medical allowance of ksh. 2000 per month.Calculate:
a) i) His taxable income per year in pounds.
ii) His monthly gross tax.
iii) The monthly net tax if he is given a relief of ksh. 1056 per month.
b) Other deductions per month are as follows
N.H.I.F sh. 320, cooperative loan sh. 5600,
WCPS sh 488, coop shares sh 2000
Find his monthly net pay.
Date posted: May 3, 2019. Answers (1)
- The diagram below represents a solid consisting of a hemispherical bottom and a conical frustrum at the top.(Solved)
The diagram below represents a solid consisting of a hemispherical bottom and a conical frustrum at the top.
a) Determine the value of x hence the height of the cone.
b) Calculate;
i) The surface area of the solid.
ii) The volume of the solid.
Date posted: May 3, 2019. Answers (1)
- The figure below shows triangle OAB in which OA = a and OB = b. M and N are points on OB and AB respectively...(Solved)
The figure below shows triangle OAB in which OA = a and OB = b. M and N are points on OB and AB respectively such
that OM = 1/3OB and AN = 2/5AB. Line AM and ON meet at P such that OP = 5/9 ON.
a) Express the following vectors in terms of a and b
i) AB
ii) ON
iii) AM
b) Express AP and PM in terms of a and b,hence show that the points A, P and M are collinear.
Date posted: May 3, 2019. Answers (1)
- Three hundred and sixty litres of a homogenous paint is made by mixing three paints A, B and C. The ratio by volume
of paints A...(Solved)
Three hundred and sixty litres of a homogenous paint is made by mixing three paints A, B and C. The ratio by volume
of paints A to paint B is 3 : 2 and paint B to paint C is 1 : 2. Paint A costs sh. 180 per litre, paint B sh. 240 per litre and
paint C sh. 127.50 per litre. Determine:
a) The volume of each type of paint in the mixture.
b) The amount of money spent in making one litre of the mixture.
c) The percentage profit made by selling the mixture at sh. 221 per litre.
Date posted: May 3, 2019. Answers (1)
- The length and breadth of a rectangle are given as (6x - 1) and (x - 2) metres respectively. If the length and breadth
are each...(Solved)
The length and breadth of a rectangle are given as (6x - 1) and (x - 2) metres respectively. If the length and breadth
are each increased by 4 metres, the new area is three times that of the original triangle.
a) Form an equation in x and solve it.
b) Find the dimension of the original rectangle.
c) Express the increase in area as a percentage of the original area.
Date posted: May 3, 2019. Answers (1)
- Evaluate the following(Solved)
Evaluate the following
Date posted: May 2, 2019. Answers (1)
- Work out the following.(Solved)
Work out the following.
Date posted: May 2, 2019. Answers (1)
- An American tourist arrives in Kenya with 1000 US$ and converted the whole amount into Kenyan shilling. He spend sh. 40000 and changed the balance...(Solved)
An American tourist arrives in Kenya with 1000 US$ and converted the whole amount into Kenyan shilling. He spend sh. 40000 and changed the balance to Sterling pounds before leaving for United Kingdom. A Kenyan bank buys and sells foreign currencies as shown.
Calculate the amount he received to the nearest sterling pound.
Date posted: May 2, 2019. Answers (1)