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- (a) Complete the table below for the function:
(b) Use the mid-ordinate rule with six ordinates to estimate the area enclosed by the curve...(Solved)
(a) Complete the table below for the function:
(b) Use the mid-ordinate rule with six ordinates to estimate the area enclosed by the curve of the functions y = x2 – 3x + 5, x – axis and the lines x = 2 and x = 8.
(c) Find the exact area of the region described in (b) above.
(d) If the mid-ordinates rule is used to estimate the area under the curve between x = 2 and x = 8, what will be the percentage error in the estimation?
Date posted: September 20, 2019. Answers (1)
- A farmer has at least 50 acres of land on which he plans to plant potatoes and cabbages.
Each acre of potatoes requires 6 men...(Solved)
A farmer has at least 50 acres of land on which he plans to plant potatoes and cabbages.
Each acre of potatoes requires 6 men and each acre of cabbages requires 2 men. The farmer has 240 men available and he must plant at least 10 acres of potatoes. The profit on potatoes is Ksh. 1000 per acre and on cabbages is Ksh. 1200 per acre. If he plants x acres of potatoes and y acres of cabbages:
(a)Write down three inequalities in x and y to describe this information.
(b)Represent these inequalities graphically.
Date posted: September 20, 2019. Answers (1)
- In the diagram M is the midpoint of XZ. OX = p + 2q. Oz = 7p – 2q and ZY = 3Kq + Mp...(Solved)
In the diagram M is the midpoint of XZ. OX = p + 2q. Oz = 7p – 2q and ZY = 3Kq + Mp where
k, and m are constants.
(a)Express the following in terms of p and q.
(i) XZ
(ii) XM
(iii) OM
(b)Express OY in terms of p, q, k and m.
(c)If y lies on OM produced with OY:OM = 3:2. Find the values of k and m.
Date posted: September 20, 2019. Answers (1)
- The table below shows monthly income tax rates.
A government employee earns a monthly salary of Ksh. 24,200 and is provided with a house at a...(Solved)
The table below shows monthly income tax rates.
A government employee earns a monthly salary of Ksh. 24,200 and is provided with a house at a nominal rent of Ksh. 700 per month.
(a)Calculate the employee’s taxable pay in K£.
(b)Calculate the total tax.
(c)The employee is entitled to a personal relief of Kshs. 1056 per month; and a monthly insurance relief at the rate of 15% of the premium paid. Calculate the net tax paid by the employee if the monthly premium amounts to Kshs. 2,400 for life insurance cover
d)Calculate his / her net pay that month.
Date posted: September 20, 2019. Answers (1)
- A blender mixes two brands of Juice A and B to obtain 70mls of the mixture worth Ksh. 165 per litre. If brand...(Solved)
A blender mixes two brands of Juice A and B to obtain 70mls of the mixture worth Ksh. 165 per litre. If brand A is valued at Ksh. 168 per 1 litre bottle and brand B at Ksh. 153 per 1 litre bottle, calculate the ratio in which the bands A and B are mixed.
Date posted: September 20, 2019. Answers (1)
- A stone is thrown vertically upwards from Point O. After t seconds the stone is S metres fromO. Given that S = 29.4t...(Solved)
A stone is thrown vertically upwards from Point O. After t seconds the stone is S metres from O. Given that S = 29.4t – 4.9t2, find the maximum height reached by the stone.
Date posted: September 20, 2019. Answers (1)
- Solve for x in the equation:
3cos2x + sin x + 1 = 0 For 0 < x < 360
(Solved)
Solve for x in the equation:
3cos2x + sin x + 1 = 0 For 0 < x < 360
Date posted: September 20, 2019. Answers (1)
- The marks of 80 students in a Mathematics test are shown in the table below.
Find the quartile deviation of the marks.
(Give your answer to the...(Solved)
The marks of 80 students in a Mathematics test are shown in the table below.
Find the quartile deviation of the marks.
(Give your answer to the nearest whole number)
Date posted: September 20, 2019. Answers (1)
- A circle whose equation is (x – 1)2 + (y – k)2 = 10 passes through point (2,5). Find the coordinates of the two...(Solved)
A circle whose equation is (x – 1)2 + (y – k)2 = 10 passes through point (2,5). Find the coordinates of the two possible centres of the circle.
Date posted: September 20, 2019. Answers (1)
- Find B given that A2 = (A + B).(Solved)
If matrix A 
. Find B given that A2 = (A + B).
Date posted: September 20, 2019. Answers (1)
- Make r the subject in the formular:(Solved)
Make r the subject in the formular:
Date posted: September 20, 2019. Answers (1)
- Evaluate without using mathematical tables or calculators:
2 Log105 – ½ Log1016 + 2 Log1040(Solved)
Evaluate without using mathematical tables or calculators:
2 Log105 – ½ Log1016 + 2 Log1040
Date posted: September 20, 2019. Answers (1)
- Expand (2 + 1/5x)8 up to the term in x3. Use your expansion to evaluate (2.04)8 correct to 4 decimal places.(Solved)
Expand (2 + 1/5x)8 up to the term in x3. Use your expansion to evaluate (2.04)8 correct to 4 decimal places.
Date posted: September 20, 2019. Answers (1)
- Expand the expression:(3v2 + 5) (3v2 – 5). Hence work out the following:
(Solved)
Expand the expression:(3√2 + 5) (3√2 – 5). Hence work out the following:
Date posted: September 20, 2019. Answers (1)
- Use logarithm table to evaluate:(Solved)
Use logarithm table to evaluate:
Date posted: September 20, 2019. Answers (1)
- The curve y =3x2- 6x + 6 passes through the point s ( 2,3)(a)Determine the gradient function of the curve.(b) Find the co-ordinates of...(Solved)
The curve y=3x2- 6x + 6 passes through the point s ( 2,3)
(a)Determine the gradient function of the curve.
(b) Find the co-ordinates of the turning point of the curve.
(c) Determine whether the point is a minima or a maxima.
(d) Find the equation of the
(i) Tangent to the curve at S.
(ii) Normal to the curve at S.
Date posted: September 20, 2019. Answers (1)
- The relationship between two variables S and T is given by the equation S = KTn where K and n are constants.
(a) Write down the...(Solved)
The relationship between two variables S and T is given by the equation S = KTn where K and n are constants.
(a) Write down the linear equation relating to S and T
(b) Hence complete the table above for the linear equation relating to S and T.
(c) Draw a suitable straight line graph to represent the data.
(d) use your graph to determine the values of K and n.
(e) find the value of S when T = 3.5
Date posted: September 20, 2019. Answers (1)
- Mr. Korir bought a tractor valued at Ksh. 800,00. the value of the tractor is depreciating at 20% p.a
(a) Calculate the value of the tractor...(Solved)
Mr. Korir bought a tractor valued at Ksh. 800,00. the value of the tractor is depreciating at 20% p.a
(a) Calculate the value of the tractor after 4 years.
(b) Find the time it would take for its value to be Ksh. 400,000. give you’re answer correct to 2 decimal
places.
(c) If after 4 years the tractor is sold through a broker who charge 5% commission find the amount received
by Mr. Korir from the sale
Date posted: September 20, 2019. Answers (1)
- Complete the table below giving the values to 2 decimal places.(Solved)
Complete the table below giving the values to 2 decimal places.
Date posted: September 20, 2019. Answers (1)
- Three quantities P,Q,and R are such that P varies jointly with Q and the square of R . if P = 900 when...(Solved)
Three quantities P,Q,and R are such that P varies jointly with Q and the square of R . if P = 900 when
Q = 20 and R = 3
Find (i) an equation connecting P, Q and R
(ii) the value of R when Q = 10 and P = 800
Date posted: September 20, 2019. Answers (1)