- (a) Find the expansion of (1 – x/3 )7 in ascending powers of x up to the term in x3.
(b) Use the expansion above to...(Solved)
(a) Find the expansion of (1 – x/3 )7 in ascending powers of x up to the term in x3.
(b) Use the expansion above to find, (0.99)7 to four significant figures.
Date posted: November 5, 2019. Answers (1)
- Solve for x
Log27 (x + 5) - log27 (x – 3) = 2/3(Solved)
Solve for x
Log27 (x + 5) - log27 (x – 3) = 2/3
Date posted: November 5, 2019. Answers (1)
- Given that A = 5i + 4j + K and B = 8i – 5j – 5k and P divides AB externally in the ratio...(Solved)
Given that A = 5i + 4j + K and B = 8i – 5j – 5k and P divides AB externally in the ratio 5:2. Find
the:-
(a) Position vector of P
(b) The magnitude of OP
Date posted: November 5, 2019. Answers (1)
- Town B is 180km on a bearing 0500 from town A. Another town C is on a bearing of 1100 from town A and on...(Solved)
Town B is 180km on a bearing 0500 from town A. Another town C is on a bearing of 1100 from town A and on a bearing of 1500 from town B. A fourth town D is 240 km on a bearing of 3200 from A. Using scale drawing, such that 1cm rep 30km,
(a) Show the relative position of the towns
(b) Using the diagram, find
(i) Distance AC
(ii) Distance CD
(iii) Compass bearing of C from D
Date posted: November 5, 2019. Answers (1)
- Nairobi and Eldoret are 600km apart. At 9.20a.m. a lorry leaves Eldoret for Nairobi at a speed of 60km/hr. At 10.00a.m. a car leaves Eldoret...(Solved)
Nairobi and Eldoret are 600km apart. At 9.20a.m. a lorry leaves Eldoret for Nairobi at a speed of 60km/hr. At 10.00a.m. a car leaves Eldoret for Nairobi at a speed of 120km/hr. After 20 minutes of travel, the car develops a mechanical problem which takes 20 minutes to repair. The car then proceeds with the journey at the same speed.
(a) Calculate the time the lorry arrived in Nairobi
(b) Find the time when the car overtakes the lorry
(c) Find the distance from Nairobi at the overtaking point
(d) Calculate how far the lorry was from Eldoret when the car reached Nairobi
Date posted: November 5, 2019. Answers (1)
- Matrix M is given by
(a) Find the inverse of M
(b) Two schools A and B purchased beans at Ksh. b per bag and...(Solved)
Matrix M is given by 
(a) Find the inverse of M
(b) Two schools A and B purchased beans at Ksh. b per bag and maize at Ksh. m per bag. School A
purchased 30 bags of beans and 40 bags of maize for sh. 72,000. School B purchased 50 bags of
beans and 20 bags of maize for sh. 64,000
(i) Form a matrix equation to represent the information above
(ii) Use the inverse matrix of M to find the price of one bag of each item
(c) The price of beans later went up by 5% and that of maize remained constant. School A bought the
same quantity of beans but spent the same total amount of money as before on the two items. State
the new ratio of beans to maize.
Date posted: November 5, 2019. Answers (1)
- The figure below shows a square based pyramid on top of a cuboid
(a) Draw the net of the solid
(b) Calculate the total surface area...(Solved)
The figure below shows a square based pyramid on top of a cuboid
(a) Draw the net of the solid
(b) Calculate the total surface area of the net.
Date posted: November 5, 2019. Answers (1)
- The gradient function of a curve is given by 3x2 + 2x – 3. If the curve passes through the point (-4, -6), Find the...(Solved)
The gradient function of a curve is given by 3x2 + 2x – 3. If the curve passes through the point (-4, -6), Find the equation of the curve.
Date posted: November 5, 2019. Answers (1)
- The diagram below represents a solid made up of a hemisphere mounted on a cone. The common radius is 6cm and the height of the...(Solved)
The diagram below represents a solid made up of a hemisphere mounted on a cone. The common radius is 6cm and the height of the solid is 15cm.
Calculate the external surface area of the solid
Date posted: November 5, 2019. Answers (1)
- Use Logarithms to evaluate(Solved)
Use Logarithms to evaluate
Date posted: November 5, 2019. Answers (1)
- Given that sin (3x – 50)0 – Cos (x + 20)0 = 0 and x is an acute angle; find the value of x(Solved)
Given that sin (3x – 50)0 – Cos (x + 20)0 = 0 and x is an acute angle; find the value of x
Date posted: November 5, 2019. Answers (1)
- Evaluate ; 36x-1 + 62x - 222 = 0(Solved)
Evaluate ; 36x-1 + 62x - 222 = 0
Date posted: November 5, 2019. Answers (1)
- The sum of interior angles of a triangle is given by (10x -2y)0 while that of a hexagon is given by (30x + 24y)0. Calculate...(Solved)
The sum of interior angles of a triangle is given by (10x -2y)0 while that of a hexagon is given by (30x + 24y)0. Calculate the values of x and y.
Date posted: November 5, 2019. Answers (1)
- The ratio of goats to cows in a farm is 2:5 while the ratio of sheep to cows is 3:4. If there are 15 sheep,...(Solved)
The ratio of goats to cows in a farm is 2:5 while the ratio of sheep to cows is 3:4. If there are 15 sheep, how many animals are there in the farm.
Date posted: November 5, 2019. Answers (1)
- Evaluate without using a calculator(Solved)
Evaluate without using a calculator
Date posted: November 5, 2019. Answers (1)
- Particle P moves in a straight line such that, t seconds after passing through a fixed point O its velocity V m/s given by the...(Solved)
Particle P moves in a straight line such that, t seconds after passing through a fixed point O its velocity V m/s given by the equation V = 3t2 -15t + 18.
Find
a) The values of t for which P is instantaneously at rest.
b) An expression in terms of t for the distance P from O after t seconds.
c) The total distance traveled by P in the first 4 seconds after passing point O.
d) The distance P from O when the acceleration of P is zero.
Date posted: November 5, 2019. Answers (1)
- The probability that our school will host soccer and rugby tournament this year is 0.8. If we host the probability of winning soccer is 0.7....(Solved)
The probability that our school will host soccer and rugby tournament this year is 0.8. If we host the probability of winning soccer is 0.7. If we do not host the probability of winning soccer is 0.4. If we win soccer the probability of winning rugby is 0.8, otherwise if we lose the probability of winning rugby is 0.3.
a) Draw a tree diagram to represent this information.
b) Use the tree diagram to find:-
i) The probability that we will lose both games.
ii) The probability that we will win only one game.
iii) The probability that we will host and lose both games.
Date posted: November 5, 2019. Answers (1)
- (a) Complete the table below for the equation y = x3 – 3x2 – 9x + 2.
b) On the grid provided draw the graph of...(Solved)
(a) Complete the table below for the equation y = x3 – 3x2 – 9x + 2.
b) On the grid provided draw the graph of y = x3 – 3x2 – 9x + 2 for -3 < x < 5.
Use the scale: 1cm rep 1 unit on x – axis
1cm rep 5 units on y – axis
c) i) Use your graph to solve the equation
x3 – 3x2 – 9x + 2 = 0
ii) By drawing a suitable straight line on the graph solve the equation.
x3 – 3x2 – 9x + 2 = -2x – 4
Date posted: November 5, 2019. Answers (1)
- The table below shows income tax rates
a) Mr. Juma claiming tax relief of Ksh 1056 per month discovered that a total of Ksh 18500 is...(Solved)
The table below shows income tax rates
a) Mr. Juma claiming tax relief of Ksh 1056 per month discovered that a total of Ksh 18500 is deducted from his total earnings in form of income tax. Calculate Mr. Juma’s taxable income in Ksh per month.
b) Mr. Juma other deductions include:
5% of basic salary as cooperative shares
2% of basic salary as WCPS
Insurance policy Ksh 2800
Co-operative shares Ksh 1500
Given that his taxable allowances is Ksh 28400, calculate his net pay.
Date posted: November 5, 2019. Answers (1)
- Find the number of terms that will give a sum of 800 in the series.
2 + 6 + 10 + …….(Solved)
Find the number of terms that will give a sum of 800 in the series.
2 + 6 + 10 + …….
Date posted: November 5, 2019. Answers (1)