- The equation of a curve is given by y = 11x – x2.(Solved)
The equation of a curve is given by y = 11x – x2.
(a) Determine coordinates of the stationary point.
(b) By integration, determine the actual area bounded by the curve y = 11x – x2 and the line y = 2x
(c) Find the equation of the normal to the curve at x =2
Date posted: April 26, 2019. Answers (1)
- The thirteen term of an arithmetic progression is 27. Given that the seventh term equals to three times the second
term, find(Solved)
The thirteen term of an arithmetic progression is 27. Given that the seventh term equals to three times the second
term, find
(a) The first term and the common difference of the progression.
(b) The sum of the first three even numbered terms of the progression.
(c) It’s given that (b-9/4), b and (b + 3.375) are the 2nd,3rd, and 4th terms of a geometric progression. Determine the value of b.
Date posted: April 26, 2019. Answers (1)
- Transmasra Sugar Company has 36 hectares of land. The company decides to prepare the land for planting wheat and
maize. The labour cost of planting maize...(Solved)
Transmasra Sugar Company has 36 hectares of land. The company decides to prepare the land for planting wheat and
maize. The labour cost of planting maize is KSh. 300 per hectare while it costs KSh. 900 to plant a hectare of wheat.
Maize takes 3 labourers per hectare while wheat takes 6 labourers per hectare. Atleast 72 labourers are to be hired
and KSh. 15,000 is to be spent for labour costs. The company hopes to make a profit of KSh. 2,000 per hectare of maize
and KSh. 4,500 per hectare of wheat. Let the number of hectares for maize be x, Let the number of hectares for wheat
be y
(a) Write down inequalities representing the above information.
(b) On the grid provided, draw the inequalities by shading unwanted regions
(c) Use the graph to:-
(i) determine the number of hectares of maize and wheat that should be prepared in order for the company to maximize profit.
(ii) Calculate the maximum profit
Date posted: April 26, 2019. Answers (1)
- The following table shows the distribution of marks obtained by 50 students of Matare Secondary School.(Solved)
The following table shows the distribution of marks obtained by 50 students of Matare Secondary School.
(a) By using an assumed of 62, calculate:
(i) The mean
(b) The variance
(c) The standard deviation
Date posted: April 26, 2019. Answers (1)
- A and B are two points on the latitude 400N. The two points lie on the longitude 200W and 1000E respectively.(Solved)
A and B are two points on the latitude 400N. The two points lie on the longitude 200W and 1000E respectively.
(a) Calculate:-
(i) The distance from A to B along a parallel of latitude.
(ii) The shortest distance from A to B along a great circle.
(b) Two planes P and Q left A for B at 400 knots and 600 knots respectively. If P flew along the great circle and Q along
parallel latitude, which one arrived earlier and by how long. Give your answer to the nearest minute. (Take R =6370 km and 𝜋 =22/7)
Date posted: April 26, 2019. Answers (1)
- The figure below shows a frustum ABCDEFGH of a right pyramid such that AB = 9cm, BC = 12cm, FG = 6cm GH = 8cm
and...(Solved)
The figure below shows a frustum ABCDEFGH of a right pyramid such that AB = 9cm, BC = 12cm, FG = 6cm GH = 8cm
and the height of the frustum is 10cm.
Find the
(a) Height of pyramid
(b) Length of
(i) AC
(ii) AH
(c) Calculate the angle between:
(i) Line AH and the plane ABCD
(ii) The planes ABHE and ABCD
Date posted: April 26, 2019. Answers (1)
- Find the equation of the tangent to the circle at L.(Solved)
Date posted: April 26, 2019. Answers (1)
- In the diagram below, PQ = 10cm, and the radius of the circle centres P and Q are 2cm and 4cm respectively, calculate
the length of...(Solved)
In the diagram below, PQ = 10cm, and the radius of the circle centres P and Q are 2cm and 4cm respectively, calculate
the length of the transverse common tangent SR.
Date posted: April 26, 2019. Answers (1)
- The points P(8,4) and Q(2,2) are the ends of a diameter of a circle. Find the equation of the circle.(Solved)
The points P(8,4) and Q(2,2) are the ends of a diameter of a circle. Find the equation of the circle.
Date posted: April 26, 2019. Answers (1)
- The top of a table is regular pentagon. Each side of the pentagon measures 40.0cm. Find the maximum percentage
error in calculating the perimeter of the...(Solved)
The top of a table is regular pentagon. Each side of the pentagon measures 40.0cm. Find the maximum percentage
error in calculating the perimeter of the top of the table.
Date posted: April 26, 2019. Answers (1)
- A die has two of its faces numbered 3. Calculate the probability of obtaining a 1 or a 3 on a single cast.(Solved)
A die has two of its faces numbered 3. Calculate the probability of obtaining a 1 or a 3 on a single cast.
Date posted: April 26, 2019. Answers (1)
- By completing the square, solve for x in the equation 2x2 – 6 = x(Solved)
By completing the square, solve for x in the equation 2x2 – 6 = x
Date posted: April 26, 2019. Answers (1)
- The resistance to the motion of a car is partly constant and partly varies as the square of the speed. At 40km/h the resistance is...(Solved)
The resistance to the motion of a car is partly constant and partly varies as the square of the speed. At 40km/h the resistance is 530 and at 60km/h it is 730N. What will be the resistance at 70km/h
Date posted: April 26, 2019. Answers (1)
- Expand the following hence find the value of (2.025)6 rounded off to 3 decimal places(Solved)
Expand
Hence find the value of (2.025)6 rounded off to 3 decimal places.
Date posted: April 26, 2019. Answers (1)
- The transformation represented by the matrix;(Solved)
Date posted: April 26, 2019. Answers (1)
- Solve for x in the following equation(Solved)
Solve for x in the following equation
3log3 x + 4 = log324
Date posted: April 26, 2019. Answers (1)
- Rationalize the denominator and simplify(Solved)
Rationalize the denominator and simplify
Date posted: April 26, 2019. Answers (1)
- The table below show tax rates on a certain year.(Solved)
The table below show tax rates on a certain year.
Robi earns a basic salary of KSh. 20,000 per month, she is given allowances amounting to KSh. 5000. She is housed by
her employer therefore pays a nominal rent of Sh. 700 per month and is entitled to a personal relief of Sh. 1200 per month. Calculate;
(i) Her taxable income in Kenya pounds per year.
(ii) Her gross tax per month.
Date posted: April 26, 2019. Answers (1)
- OA = 3i + 4j – 6k and OB = 2i + 3j + k are two position vectors. P divides a line AB in...(Solved)
OA = 3i + 4j – 6k and OB = 2i + 3j + k are two position vectors. P divides a line AB in the ratio 3:-2. Write down the
coordinates of P.
Date posted: April 26, 2019. Answers (1)
- In the figure below XY = 8cm and O is the centre of the circle.(Solved)
In the figure below XY = 8cm and O is the centre of the circle.
Determine the area of the circle if angle AOX = 150.
Date posted: April 26, 2019. Answers (1)