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- Below is a sketch of the area bounded by the curve y=x2+3 and the line x=-2, x=4 and y=0.
(a) Estimate the area of the shaded...(Solved)
Below is a sketch of the area bounded by the curve y=x2+3 and the line x=-2, x=4 and y=0.
(a) Estimate the area of the shaded region using 6 strips by:
(i) The trapezoidal rule
(ii) Integration
(b) Find the percentage error in the area for the approximation in (a)(i) if the value in (a)(ii) is taken
as the exact area.
Date posted: September 18, 2019. Answers (1)
- A farmer has two tractors, A and B. The tractors working together can plough a farm in 2½ hours. One day the tractors started to...(Solved)
A farmer has two tractors, A and B. The tractors working together can plough a farm in 2½ hours. One day the tractors started to plough the farm together. After one hour ten minutes, tractor B broke down but A continued alone and completed the job after a further four hours.
(a) The fraction of the job done by tractor A after tractor B broke down.
(b) The time each tractor working alone would have taken to plough the farm.
Date posted: September 18, 2019. Answers (1)
- A point P divides line AB in the ratio 7:-5 where A and B are the points A(2,5,4) and B(-4,7,2). Find the co-ordinates of P....(Solved)
A point P divides line AB in the ratio 7:-5 where A and B are the points A(2,5,4) and B(-4,7,2). Find the co-ordinates of P.
Date posted: September 18, 2019. Answers (1)
- A two-digit positive number is such that the sum of its digits is nine. When the digits are reversed, the new number formed exceeds...(Solved)
A two-digit positive number is such that the sum of its digits is nine. When the digits are reversed,the new number formed exceeds the original number by 27. Find the original number.
Date posted: September 18, 2019. Answers (1)
- The equation of a circle, centre (-3,5) and radius 4 units is given as x2+y2+ax+by+c=0. Find the constants a, b and c.(Solved)
The equation of a circle, centre (-3,5) and radius 4 units is given as x2+y2+ax+by+c=0. Find the constants a, b and c.
Date posted: September 18, 2019. Answers (1)
- An approximation of fraction below is obtained by rounding off each value in the numerator to 4 significant figures and truncating each value in the...(Solved)
An approximation of fraction below is obtained by rounding off each value in the numerator to 4 significant figures and truncating each value in the denominator to 2 significant figures.
Find the approximate value of the resulting quotient, correct to 1 decimal place.
Date posted: September 18, 2019. Answers (1)
- (a) Expand (1+3x)5 in ascending powers of x up to the term in x3 and simplify.
(b) Hence estimate the value of (0.97)5 correct to...(Solved)
(a) Expand (1+3x)5 in ascending powers of x up to the term in x3 and simplify.
(b) Hence estimate the value of (0.97)5 correct to 4 decimal places.
Date posted: September 18, 2019. Answers (1)
- A box open at the top with a square base is made of 300cm2 of thin sheet metal. If x cm is the length of...(Solved)
A box open at the top with a square base is made of 300cm2 of thin sheet metal. If x cm is the length of the base and Vcm3 is the maximum possible volume of the box, calculate the value of V.
Date posted: September 18, 2019. Answers (1)
- Find the sum of all terms in the Arithmetic Progression (A.P) below:
53 + 46 + 39 +……….+ -10
(Solved)
Find the sum of all terms in the Arithmetic Progression (A.P) below:
53 + 46 + 39 +……….+ -10
Date posted: September 18, 2019. Answers (1)
- Triangle ABC with vertices A (-1,4), B (-1,2) and C (5,2) is mapped onto the image triangle A1B1C1 after a transformation whose matrix is
Find...(Solved)
Triangle ABC with vertices A (-1,4), B (-1,2) and C (5,2) is mapped onto the image triangle A1B1C1 after a transformation whose matrix is
Find the area of the image.
Date posted: September 17, 2019. Answers (1)
- Solve the equation (Solved)
Solve the equation
Date posted: September 17, 2019. Answers (1)
- A town R is 1800nm west of town P (60oN, 170oE). Find the position of town R. (Solved)
A town R is 1800nm west of town P (60oN, 170oE). Find the position of town R.
Date posted: September 17, 2019. Answers (1)
- Calculate the interest on Ksh. 10,000 invested for 1½ years at 12% p.a compounded quarterly. (Give your answer to the nearest 50cts) (Solved)
Calculate the interest on Ksh. 10,000 invested for 1½ years at 12% p.a compounded quarterly. (Give your answer to the nearest 50cts)
Date posted: September 17, 2019. Answers (1)
- The total cost of making a solid metal sphere is made up of an amount which is independent of the size of the sphere and...(Solved)
The total cost of making a solid metal sphere is made up of an amount which is independent of the size of the sphere and an amount which varies as the cube of its radius. The total cost is sh.126 and sh.200 when the radius is 6cm and 8cm respectively.
Find the total cost of a sphere of radius 12 cm
Date posted: September 17, 2019. Answers (1)
- Make P the subject in (Solved)
Make P the subject in
Date posted: September 17, 2019. Answers (1)
- Using logarithm tables, evaluate:(Solved)
Using logarithm tables, evaluate:
Date posted: September 17, 2019. Answers (1)
- The figure below is a sketch of the curve whose equation is y=x2 + x +5, it cuts the line y =11 at the points...(Solved)
The figure below is a sketch of the curve whose equation is y=x2 + x +5, it cuts the line y =11 at the points P and Q
(a)Find the area bounded by the curve y = x2+ x + 5 and the line y = 11 ( shaded) using the
trapezium rule with 5 strips.
(b)Calculate the difference in area if the mid-ordinate rule with 5 ordinates was used instead of the
trapezium rule.
(c)find the exact area in (a) above using integration.
Date posted: September 17, 2019. Answers (1)
- The table below shows income tax rates.
Omari’s monthly taxable income is Kshs. 24200
(a) Calculate the tax charged on Omari’s monthly earnings.
(b) Omari is entitled...(Solved)
The table below shows income tax rates.
Omari’s monthly taxable income is Kshs. 24200
(a) Calculate the tax charged on Omari’s monthly earnings.
(b) Omari is entitled to the following tax relief of 15% of the premium pound.
Calculate the tax Omari pays each month if he pays a monthly insurance premium of Kshs. 2400
(c) During a certain month, Omari receive additional earnings which were taxed at 20%
each shilling. Given that the paid 36.3% more tax that month, calculate the percentage
increase in his earning.
Date posted: September 17, 2019. Answers (1)
- a)Complete the table below giving your values correct to 2 decimal places.
(b) Taking 1 cm to represent 15o on the x-axis and 2 cm to...(Solved)
a)Complete the table below giving your values correct to 2 decimal places.
(b) Taking 1 cm to represent 15o on the x-axis and 2 cm to represent I unit on the y –axis, draw
the graphs of y = 3 Cos xo and y = 4 sin ( 2x-10o) on the same set of axes on the grid
provided.
(c) Use your graph to find the values of x for which 3 Cos x – 4 sin ( 2x-10) = 0
(d) State
(i) the period of the graph y= 4 sin ( 2x-10o)
(ii) the amplitude of the graph y = 3 Cos x
Date posted: September 17, 2019. Answers (1)
- A tree T is on a desert island. A rock (R) is 5 km away from the tree on a bearing of...(Solved)
A tree T is on a desert island. A rock (R) is 5 km away from the tree on a bearing of 290o. An active volcano (V) is equidistant from the tree and he rock on a bearing of 70o from the rock.
(a) Using a scale of 2cm to 1km, make a scale drawing showing T,R, and V.
(b) If the volcanic erupts, anywhere within 3 km of it is in danger. Draw the boundary of
the danger area. On your diagram.
(c)A straight river runs parallel to the line RT, 1km away from it on the opposite side of RT
to the volcano. Mark the river on your diagram and its danger area.
(d)If the river floods , anywhere within 1 km of it is in danger. Shade the are on your
diagram that is in danger of both the river and the volcano.
Date posted: September 17, 2019. Answers (1)