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- 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)
- A bag contains 5 red, 4 white and 3 blue beads. Three beads are selected at random without replacement. Find the probability that
(a)...(Solved)
A bag contains 5 red, 4 white and 3 blue beads. Three beads are selected at random without replacement. Find the probability that
(a) The first red bead is the third bead picked.
(b) The beads selected were, white and blue;
(i) in that order
(ii) In any order
(c) No red bead is picked
(d) Beads picked are of the same colour.
Date posted: September 17, 2019. Answers (1)
- Find the inverse of the matrix . hence find the coordinates of the point of intersection of the line 3x+ y = 4 and ...(Solved)
Find the inverse of the matrix 
. hence find the coordinates of the point of intersection of the line 3x+ y = 4 and 2x –y = 1
Date posted: September 17, 2019. Answers (1)
- A group of 5 men can do a piece of work in 12 hours. How long would a group of 8 men take to...(Solved)
A group of 5 men can do a piece of work in 12 hours. How long would a group of 8 men take to complete the same work if they work at thrice the rate of the first group?
Date posted: September 17, 2019. Answers (1)
- Find the compound interest on shs. 15, 200 on deposited in a bank paying compound interest of 10.5% per annum for 5 year.(Solved)
Find the compound interest on shs. 15, 200 on deposited in a bank paying compound interest of 10.5% per annum for 5 year.
Date posted: September 17, 2019. Answers (1)
- The fourth term of geometric sequence is 54 and the sixth term is 486. Find the common ratio and the first term.(Solved)
The fourth term of geometric sequence is 54 and the sixth term is 486. Find the common ratio and the first term.
Date posted: September 17, 2019. Answers (1)
- Solve for x in 2 + log7 ( 3x-4) = log7 98.(Solved)
Solve for x in 2 + log7 ( 3x-4) = log7 98.
Date posted: September 17, 2019. Answers (1)
- If OA = 3 i + 2j – 4k and OB = 4i + 5j – 2k, P divides AB in the ratio 3:-2....(Solved)
If OA = 3 i + 2j – 4k and OB = 4i + 5j – 2k, P divides AB in the ratio 3:-2. Determine the modulus of Op leaving your answer to 1 decimal place. Given that O is the origin.
Date posted: September 17, 2019. Answers (1)
- Make q the subject of the formula (Solved)
Make q the subject of the formula
Date posted: September 17, 2019. Answers (1)
- After millet, the cost per kilogram of maize flour and millet flour shs 24 and shs. 40 respectively. The maize and millet flour are now...(Solved)
After millet, the cost per kilogram of maize flour and millet flour shs 24 and shs. 40 respectively. The maize and millet flour are now mixed in the ration 5:3 what should the selling price per kilogramme of the mixture be, in order to make a 25% profit?
Date posted: September 17, 2019. Answers (1)
- a) Expand ( 1+ ¼ x)4
b) use your expansion in (a) above to evaluate ( 0.975)4 to 4 significant figures.(Solved)
a) Expand ( 1+ ¼ x)4
b) use your expansion in (a) above to evaluate ( 0.975)4 to 4 significant figures.
Date posted: September 17, 2019. Answers (1)
- Find the radius and the coordinates of the centre of the circle whose equations is
2x2 + 2y2 – 6x = 10y + 9 =0
(Solved)
Find the radius and the coordinates of the centre of the circle whose equations is
2x2 + 2y2 – 6x = 10y + 9 =0
Date posted: September 17, 2019. Answers (1)
- The figure shows a circle , centre o of radius 7cm MN and PN are tangents to the circle at M and P...(Solved)
The figure shows a circle , centre o of radius 7cm MN and PN are tangents to the circle at M and P respectively. ON = 25 cm calculate the length MP
Date posted: September 17, 2019. Answers (1)
- Use logarithms, correct to 4 decimal places, to evaluate.
(Solved)
Use logarithms, correct to 4 decimal places, to evaluate.
Date posted: September 17, 2019. Answers (1)
- (a) An arithmetic progression is such that the first term is -5, the last is 135 and the sum of progression is...(Solved)
(a) An arithmetic progression is such that the first term is -5, the last is 135 and the sum of progression is 975. Calculate
(i) The number of terms in the series.
(ii) The common difference of the progression.
(b)The sum of the first three terms of a geometric progression is 27 and first term is 36.
Determine the common ratio and the value of the fourth term.
Date posted: September 17, 2019. Answers (1)
- The figure below shows a right pyramid VABCD with a square base of side 6 cm. VA = VB = VC = VD =...(Solved)
The figure below shows a right pyramid VABCD with a square base of side 6 cm. VA = VB = VC = VD = 12 cm
Calculate;
(i) The height of the pyramid correct to 2 d.p
(ii) The angle between the planes VAD and VBC correct to 2 significant figures.
Date posted: September 17, 2019. Answers (1)
- The taxation rate, for 2007 were as in the table below. In certain month in 2007, Mutai paid a tax of Ksh. 3000...(Solved)
The taxation rate, for 2007 were as in the table below.
In certain month in 2007, Mutai paid a tax of Ksh. 3000 after having been given a personal relief of Ksh. 1056 per month.
(a)How much tax per month could he have paid if he did not get tax relief.
(b)Calculate the his total taxable income in Ksh. P.m.
(c)Given that his total taxable allowance amount to Ksh. 4520 P.m. Calculate his monthly basic
salary in Kenya shillings.
Date posted: September 17, 2019. Answers (1)