- A ship leaves an Island A (600N, 45 0E) and sails due west for 120hours to another island B.The average speed of the ship is...(Solved)
A ship leaves an Island A (600N, 45 0E) and sails due west for 120hours to another island B.The average speed of the ship is 27 knots.
a) Find the position of the island B
b) Another island C is south of island B and lies on latitude 550N. Find the distance between Islands B and C in
nautical miles.
c) The ship leaves island B when the time at Island A is 12.30pm. On Monday and sailed to Island C. If the ship
increases its speed by 20% between B and C find out the time of arrival at island C to the nearest minutes and the
day.
Date posted: May 7, 2019. Answers (1)
- a) Using a ruler and pair of compasses only construct a square ABCD of sides 6cm.(Solved)
a) Using a ruler and pair of compasses only construct a square ABCD of sides 6cm.
b) A point P moves inside the square such that;
i) 𝐴𝑃 ≤ 𝑃𝐵
ii) 𝐴𝑛𝑔𝑙𝑒 𝐴𝑃𝐵 ≥ 900
iii) P is nearer to AD than AB. construction on the square in (a) show the region that P must lie by shading.
c) Find the area of the region where P must lie.
Date posted: May 7, 2019. Answers (1)
- The figure below shows a frustrum ABCDEFGH of a right pyramid where AB=40cm, BC=30cm, FG=20cm, GH=15cm and AF=BG=CH=DE=25cm.(Solved)
The figure below shows a frustrum ABCDEFGH of a right pyramid where AB=40cm, BC=30cm, FG=20cm, GH=15cm and AF=BG=CH=DE=25cm.
Find the vertical height of the frustrum.
a) Find the angle between line BE and the base ABCD
b) Find the angle between the plane BCHG and the base ABCD.
c) Find the angle between the plane ADEF and the plane AGHD
Date posted: May 7, 2019. Answers (1)
- In the figure below AOC is a diameter, ADG and BCFG are straight lines, angle ACB=420, angle CAE=740 and angle DEC=360(Solved)
In the figure below AOC is a diameter, ADG and BCFG are straight lines, angle ACB=420, angle CAE=740 and angle DEC=360
Find the following angles, giving reasons in each case.
a) Angle CDE
b) Angle BDC
c) Angle DCA
d) Reflex angle COE
e) Angle DGF
Date posted: May 7, 2019. Answers (1)
- A certain number of Jua kali artisan agreed to contribute equally to buy a welding machine worth Ksh 12,000. Five of
the artisan pulled out so...(Solved)
A certain number of Jua kali artisan agreed to contribute equally to buy a welding machine worth Ksh 12,000. Five of
the artisan pulled out so the others agreed to contribute an extra Kshs 100 each. Their contribution enabled them to
buy a machine worth Ksh 2000 more than the previous machine.
a) If the original number of artisan was n, write down:
i) An expression of how much each artisan was to contribute originally.
ii) An expression of how much each of the remaining artisan contributed.
b) Calculate how many artisan made the contribution.
c) Calculate how much each contributed.
Date posted: May 7, 2019. Answers (1)
- Mr. Korir borrowed Kshs 3,600,000 from the bank to buy a residential house. He was required to repay the loan with a
simple interest for a...(Solved)
Mr. Korir borrowed Kshs 3,600,000 from the bank to buy a residential house. He was required to repay the loan with a
simple interest for a period of four years. The repayment amounted to kshs 111 000 per month. Calculate
a) i) the interest paid to the bank.
ii) the rate per annum of the simple interest.
b) The value of the house appreciated at the rate of 15% per annum. Calculate the value of the house after 4 years to the nearest hundreds.
c) After n years, the value of the house was Kshs 8,327,019. Find the value of n.
Date posted: May 7, 2019. Answers (1)
- A farmer has 200m of fencing with which to form three sides of a rectangular enclosure, the fourth side being existing
wall of the yard. Find...(Solved)
A farmer has 200m of fencing with which to form three sides of a rectangular enclosure, the fourth side being existing
wall of the yard. Find in metres the dimension of the largest possible area that can be enclosed.
Date posted: May 7, 2019. Answers (1)
- A (-6,-2) and B (2,-4) are the end point of a diameter of a circle.(Solved)
A (-6,-2) and B (2,-4) are the end point of a diameter of a circle.
a)Find the co-ordinates of the centre of the circle
b)Find the equation of the circle expressing it in the form 𝑥2 + 𝑦2 + 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0, 𝑤ℎ𝑒𝑟𝑒 𝑎, 𝑏 𝑎𝑛𝑑 𝑐 𝑎𝑟𝑒 intergers.
Date posted: May 7, 2019. Answers (1)
- Two matrices A and B are as given below,Given that the product AB is a singular matrix, find the value of P.(Solved)
Two matrices A and B are as given below,Given that the product AB is a singular matrix, find the value of P.
Date posted: May 7, 2019. Answers (1)
- Find the maximum value and correct to three decimal places of:(Solved)
Given that 10.5 <_ x <_ 20 and 1.5 <_ y <_ 3, find the maximum value and correct to three decimal places of:
Date posted: May 7, 2019. Answers (1)
- a) Expand (a + b)5 (Solved)
a) Expand (a + b)5
b) Use the first three terms of the expansion in (a) to find the value of (1.97)5 to two decimal places.
Date posted: May 7, 2019. Answers (1)
- In the figure below ABT is straight line with AB=5cm and BT=4cm. O is the centre of the circle with radius 8 cm and
PT is...(Solved)
In the figure below ABT is straight line with AB=5cm and BT=4cm. O is the centre of the circle with radius 8 cm and
PT is a tangent to the circle at P.
a) Calculate the length of PT.
b) Calculate the area of the shaded region correct to two significant figures (Take pi = 3.142)
Date posted: May 7, 2019. Answers (1)
- Without using mathematical tables or a calculator evaluate.(Solved)
Without using mathematical tables or a calculator evaluate.
Date posted: May 7, 2019. Answers (1)
- There are two boxes A and B on the floor. Box A contains 3 red marbles and 5 white marbles while Box B contains 6
red...(Solved)
There are two boxes A and B on the floor. Box A contains 3 red marbles and 5 white marbles while Box B contains 6
red marbles and 2 white marbles. A box is chosen at random and two marbles are drawn from it one after the other
without replacement. Find the probability that the two marbles are of different colours.
Date posted: May 7, 2019. Answers (1)
- Kamau saved 2000 during the first month of employment. In each subsequent month he saved 15% more than the
preceding month. How many years did he...(Solved)
Kamau saved 2000 during the first month of employment. In each subsequent month he saved 15% more than the
preceding month. How many years did he take to save a sum of Kshs 2.028,692
Date posted: May 7, 2019. Answers (1)
- In the figure below AB and Bc are chords of a circle centre O. AB=6cm, BC=16cm and OC=10cm(Solved)
In the figure below AB and Bc are chords of a circle centre O. AB=6cm, BC=16cm and OC=10cm
Calculate angle ABC correct to three significant figures.
Date posted: May 7, 2019. Answers (1)
- A shopkeeper bought x kg of locally made sugar at Kshs 85 per kilogram and 120kg of imported sugar at ksh 102 per
kilogram. He mixed...(Solved)
A shopkeeper bought x kg of locally made sugar at Kshs 85 per kilogram and 120kg of imported sugar at ksh 102 per
kilogram. He mixed the two types of sugar and sold the mixture at Ksh 119 per kilogram making a profit of 25%. Find
the number of kilograms (x) of locally made sugar.
Date posted: May 7, 2019. Answers (1)
- Make n the subject of the formula given that(Solved)
Make n the subject of the formula given that
Date posted: May 7, 2019. Answers (1)
- Two variable V and R are such that V partly varies as R and partly varies as the square root of R. When R=9, V=144
and...(Solved)
Two variable V and R are such that V partly varies as R and partly varies as the square root of R. When R=9, V=144
and when R=16, V=272
a) Find the law connecting V and R
b) Hence find the value of V when R=56.25.
Date posted: May 7, 2019. Answers (1)
- Without using mathematical tables or a calculator, evaluate.(Solved)
Without using mathematical tables or a calculator, evaluate.
Date posted: May 7, 2019. Answers (1)