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Two places P and Q are on the parallel of latitude 26°N. The two points lie on 10°W and 30°E longitudes respectively.
(Solved)
Two places P and Q are on the parallel of latitude 26°N. The two points lie on 10°W and 30°E longitudes respectively.
(a) Find the distance between P and Q along their parallel of latitude in
(i) km (Taking R = 6370km and pi = 3.142)
(ii) nm
(b) Find in km the distance between points P and Q along a great circle.
(c) Two planes X and Y left P for Q at an average speed of 1200 knots and 5000 knots respectively. If X flew along the
great circle and Y along the parallel of latitude, which one arrived earlier and by how much time?
Date posted:
May 9, 2019
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Answers (1)
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The diagram below shows two intersecting circles with centres X and Y. HG is a tangent to the circle centre X at C.
(Solved)
The diagram below shows two intersecting circles with centres X and Y. HG is a tangent to the circle centre X at C.
(a) Determine:
(i) Angle DXE
(ii) Length DE
(b) Hence, calculate the area of the shaded region.
Date posted:
May 9, 2019
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Answers (1)
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I own a motorcycle. Out of the 21 working days in a month, I only ride to work for 18 days. If I ride to...
(Solved)
I own a motorcycle. Out of the 21 working days in a month, I only ride to work for 18 days. If I ride to work the
probability that I am bitten by a rapid dog is 4/15, otherwise it is only 1/13 when I am bitten by the dog, the probability
that I will get treatment is 4/5 and if I do not get treatment, the probability that I will get rabies is 5/7.
(a) Draw a tree diagram to show the events.
(b) Musing the tree diagram (a) above determine the probability that:
(i) I will not be bitten by a rapid dog.
(ii) I will get rabies
(iii) I will not get rabies.
Date posted:
May 9, 2019
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Answers (1)
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Use ruler and compasses only for all the constructions in this question.
(Solved)
Use ruler and compasses only for all the constructions in this question.
(a) Construct a triangle ABC in which AB= 6cm, BC = 7cm and angle ABC = 75°. Measure:
(i) the length of AC
(ii) the angle of ACB
(b) Locus of P is such that BP = PC. Construct P.
(c) Construct locus of Q such that Q is on one side of BC opposite A and angle BCQ = 30°.
(d) (i) the locus of P and locus of Q meet at X. Mark X.
(ii) Construct the locus of R in which angle BRC = 120°.
(iii) Show the locus of S inside the triangle ABC such that XS ≥ SR.
Date posted:
May 9, 2019
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Answers (1)
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The diagram below shows a right pyramid with a horizontal rectangular base PQRS and vertex V. The area of the base
is 60cm2and the volume of...
(Solved)
The diagram below shows a right pyramid with a horizontal rectangular base PQRS and vertex V. The area of the base
is 60cm2and the volume of the pyramid is 280cm3.
(a) Calculate the height of the pyramid.
(b) Given the ratio of the sides PQ: QR is 3:5 find the lengths of
(i) PQ
(ii) QR
(c) Find the length of the slanting height.
(d) Calculate the angle between the planes VRQ and PQRS.
Date posted:
May 9, 2019
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Answers (1)
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The table below shows the rates of taxation in a certain year.
(Solved)
The table below shows the rates of taxation in a certain year.
In that period, Mr. Omoit a teacher at Mundika Boys earning a basic salary of Ksh. 21,000 per month. In addition, he
was entitled to a house allowance of Kshs 9,000 p.m and a personal relief of Kshs 1056 /per month.
(a) Calculate how much income tax Mr. Omoit paid per month.
(b) Mr. Omoit’s .other deductions per month were co-operative society contributions sh 2,000 loan repayment,
sh 2,500/-. Calculate his net salary per month.
(c) Later in the same year, Mr. Omoit was transferred to Katira Secondary School where he earned hardship
allowance equivalent to 30% of his basic salary. If on top of deductions in (b) above he also had deduction of sh
2,700 p.m to KCT. Calculate the percentage change in his net salary per month.
Date posted:
May 9, 2019
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Answers (1)
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Find the sum of the first six terms of the progression given;
(Solved)
Find the sum of the first six terms of the progression given;
Log 2x + log 4x + log 8x + log 16x + ..........
leaving your answer in the form a log bx2 where a and b are integers.
Date posted:
May 9, 2019
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Answers (1)
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Given that OA = 3i + 2j - 4k and OB = 4i + 5j - 2k. P divides AB externally in the ratio 3:...
(Solved)
Given that OA = 3i + 2j - 4k and OB = 4i + 5j - 2k. P divides AB externally in the ratio 3: -2. Determine the position
vector of P in terms of i, j and k.
Date posted:
May 9, 2019
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Answers (1)
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Make P the subject of the formula.
(Solved)
Make P the subject of the formula.
Date posted:
May 9, 2019
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Answers (1)
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The cost per kg of two brand of tea x and y are Sh. 60 and Sh. 80. The two brands are mixed and sold...
(Solved)
The cost per kg of two brand of tea x and y are Sh. 60 and Sh. 80. The two brands are mixed and sold at a profit of 20%
above the cost. if 1kg mixture was sold at Sh. 78, determine the ratio in which the two brands were mixed.
Date posted:
May 9, 2019
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Answers (1)
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Simplify the expression.
(Solved)
Simplify the expression.
Date posted:
May 9, 2019
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Answers (1)
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P and Q are the points on the ends of the diameter of the circle below.
(Solved)
P and Q are the points on the ends of the diameter of the circle below.
(a) Write down in terms of x and y the equation of the circle in the form;
ax2 + by2 + x + y + c = 0
(b) Find the equation of the tangent at Q in the form ax + by + c = 0.
Date posted:
May 9, 2019
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Answers (1)
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Solve for x in the equation below
(Solved)
Solve for x in the equation below
Date posted:
May 9, 2019
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Answers (1)
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(a) Given matrices P and Q below,Find PQ.
(Solved)
(a) Given matrices P and Q below,Find PQ.
(b) Hence, find the point of intersection of the lines 4x + y = 9 and 3y =2x -1
Date posted:
May 9, 2019
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Answers (1)
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Using a calculator, simplify;
(Solved)
Using a calculator, simplify;
Date posted:
May 9, 2019
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Answers (1)
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Evaluate without using tables or calculator.
(Solved)
Evaluate without using tables or calculator.
Date posted:
May 9, 2019
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Answers (1)
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On a certain day Mwema bought plates worth Ksh 120. On another day Mrs Mwema spent the same amount of money
but bought the plates at...
(Solved)
On a certain day Mwema bought plates worth Ksh 120. On another day Mrs Mwema spent the same amount of money
but bought the plates at a discount of 20% per plate.
(a) If Mwema bought a plate at sh x write down a simplified expression for the total number of plates bought by the
two people.
(b) If Mrs. Mwema bought 6 plates more than her husband find how much each spent on a plate.
(c) Find the total number of plates bought by the family.
Date posted:
May 9, 2019
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Answers (1)
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Two circles centres O and C have radii 7.2cm and 6.5cm respectively. The two circles intersect at P and Q and PQ
=10cm.
(Solved)
Two circles centres O and C have radii 7.2cm and 6.5cm respectively. The two circles intersect at P and Q and PQ
=10cm.
(a) Find
(i) angle POQ
(ii)angle PCQ
(b) The area of the shaded part. Give answer to 4s.f.
(c) Express angle POQ in radians.
Date posted:
May 9, 2019
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Answers (1)
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A glass is in the shape of a frustum of a cone.
(Solved)
A glass is in the shape of a frustum of a cone.
The bottom of the glass is a curve of radius 2cm. A father pours water into the glass to a height of 9cm, while the
surface of the water is a circle of radius 6cm.
(a) Calculate the volume of the water in the glass.
(b) The son who is playing with marbles drops two spherical balls into the water. The water level in the glass rises by
1.5cm as a result.
Calculate:
(i) the volume of one marble.
(ii) the radius of a marble.
Date posted:
May 9, 2019
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Answers (1)
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The table below gives the marks scored by a group of students in an exam.
(Solved)
The table below gives the marks scored by a group of students in an exam.
(a) Given that the mean mark was 32.125, find x.
(b) State the modal class.
(c) Calculate the interquartile range.
Date posted:
May 9, 2019
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Answers (1)