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Four towns P, R, T and S are such that R is 80km directly to the north of P and T is on a bearing of 290º from P at a distance of 65km. S is on a bearing of 330º from T and a distance of 30 km.
Using a scale of 1cm to represent 10km, make an accurate scale drawing to show the relative position of the towns.
Find:
(a) The distance and the bearing of R from T
(b) The distance and the bearing of S from R
(c) The bearing of P from S
Date posted:
August 7, 2019
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The length of a rectangle was increased by 30% while its width decreased by 15%. Determine the % change in the area of the rectangle.
Date posted:
August 7, 2019
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A newspaper vendor has 30 bank notes with a total value of Sh. 900, if the notes are either in
Sh. 20 or Sh. 50 denominations, how many of each does he have?
Date posted:
August 7, 2019
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The diagram below represents a pillar made of cylindrical and regular tetrahedral parts. The diameter and height of the cylindrical part are 1.4m and 1m respectively. The side of the regular tetrahedral face is 0.5m and its height is 3.2m.
Calculate the volume of the :
i) Cylindrical part
ii) Tetrahedral part
Date posted:
August 7, 2019
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In the figure below DA is a diameter of the circle ABCDE centre O, radius 10cm. AB=BC and angle DAC= 360
Giving reasons, find the size of the angle;
(i) CDB;
(ii) DBC
(iii) DOC
(iv) OCA
(v) DEB
Date posted:
August 7, 2019
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Three points on a map A, B, and C are such that the bearing of B and C from A are 600 and 1500 respectively. If the distance AB is 0.45m and BC is 0.75m, determine the distance AC.
Date posted:
August 7, 2019
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The size of each interior angle of a regular polygon is four times the size of the exterior angle. Find the number of sides of the polygon.
Date posted:
August 7, 2019
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Solve for x in the following equation.
Date posted:
August 7, 2019
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Without using tables or calculators evaluate. Give your answer as a mixed number.
Date posted:
August 7, 2019
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The figure below represents below represents a prism of length 7 cm AB = AE = CD = 2 cm and BC – ED = 1 cm
Draw the net of the prism
Date posted:
August 7, 2019
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A two digit number is such that the sum of its digits is 13. The product of twice the tens digit and
the units digit minus the original number is 22. Find the number.
Date posted:
August 7, 2019
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Use the square, cube root, and reciprocal table to evaluate to 4 d.p
Date posted:
August 7, 2019
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Express the following recurring decimal as a fraction in its simplest form
Date posted:
August 7, 2019
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Water and ethanol are mixed such that the ratio of the volume of water to that of ethanol is 3: 1. Taking the density of water as 1 g/cm3 and that of ethanol as 1.2g/cm3, find the mass in grams of 2.5 litres of the mixture.
Date posted:
August 7, 2019
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Divide 
then add the result to the product of 
Find three quarters of the result and leave your answer as a fraction.
Date posted:
August 7, 2019
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Mwangi and Otieno live 60km apart. Mwangi leaves his home at 7.00am cycling towards Otieno’s house at 20km/h. Otieno leaves his home at 8.00am cycling towards Mwangi’s house at 8km/h
a) At what time did they meet?
b) How far is the meeting point from Mwangi’s house?
Date posted:
August 7, 2019
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Two lines L1 and L2 intersect at a point P. L1 passes through the points (-4,0) and (0,6). Given that L2 has the equation: y = 2x – 2, find, by calculation, the coordinates of P.
Date posted:
August 7, 2019
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The L.C.M. of three numbers is 360 and the G.C.D of the same numbers is 2. If one of the
numbers is 40. find the other 2 numbers.
Date posted:
August 7, 2019
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Find the value of x in the following equations:
Date posted:
August 7, 2019
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a) Write the odd numbers in descending order between 1 and 10 inclusive
b) Round off the number formed to 3 significant figures.
c) Find the total value of digit 7 in the new number in 1(b) above.
Date posted:
August 7, 2019
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Evaluate the expression below
Date posted:
August 7, 2019
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An arithmetic progression has the first term as a and common difference as d
(i) Write down the third, ninth and twenty fifth term of the progression
(ii) The arithmetic progression above is such that it is increasing and the third, ninth and twenty fifth terms form the first three consecutive terms e.g. a geometric progression. If the sum of the seventh term and twice the sixth term of the A.P is 78.Calculte the first term and the common difference of A.P.
Date posted:
August 7, 2019
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Every time an insect jumps forward the distance covered is half of the previous jump.
If the insect initially jumped 6.4m. Calculate
(i) The length of 7th jump
(ii) The total distance covered after the 7th jump
Date posted:
August 7, 2019
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In the figure below ABCDE is a pentagon inscribed in a circle. CX is a tangent to the circle at C and EDX is a straight line. Angle ADE = 340, angle CAD = 420, AB = BC and BC is parallel to AD. Giving reasons, determine
(a) (i) Angle ABC
(ii) Angle ACD
(iii) Angle EAD
(iv) Angle CXD
(b) Given that ED = 5cm, DX = 4cm, calculate the length of CX
Date posted:
August 7, 2019
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The figure below shows two circles intersecting at C and D. The centres are A and B with radii 8cm and 6cm respectively. AB = 10cm.
Determine
(i) Size of angle DAC
(ii) Size of angle DBC
(iii) Area of sector ACMD
(iv) Area of the shaded region
Date posted:
August 7, 2019
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Construct a parallelogram ABCD in which AB = 8.5cm, AD = 6cm and angle BAD = 750.(Use a ruler and pair of compasses only in this question)
(a) Measure the length of AC
(b) On the same diagram, construct
(i) a perpendicular from B to line AD at M. Measure BM. Hence calculate the area of the parallelogram ABCD.
(ii) The locus of a point x which moves such that it is equidistant from A and C
(iii) The locus of point Y which moves such that angle BYD = 900
Date posted:
August 7, 2019
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A plastic water tank has a shape as shown below, with a frustrum of a cone on top, a cylindrical body and a hemispherical bottom.
(a) Calculate
(i) The volume of the tank in m3.
(b) A filler pipe takes 3 hours to fill a third of the tank. If the tank is already ¼ full, at what time will the filler pipe fill the tank if the pipe is opened at 9.00 a.m.
(c) A particle falls in the tank. If its chances of being in any part of the tank are equally likely, find the probability of it being in the hemispherical part.
Date posted:
August 7, 2019
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The figure below represents a school field.
Find the length of AB given that angle BAD and angle CBD are right angles.
Date posted:
August 7, 2019
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Solve for x in the equation
Date posted:
August 7, 2019
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The interior angle of a regular polygon is 9 times the exterior angle. How many sides does the
polygon have?
Date posted:
August 7, 2019