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Solve for x in the following without using a calculator or mathematical tables.
9x( 27(x-1)) = tan 30o
(Solved)
Solve for x in the following without using a calculator or mathematical tables.
9x( 27(x-1)) = tan 30o
Date posted:
August 19, 2019
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Answers (1)
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(a) Using a ruler and compasses only, construct triangle PQR in which QR=5cm,PR = 7cm and angle PRQ = 105o
(b) Measure PQ and Angle...
(Solved)
(a) Using a ruler and compasses only, construct triangle PQR in which QR=5cm,PR = 7cm and angle PRQ = 105o
(b) Measure PQ and Angle PQR
(c) From P drop a perpendicular to meet QR produced at S
(d) Mark a point T on SP produced such that the area of triangle TQR is half the area of triangle PQR.
(e) Complete the TQR and measure angle QRT
(f) measure ST and angle QTR
Date posted:
August 19, 2019
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Answers (1)
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Four strings measuring 12cm, 18cm, 24cm and 36cm are cut into pieces of equal length so that exact number of pieces are obtained from each...
(Solved)
Four strings measuring 12cm, 18cm, 24cm and 36cm are cut into pieces of equal length so that exact number of pieces are obtained from each string without wastage. Find the longest length of each string.
Date posted:
August 19, 2019
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Answers (1)
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Three businessmen Onyango,Abdul and Mwangi decided to buy bus. The marked price of the bus was sh. 6,800,000. The dealers agreed that the three men...
(Solved)
Three businessmen Onyango,Abdul and Mwangi decided to buy bus. The marked price of the bus was sh. 6,800,000. The dealers agreed that the three men could pay a deposit of 60% of the money and the rest to be paid within one year. Onyango, Abdul and Mwangi raised the deposit in the ration 3: 2 :5 respectively.
The balances was to be paid to the dealer from the proceeds from the bus in the same ratio as the deposits. The three men shared the proceeds from the bus in the ratio as the deposits. During the year the bus realized sh. 6,080,000
(a)How much of the deposit did Abdul contribute?
(b)How much of the remaining amount did Mwangi pay at the end of the year ?
(c)After paying the remaining amount at the end of the year, how much money was Onyango left with?
Date posted:
August 19, 2019
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Answers (1)
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On the figure below, Lm is parallel to PQ. Angle MLR = 300 and angle RPQ = 700.
(Solved)
On the figure below, Lm is parallel to PQ. Angle MLR = 300 and angle RPQ = 700. Find the value of x.

Date posted:
August 19, 2019
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Answers (1)
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The marked price of a modern camera is Kes 24,000. A trader sold it to a customer at a 10% discount.
(Solved)
The marked price of a modern camera is Kes 24,000. A trader sold it to a customer at a 10% discount. If the trader still made a profit of 20% on the cost price, what was its cost price?
Date posted:
August 19, 2019
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Answers (1)
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The figure below is a semi-cylindrical solid of length 18cm and radius 3.5cm as shown
(Solved)
The figure below is a semi-cylindrical solid of length 18cm and radius 3.5cm as shown.

(a) Draw the labeled net of the solid.
(b) Find the surface area of the solid.
Date posted:
August 19, 2019
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Answers (1)
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The equation of a straight line L1 is given by 2y + 8x – 10 = 0.
(Solved)
The equation of a straight line L1 is given by 2y + 8x – 10 = 0. Another line L2 cuts L1 at right angles such that the point of intersection of the two lines has coordinates (-3, k).
(a) Find the value of k.
(b) Hence find the equation of L2.
Date posted:
August 19, 2019
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Answers (1)
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A tower is on a bearing of 030o from a point P and a distance of 100 m. From P, the angle of elevation of...
(Solved)
A tower is on a bearing of 030o from a point P and a distance of 100 m. From P, the angle of elevation of the top of the tower is 15o and the angle of depression of the foot of the tower is 1.
(a) Find the height of tower.
(b) A point Q is on the same horizontal plane as point P. The tower is on a bearing 330o from Q and a distance of 70 m.
Calculate the:-
(i) Bearing of Q from the tower.
(ii) The distance from P to Q
(iii) bearing of P from Q.
Date posted:
August 19, 2019
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Answers (1)
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The figure below shows two circles with centres O1 and O2 and intersecting at A and B.Angles AO1B = 60o, AO2B = 80o, AO1 =...
(Solved)
The figure below shows two circles with centres O1 and O2 and intersecting at A and B.Angles AO1B = 60o, AO2B = 80o, AO1 = O1B = 8cm

Calculate
(a) AB
(b) AO2
(c) Area of the shaded region.
Date posted:
August 19, 2019
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Answers (1)
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(a) A curve whose equation is in the form y = mx³ - nx where m and n are constants passes through the point (1,...
(Solved)
(a) A curve whose equation is in the form y = mx³ - nx where m and n are constants passes through the point (1, 2). Its gradient at the given point is 10. Find the values of m and n.
(b) Use the trapezium rule to find the area bounded by the curve y = x² + 4, the x-axis and the lines
x = 0 and x = 4. Use five ordinates.
(c) Calculate the exact area bounded by the curve, y = x² + 4, the x-axis and the lines x = 0 and x = 4. Hence find the percentage error in (b) above.
Date posted:
August 19, 2019
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Answers (1)
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One interior angle of a polygon is equal to 80° and each of the other interior angles are 128°
(Solved)
One interior angle of a polygon is equal to 80° and each of the other interior angles are 128°. Find the number of sides of the polygon.
Date posted:
August 19, 2019
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Answers (1)
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Using a pair of compasses and a ruler only construct a triangle ABC such that AB = 6cm, BC = 8cm
(Solved)
(a) Using a pair of compasses and a ruler only construct a triangle ABC such that AB = 6cm, BC = 8cm and ABC = 135°.
(b) Construct the height of triangle ABC in (a) above taking BC as the base and measure the height.
Date posted:
August 19, 2019
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Answers (1)
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(i) Express 48 and 6 0 as a product of their prime factors. (ii) A rectangle of side 48cm by 60cm is divided into squares...
(Solved)
(i) Express 48 and 60 as a product of their prime factors.
(ii) A rectangle of side 48cm by 60cm is divided into squares of side X cm.Find the greatest value of X.
Date posted:
August 19, 2019
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Answers (1)
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The coordinates of P and Q are P(5, 1) and Q(11, 4) point M divides line PQ in the ratio 2 : 1.
(Solved)
The coordinates of P and Q are P(5, 1) and Q(11, 4) point M divides line PQ in the ratio 2 : 1. Find the magnitude of vector OM.
Date posted:
August 19, 2019
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Answers (1)
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A translation maps triangle ABC onto A1B1C1, where A(1,-1), B( 3, 1) C ( 3,1) and C1 ( -1, 3).Find the coordinates of A1 and...
(Solved)
A translation maps triangle ABC onto A1B1C1, where A(1,-1), B( 3, 1) C ( 3,1) and C1 ( -1, 3).Find the coordinates of A1 and B1.
Date posted:
August 19, 2019
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Answers (1)
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The curved surface area of a cylindrical container is 1980 cm².
(Solved)
The curved surface area of a cylindrical container is 1980 cm². If the radius of the container is 21cm,
calculate to one decimal place the capacity of the container in litres
Date posted:
August 19, 2019
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Answers (1)
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In a class there are thrice as many boys as girls a third of the boys are from poor families while a fifth of the...
(Solved)
In a class there are thrice as many boys as girls a third of the boys are from poor families while a fifth of the girls are from rich families. Find the percentage number of pupils from rich families in the class.
Date posted:
August 19, 2019
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Answers (1)
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Fifteen men working eight hours a day can complete a certain job in exactly 24 days.
(Solved)
Fifteen men working eight hours a day can complete a certain job in exactly 24 days. For how many hours a day must sixteen men work in order to complete the same job in exactly 20 days.
Date posted:
August 19, 2019
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Answers (1)
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A rectangular tank whose length is 50 cm and width 30cm contains 36 litres of water.
a) Determine the height of water in the tank.
b)...
(Solved)
A rectangular tank whose length is 50 cm and width 30cm contains 36 litres of water.
a) Determine the height of water in the tank.
b) A heavy rectangle block has a length which is 5cm more than the width and a height of 5cm. If the width of the block is x cm, write down an expression for the volume of the block
c) The block is placed in the tank and the water level rises by 1cm. Determine the width and length of the block.
d) Determine the mass of the block given that its density is 1400kg/m3
Date posted:
August 19, 2019
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Answers (1)