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Without using a set square or a protractor construct:
a) Triangle ABC such that AB = 8cm, BC = 6cm and angle ABC= 300
b) Measure the length AC
c) Draw a circle that touches sides AB, BC and AC
d) Measure the radius of the circle.
e) Hence or otherwise calculate the area in the triangle but not in the circle.
Date posted:
August 23, 2019
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In the figure below, AC is an arc of a circle centre D. Angle ADC = 600, AD = DC = 7cm and
CB = 5cm.
Calculate:
a) The area of triangle ADB
b) The area of the shaded region.
Date posted:
August 23, 2019
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By striding 60cm or by striding 64cm, John takes an exact number of steps to cross a road. Find the least width of the road in metres.
Date posted:
August 23, 2019
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In the circle O is the centre, angle DAB = 870. Arc AB is twice arc AD. Calculate Angle AOB.
Date posted:
August 22, 2019
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Given that a = 1.2, b = 0.02 and c = 0.2, express ac + b in the form 
where m and n are integers.
Date posted:
August 22, 2019
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Onchwati deposited Ksh.50,000 in a financial institution in which interest is compounded Quarterly. If at the end of the second year he received a total of Ksh.79,692.40. Calculate the rate of interest per annum.
Date posted:
August 22, 2019
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What is the time in Hola 40oE when the time in Accra 0o Longitude is 3p.m?
Date posted:
August 22, 2019
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State two layers of atmosphere which experience Negative Lapse Rate.
Date posted:
August 22, 2019
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Explain four ways in which human activity have affected rivers in Kenya
Date posted:
August 22, 2019
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The instrument below is used to measure an element of weather .Study it and answer the questions below.
i) Name the liquid marked X.
ii) Identify the instrument above.
iii).Describe how the instrument works.
Date posted:
August 22, 2019
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If the time at 1200E is 3.00 pm Friday what is the local time and day at longitude 1650E.
Date posted:
August 22, 2019
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A test tube is made up of hemispherical bottom and a cylindrical stem. Both of internal radius 0.7cm. Calculate the capacity of the test tube given that its height is 12cm
Date posted:
August 22, 2019
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Given the points P(−6,−3) Q(−2,−1) and R(6,3) Express PQ and QR as column Vectors. Hence show that the points P,Q and R are collinear.
Date posted:
August 22, 2019
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Sodium has a work function of 2.3eV. Given that: Planck’s constant h = 6.63 x 10-34JS, velocity of light in vacuum, C = 3.0 x108m/s, 1 electron-volt (1eV) = 1.6 x 10-19 C and mass of an electron, me = 9.1 x 10-31kg, calculate:
(i) Its threshold frequency.
(ii) The maximum velocity of the photoelectrons produced when the sodium is illuminated by light of wavelength 5.0 x 10-7m.
(iii) The stopping potential V, with the light of this wavelength.
Date posted:
August 22, 2019
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Two aeroplanes P and Q, leave an airport at the same time. P flies on a bearing of 2400 at 900km/h while Q flies due east at 750 km/h.
a) Using a scale of 1 cm to represent 100 km, make a scale drawing to show the positions of the aeroplanes after 40 minutes.
b) Use the scale drawing to find the distance between the two areoplanes after 40 minutes.
c) Determine the bearings of;
i. P from Q
ii. Q from P
Date posted:
August 22, 2019
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An investment group decided to raise Shs. 960 000 to buy a piece of land costing Kshs. 80 000 per hectare. Before they paid, four of them pulled out and those that remained were supposed to pay an additional Kshs. 40 000.
a. If the initial number of members was 𝑥, write down;
i. An expression of what each was to contribute originally.
ii. An expression of what each of remaining members contributed.
b. Calculate the number of members who were initially in the group using the expression in (a) above.
c. If the land was sub divided equally, calculate what size each member got.
Date posted:
August 22, 2019
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Two towns P and Q are 550 km apart. A bus starts from town Q and travels towards P at 8:45 a.m. at an average speed of 80 km/hr. A car starts from P towards Q at 10:00 a.m. at an average speed of 100 km/hr. Calculate:
a. The distance covered by the bus before the car starts its journey.
b. How far from Q the vehicles met.
c. The time the two vehicles met.
d. The time the car arrived at town Q.
Date posted:
August 22, 2019
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A factory blends three types of juice in the ratios A:B = 3:4 and B:C = 1:2
a) Determine;
i. The ratio A:B:C
ii. The amount of type A juice in a 20 litre mixture.
b) The cost of producing one litre of A is Ksh. 80, one litre of B is Ksh. 84 and one litre of C is Ksh. 90.
i. Find the cost of producing one litre of the mixture.
ii. Calculate the selling price of one litre of the mixture if the factory makes a profit of 25%.
c) The factory uses types of machines P and Q to blend the juices. Machine P takes 7 hours to blend
14 000 litres and Q takes 5 hours to blend 12 000 litres. Determine the time it would take the factory to blend 550 000 litres.
Date posted:
August 22, 2019
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(a) Find the equation of a straight line L1 that passes through the points P (-6,-3) and Q (1,3) in the form ay+bx=c where a, b and c are constants.
(b) A second line L2 is parallel to L1 and passes through (2,-3). Find the equation of L2 in the form y = mx +c.
(c) A third line L3 passes through (2,3) and is perpendicular to L1. Find the equation of L3 in the form ay+bx=c.
(d) Use matrix method to find the coordinates of R the point where L1 and L3 intersect.
Date posted:
August 22, 2019
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The diagram below represents a solid consisting of a hemispherical bottom and a conical frustum at the top.
a) Determine the value of x and hence the height of the big cone.
b) Calculate the surface area of the solid.
c) Calculate the volume of the solid.
Date posted:
August 22, 2019
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A trader sold an article at Ksh. 4 800 after allowing a customer a 12% discount on the marked price of the article. In so doing he made a profit of 45%.
a) Calculate to 2 decimal places;
i. The marked price of the item.
ii. Price at which the trader had bought the article.
b) If the trader had sold the same article without giving a discount, calculate the percentage profit he would have made.
c) To clear his stock, the trader decided to sell all the remaining articles at a loss of 12.5%, calculate the price at which he sold each article.
Date posted:
August 22, 2019
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Find x if cos(3x-300)= sin(7x+500).
Date posted:
August 22, 2019
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It takes 40 road construction workers 8 days working 10 hours a day to complete a section of a road. How many days would 60 road construction workers working 8 hours a day take to complete the same section of the road working at the same rate?
Date posted:
August 22, 2019
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Use square roots, reciprocal and square root tables to evaluate to 4 significant figures the expression;
Date posted:
August 22, 2019
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A house has a lighting circuit operated from a 240V mains supply. Four bulbs rated 40W 240V and six bulbs rated 100W 240V are switched on for 5 hours a day. Determine the monthly bill for the consumer given that the cost of electricity is at shs. 5.50 per unit.
(Take 1 month = 30 days and the standing charge is sh. 150)
Date posted:
August 22, 2019
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The members of a photography club decided to buy a camera worth Ksh 4000 by each one contributing the same amount of money. Fifteen members fail to pay their contribution and as a result each of the other members has to pay Ksh 60 more. Find the number of members in the club.
Date posted:
August 22, 2019
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The figure below shows refraction of light at air-water interface.
Determine angle Ө if the refractive index of water is 1.33
Date posted:
August 22, 2019
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The figure below shows a frustrum made from a right pyramid,such that AB=DC=16cm,BC=AD=10cm,FG=EH=18cm,GH=FE=7.5cm, CH=BG=AF=DE=15cm.If the altitude of the frustrum is 14.6cm,find:
(a) The altitude of the pyramid made from the frustum.
(b) The surface area of the frustum.
(c) The volume of the frustum.
Date posted:
August 22, 2019
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Three people; A , B and C work together to make a certain number of tins. If person C was to work alone he will take 4 4/9 hours to complete the job. If all working together they will take 1hr 40min to complete the job. They all started working together however person B left after first 40min,while person C left 20min later. Person A took a further 1hr 46min. Calculate how long it would take if all the tins were made by;
a) Person A alone?
b) Person B alone?
c) Person A and C alone?
Date posted:
August 22, 2019
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Town B is 20km N600W from village A. Town B is 25km 0400 from town C. Village D is
due East of town C and dues South of village A
(a) Using a scale 1:500,000 draw a diagram showing a relative position of town B,
town C, village A and village D
(b) Determine
(i) Distance between village A and town C
(ii) Distance between town C and village D
(iii)Compass bearing of town C from village A
(iv) Compass bearing of village D from town
(c) Determine the area enclosed by the diagram in (a) above in hectares
Date posted:
August 22, 2019