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Solve for x in 3x – 3 x 15x = 15x
Date posted:
August 14, 2019
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The figure below represent a rectangle PQRS inscribed in a circle centre O and radius 17cm. PQ =16cm.
Calculate
(a) The length PS of the rectangle
(b) The angle ROS
(c) The area of the shaded region
Date posted:
August 14, 2019
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A newly built classroom measuring 6m long, 4.5m wide and 3.2 m high is to be cemented on the floor and all inside walls. The classroom has one door measuring 1.85m by 80cm by 80cm and four windows measuring 1.5m by 70cm each.Cementing materials cost 500 per square meter while labour costs 20% of the cost of cementing materials.Calculate:
(a) To one decimal place, the total surface are to be cemented
(b) The cost of cementing materials
(c) The total cost of cementing the classroom
Date posted:
August 14, 2019
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Solve for x in the equation below.
9(x-1) X 3(2x+1) = 243
Date posted:
August 14, 2019
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Form the quadratic equation whose roots are x= -5/3 and x=1
Date posted:
August 14, 2019
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Nyongesa spends a total of sh.970 on buying 3 text books and 5 pens. If he had bought 2 text books and 5 pens he would have saved sh.90. Find the cost of one text book.
Date posted:
August 14, 2019
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An open right circular cone has radius of 5cm and a perpendicular height of 12cm .Calculate the surface area of the cone.(Take pi to be 3.14)
Date posted:
August 14, 2019
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A surveyor recorded the measurements of a field in a field book using lines AB 260m as shown below.
a) Sketch the map of the field.
b) Find the area of the field in hectares.
Date posted:
August 14, 2019
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In the figure below E is the mid point of BC. AD: DC 3:2 and F is the meeting point of BD and AE.
If AB = b and AC = c
i) BD
ii) AE
b) If BF = t BD and AF = n AE. Find the value of t and n.
c) State the ratio of BD to BF.
Date posted:
August 14, 2019
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A group of people planned to contribute equally towards a water project which needed kshs. 2,000,000 to complete. However, 40 members of the group withdrew from the project. As a result, each of the remaining members were to contribute ksh 2500 more.
(a) Find the original number of members in the group.
(b) Forty five percent of the value of the project was funded by Constituency Development Fund (CDF). Calculate the amount that would be made by each of the remaining members of the group.
(c) Members contribution were in terms of labour provided and money contributed. The ratio of the value of labour to the money contributed was 6:19, calculate the total amount of money contributed by the members.
Date posted:
August 14, 2019
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B is 102km on the bearing of 112° from A. C is 94km on the bearing of 062° from B D is 073° from A and 336° from C.
(a) Using a scale of 1cm to represent 20km,draw a diagram to show the positions of A,B,C and D.
(b) Using your diagram, determine;
i) The bearing of B from D and A from C.
ii) The distance AC and BD
Date posted:
August 14, 2019
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Two similar containers have base areas 25cm2 and 324cm2 respectively. Calculate the Capacity of the larger container correct to one decimal place if the capacity of the smaller one is 8cm3
Date posted:
August 14, 2019
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Two trains T1 and T2, traveling in opposite directions on parallel tracks are just beginning pass one another. Train T1 is 72metres long and is traveling at 108km/hr.T2 is 78 metres Long and traveling at 72km/hr. Find the time in seconds the two take to completely pass one another.
Date posted:
August 14, 2019
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Pipe A empties a full tank in 8 hours, pipe B empties in 6 hours and pipe C empties in 3 hours. If all the three pipes are open for 30 minutes and then pipe A closed , How long will it take to empty a full tank.
Date posted:
August 14, 2019
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Find the equation of a perpendicular bisector of a line AB if the coordinates of A and B are (-4,-2) and (6,2) respectively.
Date posted:
August 14, 2019
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In the figure below DA is a diameter of the circle ABCD centre o, radius 10cm. TCS is a tangent to the circle at c, AB = BC and angle DAC = 38º
a) Find the size of the angle
i) ACS
ii) BCA
b) Calculate the length of;
i) AC
ii) AB
Date posted:
August 14, 2019
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A frequency distribution of marks obtained by 120 candidates is to be represented in a histogram. The table below shows the grouped marks , frequencies for all the groups and also the area and height of the rectangle for the group 30 – 60 marks.
a) i) Complete the table.
ii) On the grid provided,draw the histogram.
b) i) State the group in which the median mark lies.
ii) A vertical line drawn through the median mark divides the total area of the histogram into two equal parts. Using this information or otherwise, estimate the median mark.
Date posted:
August 14, 2019
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In the figure below, O is the centre of the circle of radius 3cm and AB is a chord such that its shortest distance from O is 1cm.
Calculate :
a) The length of the chord AB.
b) Angle AOB
c) The area of the minor sector OAB.
d) The area of the shaded segment.
Date posted:
August 14, 2019
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Mr. Barmuriat a farmer in Ainamoi division , Kericho District has a triangular field, ABC. The ratio of the length AB: AC = 6:7. If BC = 40m and the perimeter of the field is 118m,.
a) Calculate the length AB and the area of the field.
b) A water tap is installed inside the field such that the tap is equidistant from each of the vertices of the plot. Calculate the distance of the tap from vertex A.
c) Find the size of the acute angles between the edges AB and BC.
Date posted:
August 14, 2019
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Two types of tea in Kericho grade A and grade B are mixed. Grade A costs sh. 85 per kg, and grade B costs sh. 70 per kg.
a) If the tea are mixed in the ratio 2:1, find the cost 2kg of the mixture.
b) The tea is to be sold in 2kg boxes at a 30% profit. Find the selling price of the tea.
c) At the end of the week the price of a 2kg box is reduced to sh. 125. Find the percentage reduction in the price .
d) Origianally 200kg of grade A and 100kg of grade B were bought 240kg of the mixture was sold at the price of part b, and the rest was sold at the reduced price of part C. Find the overall percentage profit.
Date posted:
August 14, 2019
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Construct a net of the triangular prism shown, where the cross section is an equilateral triangle.Hence calculate the surface area of the prism.
Date posted:
August 14, 2019
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The angles of a quadrilateral are 3x, 2x, x +14 and 2( x – 7) degrees. Find the smallest angle.
Date posted:
August 13, 2019
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Three quantities t, x and y are such that t varies directly as x and inversely as the square root of y.
Find the percentage decrease in t if x decreases by 44%.
Date posted:
August 13, 2019
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The heights (cm) of some seedlings in a nursery are recorded in the table below.
a) Calculate the mean height of seedlings in the nursery.
b) Estimate the median height of the seedlings in the nursery.
c) On the grid provided, draw a histogram to represent the information.
Date posted:
August 13, 2019
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In the figure below (not drawn to scale) OABC is a parallelogram. AB is produced to T such that AB:BT = 3 : 1 and OA is produced to R such that OA : OR = 3 : 5. Given that OA = a and OC = c;
Express in terms of a and c vectors.
a) AC
b) CR
c) AT
d) CT
e) RT
Date posted:
August 13, 2019
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Town Q is 180km on bearing of 050o from town P. Another town R is on a bearing 110o from P and also on compass bearing S 30oE from Q. Town S is South of P and also West of R
Using scale 1 cm rep. 20 km;
a) Draw the scale diagram to show the positions of the four towns.
b) Use your scale diagram in (a) above to find;
i) The distance of R from P.
ii) The bearing of Q from S.
iii) The distance of Q from S.
iv) How far P is North of S.
Date posted:
August 13, 2019
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Two friends Jane and Tom live 40km apart. One day Jane left her house at 9.00am and cycled towards Tom’s house at an average speed of 15km/hr. Tom left at 10.30am on the same day and cycled towards Jane’s house at an average speed of 25km/hr.
a) Determine;
i) The distance from Jane’s house, where the two friends met.
ii) The time they met.
iii) How far Jane was from Tom’s house when they met?
b) The two friends took 10 minutes at the meeting point and they cycled to Tom’s house at an average speed of 12km/hr. Find the time they arrived at Tom’s house.
Date posted:
August 13, 2019
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The figure below shows a glass in form of a frustrum of a cone whose top and bottom diameter of 7cm and 3.5cm respectively. Its depth is 10cm.
Calculate;
a) Its total surface area.
b) Its capacity.
Date posted:
August 13, 2019
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Determine the obtuse angle made by line 3x – 2y = 6 and x-axis.
Date posted:
August 13, 2019
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Solve for x in the logarithm equation.
log (3x – 4) – log (3 – x) = 1
Date posted:
August 13, 2019