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KCSE Mathematics Paper 1 Revision Exercise Set 4
By writing your answer in the form #a^b#, simplify
#root(3)(2^y times 3^(2y) div 2(-2y) times 3^y)#
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1.
Factories completely #(a + b) (3a – 4b) – (a +b)^2#
2.
The line which joins the points A (3, k) and B (-2, 5) is parallel to the line whose equation is 5y + 2x = 7. Find the value of k.
3.
The base of a triangle is 3 cm longer than its height. Given that the area of triangle is 35#cm^2#, determine the height of the triangle.
4.
Three town are situated in such a way the town B is 40 km due south of town A and town C is 30 km due east of town B. a) Draw a sketch diagram showing the position of towns A, B and C. b) From your sketch, calculate i. Distance AC. ii. To the nearest degree, the bearing of town A from town C.
5.
Simplify the following equation by reducing it to a single fraction. #(2x-3)/(3)-(x-2)/(2)-(1-x)/(4)#
6.
On a certain map a road 20 km long is represented by a line 4cm long. Find the area in hectares of a ranch represented by a rectangle measuring 2.8 cm by 1.6 cm on this map
7.
The figure shows a right pyramid standing on a square base ABCD and with a path marked on it. a) Sketch the net of the pyramid and label all the vertices. b) On the sketch show the path marked on the diagram.
8.
Hassan has eight times as many one -shilling coins as twenty – shillings coins, half as many five – shillings coins as one -shilling coins and three times as many ten- shilling coins as twenty – shilling coins. If in total he has sh 156, find the number of coins he has.
9.
The figure shows a circle centre O and AOC as its diameter. Chords BD and AC intersect at F. Given that angle AOB = 68° and angle ACD = 70°, find the size of a) angle DAC b) angle BFC
10.
It would take 15 men 8 days to dig a trench 240 metres long. Find how many days it would take 18 men to dig a trench 360 metres long working at same rate.
11.
By selling an article for sh 810 Waswa makes a profit of 35%. During a sale he reduced the price of the article to sh 750. What percentage profit did he make?
12.
Fig.(i) above shows a triangle ABC in which AC = 8 cm, BC = a cm, and angle ACB = 30°. Fig(ii) shows a trapezium PQRS in which PQ = 7 cm, SR = 3cm, PQ is parallel to SR and the distance between them is d cm. Given that the triangle and the trapezium have the same area, determine the ratio d: a.
13.
Moraa bought 4 newspaper and 3 magazines at a total cost of sh 425. If she had bought 2 newspapers more and 1 magazine less, she would have spent sh 25 less. On another occasion Moraa bought 3 newspapers and 3 magazines at the same price. Find how she spent on the second occasion.
14.
By writing your answer in the form #a^b#, simplify #root(3)(2^y times 3^(2y) div 2(-2y) times 3^y)#
15.
From a point A the angle of elevation of the top of a tree is 25°.From another point B which is 10 metres from the base of the tree, the angle of elevation of the top of the tree is 36.5°. Giving your answer to one decimal place, determine the height of the tree and hence calculate the distance between A and B.
16.
A closed cylindrical tank of diameter 7 metres has a total surface area of 110m2. The tank which is initially one – third of water is filled by a pump which pumps water at the rate of 2.5 litres per second. a)Taking #pi# = #22/7#, determine i. The height of the tank. ii. The volume of water required to fill the tank in litres. iii. The time in hours and minutes, to the nearest minute, it takes to
17.
A rectangular sheet measuring 80 cm by 50 cm is 2 mm thick and is made of metal whose density is 2.5g/#cm^3#. A square of side 5 cm is removed from each corner of the rectangle and the remaining part folded to form an open cuboid. a) Calculate i. the area of metal which forms the cuboid. ii. the mass of the empty cuboid in kilograms. b) The cuboid is filled with water whose density is 1 g/#cm^3#.
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