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Form 2 Mathematics Revision Questions and Answers Set 1
Given cos x = sin 2x, find x.
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1.
Without using a calculator or mathematical tables simplify. #sqrt((0.504 times 14.3 times 910)/(0.28 times1.17 times 28.6 times7))#
2.
Find the value of x: #(27/8)^(x+7) = (4/9)^(-3x)#
3.
A wholesaler sold a cell phone to a retailer making a profit of 20%. The retailer later sold the cell phone for Ksh.3120 making a profit of 30% calculate the amount of money the wholesaler had paid for the cell phone.
4.
The exterior angle of a regular polygon is #(x - 50)^0# and the interior angle is #(2x+ 20)^0# Find the number of sides of the polygon.
5.
Simplify #(3t^2 – 12)/(3- (1+t))#
6.
A straight line through the points A (2, 1) and B (4, m) is perpendicular to the line whose equation is 3y = 5-2x. Determine the value of m.
7.
A liquid spray of mass 384 g is packed in a cylindrical container of internal radius 3.2 cm. Given that the density of the liquid is 0.6g/#cm^3#, calculate to 2 decimal places the height of the liquid in the container.
8.
If x:y=9:11, find the ratio (5x-3y):(2x +3y).
9.
Timmons sold a TV set costing Ksh. 47,000 at a profit of 20%. He earned a commission of 22.5% on the profit. Find the commission he earned.
10.
A car uses 1 litre of petrol for every 8 kilometres. The car was to travel 480 kilometres and had 15 litres of petrol at the beginning of the journey. Each litre of petrol cost sh. 112.00. How much did it cost for the extra petrol added?
11.
Find the area of a triangular piece of land whose sides are 7m, 9m and 14m.
12.
Solve #2^(8x)# = 512
13.
The ratio of the area of two similar rooms is #4/25#. (a) Find the ratio of their length. (b) Find the area of the bigger room if the area of the smaller room is #8m^2#.
14.
Given cos x = sin 2x, find x.
15.
Solve the following quadratic equation. #5x^2 – 21x + 4=0#
16.
Solve the following simultaneous equations. 3x + 2y = 13 5x + 3y = 15
17.
The ratio of boys to girls is 3:2. When #1/3# of the boys and 6 girls are absent, the ratio remains the same. Find the number of students in the class.
18.
Evaluate #(-8÷2+12 times 9-4 times 6)/(56 ÷7 times2)#
19.
The diagonals of a rhombus measure 9.2 cm and 7.5 cm respectively. Calculate the area of the rhombus
20.
A man is three times as old as his daughter. In twelve years’ time he will be twice as old as his daughter. Find their present age.
21.
A car is moving with a velocity of 50 km/h then the brakes are applied so that it stops after 20 seconds.Find its acceleration.
22.
A van left Nairobi for kakamega at an average speed of 80 km/h. After half an hour, a car left Nairobi for Kakamega at a speed of 100 km/h. a.) Find the relative speed of the two vehicles. b.) How far from Nairobi did the car over take the van
23.
A truck left Nyeri at 7.00 am for Nairobi at an average speed of 60 km/h. At 8.00 am a bus left Nairobi for Nyeri at speed of 120 km/h .How far from nyeri did the vehicles meet if Nyeri is 160 km from Nairobi?
24.
The points A (-4 ,4 ) , B (-2 ,3) , C (-4 , 1 ) and D ( - 5 , 3) are vertices of a quadrilateral. If the quadrilateral is given the translation T defined by the vector #((3),(-2))#.Find the image.
25.
The scale of a map is given in a statement as 1 cm represents 4 km. convert this to a representative fraction (R.F).
26.
A salesman earns a basic salary of sh. 9,000 per month. In addition he is also paid a commission of 5% for sales above sh. 15,000. In a certain month he sold goods worth sh. 120,000 at a discount of 2½%. Calculate his total earnings that month.
27.
Mr. Neasa, a salesman in a soap industry, sold 250 pieces of toilet soap at sh 45.00 and 215 packets of detergent at sh 75.00 per packet. If he got a 5% commission on the sales, how much money did he get as commission?
28.
The price of an article is marked at sh 120.A discount is allowed and the article sold at sh 96.Calculate the percentage discount.
29.
Johnny bought a dress at 3500 and later sold it at sh.2800.what percentage loss did he incur?
30.
Ollie bought a cow at sh 18000 and sold it at sh 21000.What percentage profit did he make?
31.
The cost of two skirts and three blouses is sh 600.If the cost of one skirt and two blouses of the same quality sh 350,find the cost of each item.
32.
Solve for x in the equation: 3(x + 3) – 2 (x – 4) = 24
33.
Mary bought a number of oranges from Anita’s kiosk. She then went to Marks kiosk and bought the same number of oranges. Mark then gave her three more oranges. The oranges from the two kiosks were wrapped in different paper bags. On reaching her house, she found that a quarter of the first Lot oranges and a fifth of the second were bad. If in total six oranges were bad, find how many oranges she
34.
Solve for the unknown in the following 3x + 4 = 10
35.
A rectangular slab of glass measures 8 cm by 2 cm by 14 cm and has a mass of 610g. calculate the density of the glass in kg/m³
36.
Evaluate #8 3/5 ÷ 12 1/5#
37.
Two pipes A and B can fill an empty tank in 3hrs and 5hrs respectively. Pipe C can empty the tank in 4hrs. If the three pipes A, B and C are opened at the same time find how long it will take for the tank to be full.
38.
A cone of radius 5cm has a curved surface of area of #109.9cm^2#. Calculate the volume of the cone.
39.
Given that #[(3-4m)/m=(2-9)/m]#, find the value of m.
40.
A solid metal cone has a diameter of 14cm and a height of 24cm. calculate the surface area of the cone.
41.
Each exterior angle of a regular polygon is a fifth of the interior angle. a).Find the size of the exterior angle. b).Find the number of sides of the polygon.
42.
Find the mass of a wooden beam 4m long, 25 cm wide and 18cm deep if the density of the wood is 625kg/#m^3#
43.
The length of an arc of a circle is of its circumference. If the area of the circle is #346.5cm^2#, find the angle subtended by the arc at the Centre of the circle.
44.
Evaluate without using tables or calculators. #(0.036 times 0.0049)/(0.07 times 0.048)#
45.
Given that x=2y and 3y=5z. find the ratio x:y:z hence or otherwise find the amount of money Ali got if Ali, Ben and Chris shared Kshs. 36000 in the ratio x:y:z respectively.
46.
A plane leaves town A for town B at 0540 hours. If the journey takes 6.5 hours, at what time does the plane reach its destination?
47.
A cylindrical solid metal is 3m long and has a mass of 4kg. if its density is 5.6g/#cm^3#, find the radius of its end. #(take pi=3.142)#
48.
A man walks to work at 16km/hr and back home at 5km/hr. find the distance from his work place if the whole journey takes him 2 hours 12 minutes.
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