Class 8 Revision 2009 -2010
Square and square roots
Enrichment Excercise:
1) The number of days in a year 365, can be written as a sum of the
squares of three consecutive numbers . Find them.
2) 13 and 31 are the mirror images of each other and their squares 169
and 961 are also such mirror images . Find two other such numbers
1. Assessment: (10 marks)
1 Find greatest number of seven digits which is a perfect square. (2)
56
2 Evaluate the square root of : 1 (2)
169
3 Find the length of the diagonal of a square whose perimeter is equal
to the perimeter of an equilateral triangle of side 4cm. (3)
4.The area of a square field is 60025m2.A man cycles along its boundary
at 18 Km/hr. In how much time will he return to the starting point?(3)
Cube and cube roots
Enrichment Excercise:
1. Can you find the different ways in which 1729 can be expressed as the
sum of two cubes?
2. Three of the numbers in each of the following squares are related to
the remaining number. Find the relationship?
3 4 1 6
5 6 9 8
8. Assessment: (10 marks)
a. Find the cube root of the following by prime factorization:
i. 438976
ii. 614125 (3)
3
b. The volume of a cubical box is 3375 cm . Find the side of the box.
(3)
c. Find the smallest number by which 5400 be multiplied so that the
product is a perfect cube. (2)
d. What is the smallest number by which 1372 must be divided so that
the quotient is a perfect cube (2)
Exponents
Enrichment Excercise:
a. Evaluate:
b. Prove
8.Assessment: [10 marks]
7
3 4
5
Evaluate : i) ii) [2}
6 5
1. Express each of the following rational numbers in exponential form:
256 243
i) ii) 32 [2]
81
2. If 5z , Find the value of z.
2 1
25125 [2]
3. Simplify and express the following in exponential form: [2]
7 5
4 4
5 10
2 2
i) ii)
3 3 7 7
3 2 2 3
2 2 3 3
iii)
iv)
3 3 2 2
1
1
4. By what number should be multiplied so that the product
2
1
5
is ?
4
[2]
Operations on Algebraic Expression
Enrichment Exercise:
1. I was asked to think of a number add 9 to it, find the square of the sum,
subtract 61 more than the square of the original number, double the
balance, add 24, subtract 36 times the original number. Do it three times
and check your answer. Explain.
2. Think of a number. Find the product of the numbers one greater than
and one less than the number you thought of. Add one to it. The result is
the square of the number you thought of. Can you explain why this is so?
3. Find : 1234567890
(1234567891)2 - (1234567890) (1234567892)
8 .Assessment: (10)
1. Evaluate ( 117 ) x ( 83 ) using identity (1)
2. . Find the product of y2 + 3y + 1 and y3 – y2 + 4. (2)
3. .Evaluate: 1042 and 9992 (1)
2
4. Given ( x + 1/x ) = 11 , find i) x +
ii) x4 + 1/x4 (2)
5.From the sum of x4 - 3x3 + 2x + 6 and x4 - 3x2 + 6x + 2
subtract x3 - 3x + 4. ( 2)
6.Divide 5y3 + 7y – 6 by y2 + y + 1 (2)
Factorisation
Assessment: (10 Marks)
Resolve the following into factors:
1. 8p4q + 18p3q2 – 16p2q3 + 2pq4 (1)
2. 4x2 + 12xy + 9y2 (1)
3. z4 – 81 (2)
4. 12x2 + 23x + 10 (2)
5. 7x2 – 19x – 6 (2)
6. 9x2 + 25y2 – 2
(2)
25y2 9x2
Quadrilaterals
Assessment: (10 marks)
1. The measure of two adjacent angles of a quadrilateral are 125 0 and 650
and the other two angles are equal. Find the measure of each angle.(2)
2 A quadrilateral has four angles of the same measure. Find the angle.
What kind of a figure it would be? (2)
3. The four angle of a quadrilateral are in the ratio 2:4:5:7. Find the angles.
(3)
4. In the given fig. the external bisector of
If
D C
1100 1200
A B
O
Construction of Quadrilaterals
2. Assessment: ( 15 marks )
1. Give Reasons
i. Is it possible to construct a quadrilateral ABCD in which
AB=3cm, BC=4cm, CD = 5.5 cm, DA =6cm and BD = 9cm?
If not, give reasons.
ii. Is it possible to construct a quadrilateral ABCD in which
AB=5cm, BC=7.5cm, A = 800, B = 1400 and C =1450 ?
If not, give reasons. (3)
2. Construct a quadrilateral ABCD in which AB = 4.5 cm, BC = 5.5 cm,
CD = 4 cm, DA = 6 cm and AC = 7 cm (3)
3. Construct a quadrilateral ABCD such that AB = 2.7 cm,
BC =3.5cm, CD = 4cm, AD = 6cm and B = 90o. (3)
4. Construct a parallelogram one of whose sides is 5.2cm and whose
diagonals are 6cm and 6.4cm. (3)
5 .Construct a rhombus ABCD, given that AB = 5 cm and an angle is 700.
(3)
Area of a Trapezium and a Polygon
Enrichment Exercise:
1. Use the formula for the area of a trapezium to work out the missing
values in this table.
Length a Length b Height Area
3 cm 8 cm 4 cm
20 cm 0.3cm 0.25 cm
10 cm 20 cm 500 cm2
0.25 cm 40 cm 1100 cm2
45 cm 0.04 m 150 cm2
2. The rectangular garden is split into four sections. Section A and D are
trapeziums ; section B and C are triangles. The area of section A is
twice of section B.
Calculate the following:-
i. Area of the whole garden
ii. Area of section A
iii. Area of section B
iv. Length of side marked x
v. Area of section C
vi. Area of section D
8. Assessment: (15 marks)
1. The area of a trapezium is 1080cm2 . If the lengths of its parallel sides
are 55.6cm and 34.4 cm. Find the distance between them. (2)
2. The area of a trapezium is 105cm2 and its height is 7cm . If one of
the parallel sides is longer than the other by 6 cm, find the two
parallel sides. (2)
3. The area of a trapezium is 234 cm2. The length of its parallel sides
are 20cm and 32cm. Find its altitude. (2)
4. The parallel sides of a trapezium are 20 cm and 10 cm. Its non parallel
sides are both equal, each being 13cm. Find the area of the trapezium
(3)
5. ABCD is a trapezium in which D C
parallel sides AB and DC are of lengths
24 m and 10 m respectively. If area of
∆ CEB is 84m2 then find the area of the
given trapezium.
A E B
(3)
6. In trapezium ABCD, AB = AD = BC = 13cm and CD =23cm. Find
the area of the trapezium. (3)
Ratio and Proportion
Assessment: ( 15 marks )
1. In which of the following cases is there direct or increase variation.
(3)
a. A tank can be filled in 3 hours. How much can it fill in 1 hour 30
minutes.
b. The price of rice is Rs.20 per kg. I can buy 12kg for Rs.240.If
the price goes up by Rs.2 per kg. how much rice can I buy for
Rs.240?
c. Cloth was purchased at Rs.6 per mt. How much will 19 metres
of cloth cost.
2. If x 2 y 2 4xy 1 , then prove that x and y vary inversely to each
other. (2)
3. At a party, 6 bottles of juice are served for every batch of 14 children.
How many bottles would be served if 56 children are present at the
party? (2)
4. A map is drawn to 1 : 5000000 scale. If a river measures 11.72 cm in
length on the map, what is the actual length of the river? (2)
5. A bicycle dealer has Rs.20,000 to invest, when a bicycle is available
for Rs.800. If the price of a bicycle increases by 25%, find the number
of cycles he can purchase with the same sum? (3)
6. In a fort under siege there is enough food to feed the 90 inmates for 7
days. 20 inmates quietly slip away and escape. How many days will
the food now last for the rest of the inmates ? (3)
LINEAR EQUATIONS
Enrichment Exercise:
1. On a particular day, when the students of a class had an unexpected
Geography lesson, they had to share some books amongst
themselves. Though each student had his note book, every two
students shared a Geography text, every three had to share a
reference book, and each group of four students shared an Atlas. If a
total of 125 books and notebooks were used by the students, how
many students were there?
2. At an international meeting of Chinese and Indian officials, twenty
Indian and Chinese officials shook hands. Monali shook hands with the
least number of Chinese officials – seven,Sanjeev shook hands with
eight of the Chinese, Vijaya with nine Chinese and so forth up to Neeta
who shook hands with all the Chinese. How many Chinese were there
at the meeting?
8.Assessment: ( 15 marks)
1. Solve the following equations for x :
5(7 x 5) 2 4( x 1 / 2)
7 13
i) 3 3 3
x 2 x 1 x 3 1 (5)
ii) 3 5 4
2. In an objective type mathematics examination consisting of 100
problems, one mark is given for every correct answer and half a mark
is subtracted for each incorrect answer. If a student attempted all 100
questions and scored 70 marks, how many of her answers were
correct? (5)
3. The sum of the two digits in two digit number is 13. If 45 is added to
the number, the digits are reversed. Find the original two digit number.
(5)
Time and work
Enrichment Exercise:
1. It takes five minutes to boil a single potato. How many minutes will it
take to boil 2 potatoes together?
2. A takes 30 minutes to walk from home to the school and B takes the
same time to walk the same distance. How long will it take them if they
both walk together?
3. Sonal and Gunjan work on a job together for four days and
complete 60% of it. Sonal leaves and then Gunjan works for eight
more days to complete the job. How long would Sonal alone take
to complete the entire job?
8.Assessment: : (15 Marks)
1. At a community feast if 6 ladies can make 540 rotis in an hour, how
many ladies will be needed to make 990 rotis in an hour? (2)
2 .A can build a room in 50 days. A & B together can build a room in
25 days. They worked together for 15 days and then B goes away.
In how many days will A finish the remaining work? (3)
3. Jyoti takes 2 hours to clean the room. Her elder sister Smita takes
1 ½ hours while their mother takes only an hour to do the same
job. If the two daughters help their mother what fraction of the
room will remain to be cleaned after 18 minutes? (3)
4.Tap A can fill a tank in 8 minutes, outlet B can empty the tank in
12 minutes. If both are kept open, how long will it take to fill the
tank?
(3)
5.Tap A fills a tank in 3 hours, outlet pipes B and C can empty the tank in 4
hours and 6 hours respectively. If the tank is empty and A and B are turned
on how long will it take to fill up? After the tank is full A, B and C are all turned
on. How long will the tank tape to be empty?
(4)
Circles
Assessment: (15 marks)
1. Sides of a triangle ABC are equidistant from the centre O of its
circumcircle. What type of triangle is ABC? (2)
2. ABCD is a cyclic quadrilateral whose side AB is a diameter of the
circle. If ADC= 1400, find BAC (3)
A
3. In the fig , BD= DC and
DBC= 300. Find measure of BAC
A
.
B C
D (3)
4..In the given fig , ABC is a triangle in which BAC= 300. Show that BC is
the radius of the circumcircle of ∆ABC, whose centre is O. (3)
A
300
.O
B C
5.PQ and RS are two chords of a circle such that PQ=10cm, RS=24cm
and PQ ll RS. Find the radius of the circle if the distance between PQ
and RS is17cm. (4)
Profit, Loss and Discount
Assessment: (15 marks)
1. An almirah was bought for Rs.2560 and Rs.150 was spent on its
transportation. At what price should it be sold to have a gain
of 10% ? (2)
2. A saree is sold for Rs.3900 after allowing a discount of 35%, what is
the marked price? (2)
3. The marked price of a fan is Rs. 1250 and the shopkeeper allows a
discount of 6% on it. Find the selling price of the fan. (2)
4. Two horses are sold at Rs.9000 each. On one he gains 10% and on
another he losses 10%. How much is his gain % or loss% in the
whole transaction? (3)
5. If the selling price of 10 articles is equal to the cost price of 11articles,
find gain or loss %. (3)
6. A radio dealer marks a radio with a price 25% more than the cost price. If
he sells it at a discount of 10%, what will be his gain or loss%?
(3)
Compound Interest
Enrichment Exercise:
1. Anubhav wanted to put Rs. 10,000 in a savings account.
Bank A paid annual interest of 8% charged Rs. 20 per month in
service charges, and charged Rs. 10 as fees.
Bank B paid annual interest of 5%. But charged no service fees.
Bank C paid annual interest of 7% , but charged Rs. 10 per
month in service charges and Rs 20 as fees.
Bank D paid annual interest of 6% , with Rs.50 as fees and no
other service charge which bank would result in Anubhav having
the maximum amount of money after 1 year, if they all compound
their interest quarterly?
2. Ramu borrows Rs. 50,000 at 12% interest per annum compounded
half yearly from a bank, for sawing during the seasons. He hopes to
repay the loan after 6 months when the harvest occurs. How much
would he be paying as interest after 6 months?
8.Assessment: (15 marks)
1.Find the amount on a sum of Rs.125000 for 9 months at the rate of
8% per annum, compounded quarterly. Hence find the compound
interest. (3)
2. At what rate percent per annum will a sum of Rs. 2000 amount to
Rs. 2205 in 2 years, compounded annually. (3)
3..The simple interest on a sum of money for 3 years at 6 2/3% per
annum is Rs.6750. What will be the compound interest on the same
sum at the same rate for the same period, compounded annually.
(4)
4. The difference between compound interest and simple interest on
a certain sum of money for two years at 5% per annum is 2.50, find
the sum. (5)
Data Handling and Bar Graph
Assessment: (15 marks)
Q.1 Seema wanted to find out about the type of pets and the number of
students who have pets. She found that 24 of her classmates have pets.
Given below is the information she got. Prepare a frequency table using tally
marks.
Cat, cat, rabbit, dog, dog, dog, cat, dog, rabbit, parrot, rabbit, pigeon, cat,
dog, rabbit, parrot, pigeon, pigeon, parrot, pigeon, dog, dog, rabbit, rabbit.
(3)
Q.2 The following table shows the market positions of different brands of soaps.
Brand A B C D Others
% of Buyers 45 25 15 10 5
Draw a bar graph to represent the above data. (3)
3.
Study the bar graph given below and state that who scored maximum percentage
marks in science if each paper is of 100 marks each.
(3)
Q.4 Following is the data collected from 50 students about their favourite
fruits. The categories are : a) stands for mangoes, b) for apples, c) for
oranges, d)for bananas and e) for grapes. The raw data is as follows.
c, d, a, c, b, d, a, c, b, e, e, b, c, a, a, a, c, b, b, a, c , d, d, e, e, a, a, b, c, c, e,
d, a, b, b, b, a, d, e, d, d, a, b, b, d, d, a, b, b, c
Prepare a frequency chart.
(3)
Q5. Anil, Tina, Neelu and Manju collected some lady bugs on a trip
Anil |
Tina
Neelu
Manju ||
Using the information given above, answer the following questions:
(i) Who collected the maximum number of ladybugs?
(ii) Who collected the least number of ladybugs?
(iii) What is the total number of ladybugs collected?
(3)
TOPIC – Graphs
Assessment : ( 10 marks )
1. Draw the graph of y = 5x (5)
2. The side of an equilateral triangle is 4 cm, its perimeter is 12 cm.
Plot a graph of perimeter against length of side. (5)
Volume and Surface Area
Enrichment Exercise:
1. The cross- section of a swimming pool is shaped like a
trapezium. The shallow end of the swimming pool is 1.1 m and the
deep end is 3 mts. If the pool is 100 mts. Long and 30 mts. Wide,
find its volume ?
2. A hair oil manufacturer is trying to choose a cylindrical container for a
new brand of hair oil he is introducing into the market. The possible
containers given to him are as shown.
5 8 10 12
10
7
5 4
The metal for the containers is brought in sheets of uniform thickness
which size would he choose if he wants to use the minimum area of
metal for a given volume.
3. Four identical cylinders with a circular base, and a radius of 10 cm are
placed inside a much larger cylinder with a radius of 100 cm. the
height of all five cylinders in 200 cm. find the volume of the
unoccupied region.
8. Assessment : (15 marks)
1. Find the volume of the cylinder given the area of its base is 154 cm 2
and height = 8 cm. (2)
2. The surface area of a cuboid of length 12 cm and width 8m cm is 552
cm2. What is the height and volume of the cuboid? (3)
3. The volume of a cylinder of radius 4 cm and height 9 cm is the same
as that of another cylinder with radius 3 cm. what is the height of the
second cylinder ? (3)
4. A metallic pipe whose internal and external diameters are 6 cm and 8
cm, has a length of 2.1 cm. find the volume of the metal? (3)
5. The area of the base of a cuboid is 126 cm2. The area of each and is
45 cm2. The area of the front is 70 cm2. Find the surface area,
dimensions and volume of the cuboid. (4)