You have learnt fractions and decimals in earlier classes. The study of fractions included
proper, improper and mixed fractions as well as their addition and subtraction. We also
studied comparison of fractions, equ
LINES AND ANGLES
In Chapter 5, you have studied that a minimum of two points are required to draw a
line. You have also studied some axioms and, with the help of these axioms, you
proved some ot
Do you know what the mass of earth is? It is
Can you read this number?
Mass of Uranus is 86,800,000,000,000,000,000,000,000 kg.
Which has greater mass, Earth or Uranus?
We have learnt about whole numbers and integers in Class VI.
We know that integers form a bigger collection of numbers
which contains whole numbers and negative numbers. What
other differences do you find between whole numbers and
4.1 A MIND-READING GAME!
The teacher has said that she would be starting a new chapter in
mathematics and it is going to be simple equations. Appu, Sarita
and Ameena have revised what they learnt in algebra chapter in
Class VI. Have you?
In your previous classes, you have dealt with various types of data. You have learnt to
collect data, tabulate and put it in the form of bar graphs. The collection, recording and
presentation of da
You may have come across many objects in daily life, which are round in shape, such
as wheels of a vehicle, bangles, dials of many clocks, coins of denominations 50
Linear Equations in
In the earlier classes, you have come across several algebraic expressions and equations.
Some examples of expressions we have so far worked with are:
5x, 2x 3, 3x + y,
15.1 INTRODUCTION: PLANE FIGURES
In this chapter, you will classify figures you have seen in terms of what is known as dimension.
In our day to day life, we see several objects like books, balls, ice-cream cones e
In Class VI, you have already learnt perimeters of plane figures and areas of squares and
rectangles. Perimeter is the distance around a closed figure while area is the part of plane or
region occupied by the closed fi
You have studied algebraic expressions, their addition, subtraction, multiplication and
division in earlier classes. You also have studied how to factorise some algebraic
expressions. You may recall th
Ramesh has 6 marbles with him. He wants to arrange them in rows in such a way
that each row has the same number of marbles. He arranges them in the following
ways and matches the total number of marbles.
LINEAR EQUATIONS IN TWO VARIABLES
The principal use of the Analytic Art is to bring Mathematical Problems to
Equations and to exhibit those Equations in the most simple terms that can be.
You have studied in earlier classes about figures of different shapes such as squares,
rectangles, triangles and quadrilaterals. You have also calculated perimeters and the
areas of some of these figures like re
In your earlier classes, you have learnt about the number line and how to represent
various types of numbers on it (see Fig. 1.1).
Fig. 1.1 : The number line
Just imagine you start from zero and g
We have already come across simple algebraic expressions like x + 3, y 5, 4x + 5,
10y 5 and so on. In Class VI, we have seen how these expressions are useful in formulating
puzzles and problems. We have also seen ex
When we talk about some plane figures as shown below we think of their
regions and their boundaries. We need some measures to compare them. We
look into these now.
Look at the following figures (Fig.
Savita and Shama were going to market to buy some stationary items.
Savita said, I have 5 rupees and 75 paise. Shama said, I have 7 rupees
and 50 paise.
They knew how to write rupees and paise using decimals.
Whats the good of Mercators North Poles and Equators, Tropics, Zones and
Meridian Lines? So the Bellman would cry; and crew would reply They are
merely conventional signs!
Our study so far has been with numbers and shapes. We have learnt numbers,
operations on numbers and properties of numbers. We applied our knowledge
of numbers to various problems in our life. The branch of mathematics
Geometry has a long and rich history. The term Geometry is the English
equivalent of the Greek word Geometron. Geo means Earth and metron
means Measurement. According to
historians, the geometrical ideas
Symmetry is quite a common term used in day to day life. When we see
certain figures with evenly balanced proportions, we say, They are
Thiruvannamalai (Tamil Nadu)
These pictures of archi
You must have observed your teacher recording the attendance of students in
your class everyday, or recording marks obtained by you after every test or
examination. Similarly, you must have also seen a cricket scor
Sunitas mother has 8 bananas. Sunita has to
go for a picnic with her friends. She wants to
carry 10 bananas with her. Can her mother
give 10 bananas to her? She does not have
enough, so she borrows 2 bananas from her
In earlier chapters, the diagrams, which were necessary to prove a theorem or solving
exercises were not necessarily precise. They were drawn only to give you
The Triangle and
A triangle, you have seen, is a simple closed curve made of three line
segments. It has three vertices, three sides and three angles.
Here is ABC (Fig 6.1). It has
AB , BC , CA
You are familiar with a number of shapes. You learnt how to draw some of them in the earlier
classes. For example, you can draw a line segment of given length, a line perpendicular to a
given line segment, an angle, an