Topics
Part 1
Fractions in Disguise
A Square and A Cube
Rational Numbers
- Rational Numbers
- Closure Property of Rational Numbers
- Commutative Property of Rational Numbers
- Associative Property of Rational Numbers
- Distributive Property of Multiplication Over Addition for Rational Numbers
- Identity of Addition and Multiplication of Rational Numbers
- Negative Or Additive Inverse of Rational Numbers
- Concept of Reciprocals or Multiplicative Inverses
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers
- Multiples and Common Multiples
Part 2
Power Play
The Baudhayana-Pythagoras Theorem
Linear Equations in One Variable
- Constants and Variables in Mathematics
- Equation in Mathematics
- Expressions with Variables
- Word Problems on Linear Equations
- Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Solving Equations Having the Variable on Both Sides
- Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
- Reducing Equations to Simpler Form
- Equations Reducible to Linear Equations
A Story of Numbers
Understanding Quadrilaterals
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Basic Concept of Polygons
- Classification of Polygons
- Properties of Quadrilateral
- Sum of Interior Angles of a Polygon
- Sum of Exterior Angles of a Polygon
- Quadrilaterals
- Properties of Trapezium
- Properties of Kite
- Properties of a Parallelogram
- Properties of Rhombus
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The adjacent angles in a parallelogram are supplementary.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Properties of Rectangle
- Properties of a Square
- Property: The diagonals of a square are perpendicular bisectors of each other.
Proportional Reasoning-2
Quadrilaterals
Data Handling
Practical Geometry
- Geometric Tool
- Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
- Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
- Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
- Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
- Some Special Cases
Exploring Some Geometric Themes
Tales by Dots and Lines
Number Play
Squares and Square Roots
- Concept of Square Number
- Properties of Square Numbers
- Some More Interesting Patterns of Square Number
- Finding the Square of a Number
- Concept of Square Roots
- Finding Square Root Through Repeated Subtraction
- Finding Square Root Through Prime Factorisation
- Finding Square Root by Division Method
- Square Root of Decimal Numbers
- Estimating Square Root
Algebra Play
Cubes and Cube Roots
We Distribute, Yet Things Multiply
Proportional Reasoning-1
Comparing Quantities
- Ratio
- Increase Or Decrease as Percent
- Concept of Discount
- Estimation in Percentages
- Basic Concepts of Profit and Loss
- Calculation of Interest
- Concept of Compound Interest
- Deducing a Formula for Compound Interest
- Rate Compounded Annually Or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula
Area
Algebraic Expressions and Identities
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Classification of Terms in Algebra
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Monomial by a Trinomial
- Multiplying a Binomial by a Binomial
- Multiplying a Binomial by a Trinomial
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b) = a2-b2
- Expansion of (x + a)(x + b)
Mensuration
Visualizing Solid Shapes
Exponents and Powers
Direct and Inverse Proportions
Factorization
- Factors and Common Factors
- Factorising Algebraic Expressions
- Factorisation by Taking Out Common Factors
- Factorisation by Regrouping Terms
- Factorisation Using Identities
- Factors of the Form (x + a)(x + b)
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Concept of Find the Error
Introduction to Graphs
Playing with Numbers
- Location of a Point
- Coordinates
Definition
- Linear graph: A line graph which is a whole unbroken line is called a linear graph.
- Cartesian system: The system used to describe the position of a point in a plane is called the Cartesian system.
- Origin: The point of intersection of x and y lines is called the origin.
- Abscissa: X-coordinate tells how many units to move right or left. It is also called the Abscissa.
- Ordinate: Y-coordinate tells how many units to move up or down. It is also called the Ordinate.
- Cartesian Coordinate: X-coordinate and y-coordinate taken together are called cartesian coordinates or coordinates of a point and denoted by (x, y).
- Ordered pair: The x-coordinate comes first, and after this y-coordinate comes. (x, y) is called an ordered pair.
Notes
Linear Graphs:
A line graph which is a whole unbroken line is called a linear graph.
1. Location of a point:
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The system used to describe the position of a point in a plane is called the Cartesian system.
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In the Cartesian system, there are two perpendicular directed straight lines XX’ and YY’ which intersect at point 0, then line XX’ will be a horizontal line and YY’ will be a vertical line.
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The point of intersection of these lines is called origin and it is denoted by O. In other words, the point from which distances are marked is called an origin.
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The horizontal line XOX’ is called X-axis and the vertical line YOY’ is called Y-axis.
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Directions OX and OY are called the positive directions of the X-axis and Y-axis, respectively, and directions OX’ and OY’ are called the negative directions of the X-axis and Y-axis, respectively.
2. Coordinates:
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For fixing a point on the graph sheet we need, x-coordinate and y-coordinate.
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x-coordinate tells how many units to move right or left. It is also called the Abscissa.
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y-coordinate tells how many units to move up or down. It is also called the Ordinate.
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x-coordinate and y-coordinate taken together are called cartesian coordinates or coordinates of a point and denoted by (x, y). Here, the x-coordinate comes first, and after this y-coordinate comes. (x, y) is called an ordered pair.
Example
Example
Example
These lie on a line. The line is the y-axis.
Example
Example
Example
Shaalaa.com | How to Plot points on a graph
Series: Linear Graphs
Related QuestionsVIEW ALL [102]
Match the coordinates given in Column A with the items mentioned in Column B.
| Column A | Column B |
| (1) (0, 5) | (a) y coordinate is 2 × x - coordinate + 1. |
| (2) (2, 3) | (b) Coordinates of origin. |
| (3) (4, 8) | (c) Only y–coordinate is zero. |
| (4) (3, 7) | (d) The distance from x-axis is 5. |
| (5) (0, 0) | (e) y coordinate is double of x-coordinate. |
| (6) (5, 0) | (f) The distance from y-axis is 2. |
Draw a parallelogram ABCD on a graph paper with the coordinates given in Table I. Use this table to complete Tables II and III to get the coordinates of E, F, G, H and J, K, L, M.
| Point | (x, y) |
| A | (1, 1) |
| B | (4. 4) |
| C | (8, 4) |
| D | (5, 1) |
Table I
| Point | (0.5x, 0.5y) |
| E | (0.5, 0.5) |
| F | |
| G | |
| H |
Table II
| Point | (2x, 1.5y) |
| J | (2, 1.5) |
| K | |
| L | |
| M |
Table III
Draw parallelograms EFGH and JKLM on the same graph paper.
Plot the points (2, 4) and (4, 2) on a graph paper, then draw a line segment joining these two points.
