Topics
Rational Numbers
 Concept of 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
 Reciprocal Or Multiplicative Inverse of Rational Numbers
 Rational Numbers on a Number Line
 Rational Numbers Between Two Rational Numbers
Linear Equations in One Variable
 The Idea of a Variable
 Expressions with Variables
 Concept of Equation
 Balancing an Equation
 The Solution of an Equation
 Linear Equation in One Variable
 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 the Linear Form
Understanding Quadrilaterals
 Concept of Curves
 Different Types of Curves  Closed Curve, Open Curve, Simple Curve.
 Concept of Polygons  Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
 Classification of Polygons  Regular Polygon, Irregular Polygon, Convex Polygon, Concave Polygon, Simple Polygon and Complex Polygon
 Angle Sum Property of a Quadrilateral
 Interior Angles of a Polygon
 Exterior Angles of a Polygon and Its Property
 Concept of Quadrilaterals  Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
 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.
Practical Geometry
 Introduction to Practical Geometry
 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
Data Handling
 Concept of Data Handling
 Interpretation of a Pictograph
 Interpretation of Bar Graphs
 Drawing a Bar Graph
 Interpretation of a Double Bar Graph
 Drawing a Double Bar Graph
 Organisation of Data
 Frequency Distribution Table
 Graphical Representation of Data as Histograms
 Concept of Pie Graph (Or a Circlegraph)
 Interpretation of Pie Diagram
 Chance and Probability  Chance
 Basic Ideas of Probability
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
Cubes and Cube Roots
Comparing Quantities
 Concept of Ratio
 Concept of Percent and Percentage
 Increase Or Decrease as Percent
 Concept of Discount
 Estimation in Percentages
 Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
 Sales Tax, Value Added Tax, and Good and Services Tax
 Concept of Principal, Interest, Amount, and Simple Interest
 Concept of Compound Interest
 Deducing a Formula for Compound Interest
 Rate Compounded Annually Or Half Yearly (Semi Annually)
 Applications of Compound Interest Formula
Algebraic Expressions and Identities
 Algebraic Expressions
 Terms, Factors and Coefficients of Expression
 Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
 Like and Unlike Terms
 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)
 Expansion of (x + a)(x + b)
Visualizing Solid Shapes
Mensuration
Exponents and Powers
Direct and Inverse Proportions
Factorization
 Factors and Multiples
 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
 Concept of Bar Graph
 Interpretation of Bar Graphs
 Drawing a Bar Graph
 Concept of Double Bar Graph
 Interpretation of a Double Bar Graph
 Drawing a Double Bar Graph
 Concept of Pie Graph (Or a Circlegraph)
 Graphical Representation of Data as Histograms
 Concept of a Line Graph
 Linear Graphs
 Linear Graphs
 Some Application of Linear Graphs
Playing with Numbers
description
 Independent variable
 Dependent variable
 Quantity and Cost
 Principal and Simple Interest
 Time and Distance
definition

Independent Variable: Anything which is completely independent and its quantity do not depend on any other factor then it is called Independent Variable.

Dependent Variable: Anything which increases or decreases with the quantity of any other factor or it is dependent on any other factor then it is called Dependent Variable.
notes
Some Applications:

Independent Variable: Anything which is completely independent and its quantity do not depend on any other factor then it is called Independent Variable.

Dependent Variable: Anything which increases or decreases with the quantity of any other factor or it is dependent on any other factor then it is called a Dependent Variable.

For example, If more electricity is consumed, the bill is bound to be high. The amount of electric bill depends on the quantity of electricity used. We say that the quantity of electricity is an independent variable (or sometimes control variable) and the amount of electric bill is the dependent variable.

The relation between the dependent variable and the independent variable is shown through a graph.
For example,
The following table gives the quantity of petrol and its cost.
No. of Litres of petrol  10  15  20  25 
Cost of petrol in ₹  500  750  1000  1250 
Plot a graph to show the data.
Solution:
 Let us take a suitable scale on both the axes.
 Mark the number of litres along the horizontal axis.
 Mark cost of petrol along the vertical axis.
 Plot the points: (10,500), (15,750), (20,1000), (25,1250).
 Join the points.
Example
Sum deposited  Simple interest for a year 
₹ 100  ₹ `(100 xx 1 xx 10)/100` = ₹ 10 
₹ 200  ₹ `(200 xx 1 xx 10)/100` = ₹ 20 
₹ 300  ₹ `(300 xx 1 xx 10)/100` = ₹ 30 
₹ 500  ₹ `(500 xx 1 xx 10)/100` = ₹ 50 
₹ 1000  ₹ 100 
Deposit (in ₹)  100  200  300  500  1000 
Annual S.I. (in ₹)  10  20  30  50  100 
 Corresponding to ₹ 250 on the horizontal axis, we get the interest to be ₹ 25 on the vertical axis.
 Corresponding to ₹ 70 on the vertical axis, we get the sum to be ₹ 700 on the horizontal axis.
Example
Hours of ride  Distance covered 
1 hour  30 km 
2 hours  2 × 30 km = 60 km 
3 hours  3 × 30 km = 90 km 
4 hours  4 × 30 km = 120 km and so on. 
Time (in hours)  1  2  3  4 
Distance covered (in km)  30  60  90  120 
Horizontal: 2
Shaalaa.com  Some Application of Linear Graphs
Series: Some Application of Linear Graphs
Related QuestionsVIEW ALL [7]
Draw a graph for the following.
Side of square (in cm)  2  3  3.5  5  5 
Perimeter (in cm)  8  12  14  20  24 
Is it a linear graph?
Draw the graphs for the following tables of values, with suitable scales on the axes.
Distance travelled by a car
Time (in hours)  6 a.m  7 a.m  8 a.m  9 a.m 
Distance (in km)  40  80  120  160 
1) How much distance did the car cover during the period 7.30 a.m. to 8 a.m.?
2) What was the time when the car had covered a distance of 100 km since its start?
Draw a graph for the following.
Side of square (in cm)  2  3  4  5  6 
Area (in cm^{2})  4  9  16  25  36 
Is it a linear graph?
Draw the graphs for the following tables of values, with suitable scales on the axes.
Interest on deposits for a year:
Deposit (in Rs)  1000  2000  3000  4000  5000 
Simple interest (in Rs)  80  160  240  320  400 
1) Does the graph pass through the origin?
2) Use the graph to find the interest on Rs 2500 for a year:
3) To get an interest of Rs 280 per year, how much money should be deposited?
Draw the graphs for the following tables of values, with suitable scales on the axes.
Cost of apples
Number of apples  1  2  3  4  5 
Cost (in Rs)  5  10  15  20  25 