Topics
Fractions in Disguise
Part 1
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
A Square and A Cube
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
The Baudhayana-Pythagoras Theorem
Part 2
Power Play
Proportional Reasoning-2
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.
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
Quadrilaterals
Number Play
Tales by Dots and Lines
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
- Definition: Graph
- Graph Paper
- X-axis and Y-axis
- Use of Scale
Definition
A Pictograph is a chart that uses pictures or symbols to represent data. Each picture stands for a specific number of items, making the data easy to understand at a glance.
Graph Paper
Structure of Graph Paper:
1. Grid Formation:
Graph paper consists of a network of bold and faint lines.
The bold lines represent larger units, while the faint lines divide these units into smaller, equal parts.
2. Purpose of the Grid:
This structure helps in choosing a suitable scale.
It also assists in drawing accurate columns or bars based on data values.
3. Axes on Graph Paper:
A horizontal line is drawn near the bottom edge of the paper, known as the X-axis.
On the left side, draw a vertical line perpendicular to the X-axis, which we call the Y-axis.
Example:
The following information is to be represented as a bar graph: The number of different types of vehicles is: 5, 15, 25, and 30. Use the X-axis to represent the types of vehicles. Use the Y-axis to represent the number of vehicles. Take a scale of 5 vehicles = 1 big unit.
Shaalaa.com | Selecting Right Scale
Series: Concept of Bar Graph
Related QuestionsVIEW ALL [61]
The following table gives the number of vehicles passing through a toll gate, every hour from 8.00 am. to 1.00 pm:
| Time Interval |
8.00 to 9.00 |
9.00 to 10.00 |
10.00 to 11.00 |
11.00 to 12.00 |
12.00 to 1.00 |
| Number of vehicles |
250 | 450 | 300 | 250 | 150 |
Draw a bar graph representing the above data.
Below is a list of 10 tallest buildings in India.
This list ranks buildings in India that stand at least 150 m (492 ft.) tall, based on standard height measurement. This includes spires and architectural details but does not include antenna marks. Following data is given as per the available information till 2009. Since new buildings are always under construction, go on-line to check new taller buildings.
Use the information given in the table about sky scrapers to answer the following questions:
| Name | City | Height | Floors | Year |
| Planet | Mumbai | 181 m | 51 | 2009 |
| UB Tower | Bengaluru | 184 m | 20 | 2006 |
| Ashok Towers | Mumbai | 193 m | 49 | 2009 |
| The Imperial I | Mumbai | 249 m | 60 | 2009 |
| The Imperial II | Mumbai | 249 m | 60 | 2009 |
| RNA Mirage | Mumbai | 180 m | 40 | 2009 |
| Oberoi Woods Tower I | Mumbai | 170 m | 40 | 2009 |
| Oberoi Woods Tower II | Mumbai | 170 m | 40 | 2009 |
| Oberoi Woods Tower III | Mumbai | 170 m | 40 | 2009 |
| MVRDC | Mumbai | 156 m | 35 | 2002 |
(a) Find the height of each storey of the three tallest buildings and write them in the following table:
| Building | Height | Number of storeys | Height of each storey |
(b) The average height of one storey for the buildings given in (a) is ______.
(c) Which city in this list has the largest percentage of skyscrapers? What is the percentage?
(d) What is the range of data?
(e) Find the median of the data.
(f) Draw a bar graph for given data.
In the table given below, the information is given about roads. Using this draw a sub-divided and percentage bar diagram (Approximate the percentages to the nearest integer).
| Year | Permanent Roads ( Lakh km.) |
Temporary Roads ( Lakh km.) |
| 2000-2001 | 14 | 10 |
| 2001-2002 | 15 | 11 |
| 2002-2003 | 17 | 13 |
| 2003-2004 | 20 | 19 |
