Topics
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 Reciprocal or Multiplicative Inverse
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers
Linear Equations in One Variable
- Variable of Equation
- Concept of Equation
- Expressions with Variables
- 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
- Classification of Polygons
- Properties of a Quadrilateral
- Interior Angles of a Polygon
- Exterior Angles of a Polygon and Its Property
- Concept of 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.
Practical Geometry
- Introduction to 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
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 Circle-graph)
- 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
- Basic Concept of Percentage
- Increase Or Decrease as Percent
- Concept of Discount
- Estimation in Percentages
- Basic Concepts of Profit and Loss
- Sales Tax, Value Added Tax, and Good and Services Tax
- 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
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) = a2-b2
- Expansion of (x + a)(x + b)
Mensuration
Visualizing Solid Shapes
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 Circle-graph)
- Graphical Representation of Data as Histograms
- Concept of a Line Graph
- Linear Graphs
- Some Application of Linear Graphs
Playing with Numbers
Notes
Drawing a bar graph:
1) Information about the plants in a nursery is given here. Show it in a bar graph.
| Names of Plants | Rose | Mogra |
Hibiscus |
Chrysanthemum |
| Number of Plants | 70 | 50 | 45 | 80 |
Solution:
Take a graph paper.
-
Draw the X and Y axes, and mark O, their point of intersection. In the centre, write the title ‘Types and number of plants’.
-
Write the names of the plants on the X-axis at equal distances.
-
The number of plants is divisible by 5. So, take the scale 0.5 cm = 5 plants, that is, 1cm = 10 plants on the Y-axis as it can be easily shown on the graph paper. Write the scale in the top right-hand corner.
-
Draw a bar of the appropriate height above the name of each plant on the X-axis.
2) The following table shows the monthly expenditure of Imran’s family on various items.
Items |
Expenditure (in Rs.) |
| House rent | 1200 |
| Food | 1400 |
| Education | 800 |
| Electricity | 400 |
| Transport | 600 |
| Miscellaneous | 1000 |
To represent this data in the form of a bar diagram, here are the steps.
(a) Draw two perpendicular lines, one vertical and one horizontal.
(b) Along the horizontal line, mark the ‘items’ and along the vertical line, mark the corresponding expenditure.
(c) Take bars of the same width keeping the uniform gap between them.
(d) Choose a suitable scale along the vertical line. Let 1 unit length = 200 and then mark the corresponding values.
Calculate the heights of the bars for various items as shown below.
House rent: 1200 ÷ 200 = 6 units
Food: 1400 ÷ 200 = 7 units
Education: 800 ÷ 200 = 4 units
Electricity: 400 ÷ 200 = 2 units
Transport: 600 ÷ 200 = 3 units
Miscellaneous: 1000 ÷ 200 = 5 units.
Shaalaa.com | How To Draw A Bar Graph?
Related QuestionsVIEW ALL [35]
In a botanical garden, the number of different types of plants are found as follows:
| Type of the plants | Number of plants |
| Herb | 50 |
| Shrub | 60 |
| Creeper | 20 |
| Climber | 45 |
| Tree | 95 |
Draw a bar graph to represent the above information and answer the following questions:
(a) Which type of plant is maximum in number in the garden?
(b) Which type of plant is minimum in number in the garden?
The lengths (in the nearest centimetre) of 30 drumsticks are given as follows.
| Lengths | Number of drumsticks |
| 24 | |||| |
| 25 | -- |
| 26 | -- |
| 27 | |||| | |
| 28 | -- |
| 29 | |||| ||| |
| 30 | |||| | |
| 31 | |||| |
Draw the bar graph showing the same information.
The number of people in various age groups in a town is given in the following table.
| Age group | 1-14 | 15-29 | 30-44 | 45-59 | 60-74 | 75 and above |
| Number of persons | 2 lakhs |
1 lakh |
1 lakh |
1 lakh |
80 thousand | 40 thousand |
Draw a bar graph to represent the above information and answer the following questions. (take 1 unit length = 20 thousands)
- Which two age groups have the same population?
- All persons in the age group of 60 and above are called senior citizens. How many senior citizens are there in the town?
The bar graph illustrates the results of a survey conducted on vehicles crossing over a Toll Plaza in one hour.
Observe the bar graph carefully and fill up the following table.
| Vehicles | Buses | _____ | Cars | Vans | _____ | Others | Total vehicles |
| Number of Vehicles |
_____ | 45 | _____ | _____ | 30 | ______ | ______ |
