- Concept for Natural Numbers
- Concept for Whole Numbers
- Concept of Negative Numbers
- Concept of Integers
- Representation of Integers on the Number Line
- Concept for Ordering of Integers
- Addition of Integers
- Addition of Integers on Number line
- Subtraction of Integers
- Properties of Addition and Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Product of Three Or More Negative Integers
- Closure Property of Multiplication of Integers
- Commutative Property of Multiplication of Integers
- Associative Property of Multiplication of Integers
- Distributive Property of Multiplication of Integers
- Multiplication of Integers with Zero
- Multiplicative Identity of Integers
- Making Multiplication Easier
- Division of Integers
- Properties of Division of Integers
Fractions and Decimals
- Concept of Fractions
- Types of Fraction
- Concept of Proper Fractions.
- Improper Fraction and Mixed Fraction
- Concept for Equivalent Fractions
- Like and Unlike Fraction
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of a Fraction by a Whole Number
- Fraction as an Operator 'Of'
- Multiplication of a Fraction by a Fraction
- Division of Fractions
- Concept for Reciprocal of a Fraction
- Concept of Decimal Numbers
- Multiplication of Decimal Numbers
- Multiplication of Decimal Numbers by 10, 100 and 1000
- Division by 10, 100 and 1000
- Division of a Decimal Number by a Whole Number
- Division of a Decimal Number by Another Decimal Number
Lines and Angles
- Concept of Points
- Concept of Line
- Concept of Line Segment
- Concept of Intersecting Lines
- Concept of Angle - Arms, Vertex, Interior and Exterior Region
- Complementary Angles
- Supplementary Angles
- Adjacent Angles
- Concept of Linear Pair
- Concept of Vertically Opposite Angles
- Concept of Intersecting Lines
- Concept of Parallel Lines
- Pairs of Lines - Transversal
- Pairs of Lines - Angles Made by a Transversal
- Pairs of Lines - Transversal of Parallel Lines
- Checking Parallel Lines
The Triangle and Its Properties
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Classification of Triangles (On the Basis of Sides, and of Angles)
- Equilateral Triangle
- Isosceles Triangles
- Scalene Triangle
- Acute Angled Triangle
- Obtuse Angled Triangle
- Right Angled Triangle
- Median of a Triangle
- Altitudes of a Triangle
- Exterior Angle of a Triangle and Its Property
- Angle Sum Property of a Triangle
- Some Special Types of Triangles - Equilateral and Isosceles Triangles
- Sum of the Lengths of Two Sides of a Triangle
- Right-angled Triangles and Pythagoras Property
Congruence of Triangles
- Concept of Ratio
- Concept of Equivalent Ratios
- Concept of Proportion
- Concept of Unitary Method
- Concept of Percent and Percentage
- Converting Fractional Numbers to Percentage
- Converting Decimals to Percentage
- Converting Percentages to Fractions
- Converting Percentages to Decimals
- Estimation in Percentages
- Interpreting Percentages
- Converting Percentages to “How Many”
- Ratios to Percents
- Increase Or Decrease as Percent
- Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
- Profit or Loss as a Percentage
- Concept of Principal, Interest, Amount, and Simple Interest
- Concept of Rational Numbers
- Equivalent Rational Number
- Positive and Negative Rational Numbers
- Rational Numbers on a Number Line
- Rational Numbers in Standard Form
- Comparison of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Construction of a Line Parallel to a Given Line, Through a Point Not on the Line
- Construct a Triangle Given the Lengths of Its Three Sides
- Constructing a Triangle When the Length of Its Sides Are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
- Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion)
- Constructing a Right-angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion)
Perimeter and Area
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangles
- Perimeter of Polygon
- Concept of Area
- Area of Square
- Area of Rectangle
- Triangles as Parts of Rectangles and Square
- Generalising for Other Congruent Parts of Rectangles
- Area of a Triangle
- Area of a Parallelogram
- Circumference of a Circle
- Area of Circle
- Conversion of Units
- Problems based on Perimeter and Area
- Problems based on Perimeter and Area
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Like and Unlike Terms
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials Or Polynomials
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Evaluation of Algebraic Expressions by Substituting a Value for the Variable.
- Use of Variables in Common Rules
Exponents and Powers
- Concept of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Decimal Number System Using Exponents and Powers
- Expressing Large Numbers in the Standard Form
Visualizing Solid Shapes
- Plane Figures and Solid Shapes
- Faces, Edges and Vertices
- Nets for Building 3-d Shapes - Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism
- Drawing Solids on a Flat Surface - Oblique Sketches
- Drawing Solids on a Flat Surface - Isometric Sketches
- Visualising Solid Objects
- Viewing Different Sections of a Solid
Range: The difference between the highest and the lowest values in the data is called the range of the data.
∴ Range = Maximum value - Minimum value
- A range is the collection of values spread between the Maximum value and the Minimum value.
- In mathematical terms, a range is a difference between the Largest (maximum) value and the Shortest (minimum) value in a given dataset.
- Range defines the spread of values in any dataset.
- Steps to find range:
1. Arrange the data in ascending order
2. Find maximum and minimum value of given dataset.
3. Put the maximum and minimum value in the below formula to find the value of the range.
∴ Range = Maximum value - Minimum value.
Find range of following data: 1, 0, 2, 3, 2, 6, 8, 10, 12, 12, 13.
Arrange the following data in ascending order:
0, 1, 2, 2, 3, 6, 8, 10, 12, 12, 13.
Maximum number = 13 and Minimum number = 0
Range = Maximum number - Minimum number
Range = 13 - 0
Range = 13.
The ages in years of 10 teachers of a school are:
32, 41, 28, 54, 35, 26, 23, 33, 38, 40
(i) What is the age of the oldest teacher and that of the youngest teacher?(ii) What is the range of the ages of the teachers?
(i) Arranging the ages in ascending order, we get:
23, 26, 28, 32, 33, 35, 38, 40, 41, 54.
We find that the age of the oldest teacher is 54 years and the age of the youngest teacher is 23 years.
(ii) Range of the ages of the teachers = (54 – 23) years = 31 years
Shaalaa.com | Range
The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:
|Days||Rain fall (in mm|
1) Find the range of the rainfall in the above data.
2) Find the mean rainfall for the week.
3) On how many days was the rainfall less than the mean rainfall.
The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Find the:
1) Highest and the lowest marks obtained by the students.
2) Range of the marks obtained.
3) Mean marks obtained by the group.
The heights of 10 girls were measured in cm and the results are as follows:
135, 150, 139, 128, 151, 132, 146, 149, 143, 141
1) What is the height of the tallest girl?
2) What is the height of the shortest girl?
3) What is the range of the data?
4) What is the mean height of the girls?
5) How many girls have heights more than the mean height.