Topics
A Square and A Cube
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
Fractions in Disguise
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
Power Play
The Baudhayana-Pythagoras Theorem
Part 2
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
A Story of Numbers
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
Data Handling
Quadrilaterals
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
We Distribute, Yet Things Multiply
Cubes and Cube Roots
Algebra Play
Area
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
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
Exponents and Powers
Visualizing Solid Shapes
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
Notes
Increase or Decrease as a percent:
The increase or decrease in a certain quantity can also be expressed as a percentage.
There are times when we need to know the increase or decrease in a certain quantity as a percentage.
For example, if the population of a state increased from 5,50,000 to 6,05,000. Then the increase in population can be understood better if we say, the population increased by 10 %.
Example
A school team won 6 games this year against 4 games won last year. What is the percent increase
The increase in the number of wins (or amount of change) = 6 – 4 = 2.
Percentage increase = `"Amount of change"/"Original amount or base" xx 100`
= `"Increase in the number of wins"/"Original amount of wins" xx 100`
= `2/4 xx 100 = 50`.
Example
The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease?
Original amount = the number of illiterate persons initially = 150 lakhs.
Amount of change = decrease in the number of illiterate persons = 150 – 100 = 50 lakhs.
Therefore, the percentage of decrease = `"Amount of change"/"Original amount" xx 100`
= `(550)/(150) × 100`
= `33 1/3`.
Example
20% increase means, Rs. 100 increased to Rs. 120.
So, Rs. 34,000 will increase to?
Increased price = Rs. `120/100 xx 34000` = 40,800.
Shaalaa.com | Increase Or Decrease in Quantity as Per Cent
Series: Increase Or Decrease as percent
Related QuestionsVIEW ALL [27]
The food labels given below give information about 2 types of soup: cream of tomato and sweet corn. Use these labels to answer the given questions. (All the servings are based on a 2000 calorie diet.)
| Sweet Corn | Cream of Tomato | ||
| Nutrition Facts | Nutrition Facts | ||
| Serving Size 1 cup (240ml) | Serving Size 1 cup (240ml) | ||
| About 2 serving per Container | About 2 serving per Container | ||
| Amount Per Serving | Amount Per Serving | ||
| Calories 90 | Calories from Fat 9 | Calories 100 | Calories from Fat 20 |
| % Daily Value* | % Daily Value* | ||
| Total Fat 2g | 2% | Total Fat 2g | 3% |
| Saturated Fat-0g | 0% | Saturated Fat-1.5g | 6% |
| Cholesterol 0mg | 0% | Cholesterol 10mg | 3% |
| Sodium 540mg | 22% | Sodium 690mg | 29% |
| Total Carbohydrate 17g | 6% | Total Carbohydrate 17g | 6% |
| Dietary Fibre 3 gram | 14% | Dietary Fibre 4 gram | 18% |
| Sugar 5g | Sugar 11g | ||
| Protein 3g | Protein 2g | ||
| Vitamin A 30% | Vitamin C 10% | Vitamin A 20% | Vitamin C 20% |
| Calcium 2% | Iron 6% | Calcium 0% | Iron 8% |
| *Per cent Daily Values are based on a 2,000 calorie diet. |
*Per cent Daily Values are based on a 2,000 calorie diet. |
||
Find the increase per cent of sugar consumed if cream of tomato soup is chosen over sweet corn soup.
If the price of petrol, diesel and LPG is slashed as follows:
| Fuel | Old prices/ litre (in Rs) |
New price/ litre (in Rs) |
% Decrease |
| Petrol / L | 45.62 | 40.62 | ______ |
| Diesel / L | 32.86 | 30.86 | ______ |
| LPG/14.2kg | 304.70 | 279.70 | ______ |
Complete the above table.
What is the percentage increase or decrease in the number of seats won by A, B, C and D in the general elections of 2009 as compared to the results of 2004?
| Political party | Number of seats won in 2004 |
Number of seats won in 2009 |
| A | 206 | 145 |
| B | 116 | 138 |
| C | 4 | 24 |
| D | 11 | 12 |
