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 Reciprocals or Multiplicative Inverses
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers
- Multiples and Common Multiples
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
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
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
- 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
- Introduction
- Important Terms
- Formula: Simple Interest
- Calculation of Interest
- Examples
Introduction
Interest: Banks pay interest to account holders for keeping money in the bank. Banks charge interest from people who borrow money (take a loan). The extra amount paid or received is called interest.
Principal: The term "Principal" refers to the initial deposit or borrowed amount.
Rate of Interest : The rate of interest is the percentage of the principal (original amount) that is paid or charged as interest for using the money.
The rate of interest is written as:
p.c.p.a. → per cent per annum
Time (T): It is the time for which the sum (principal) is borrowed or lent.
Amount (A): It is the sum of the Principal and the Interest on it.
Amount = Principal + Interest,
i.e., A = P + I
Simple Interest
Simple Interest: It is the extra money, which the lender gets from a borrower, in consideration of the sum (money borrowed) used by the borrower.
Important components of the interest formula:
The simple interest (S.I.) and the interest (I) mean the same, Principal (P), Rate of Interest (R), and Time Period (T)
Formula:
S.I = `"Principal × Rate × Time" / "100"`
I = `"P × R × T" / "100"`
Example
Anita takes a loan of Rs. 5,000 at 15% per year as the rate of interest. Find the interest she has to pay at the end of one year.
The sum borrowed = Rs. 5,000, Rate of interest = 15% per year.
This means if Rs. 100 is borrowed, she has to pay Rs. 15 as interest for one year.
If she has borrowed Rs. 5,000, then the interest she has to pay for one year.
= Rs. `15/100 × 5000 = Rs. 750.`
So, at the end of the year she has to give an amount of Rs. 5,000 + Rs. 750 = Rs. 5,750.
Example
If Manohar pays an interest of Rs. 750 for 2 years on a sum of Rs. 4,500, find the rate of interest.
I = `(P × T × R)/(100)`
750 = `(4500 × 2 × R)/(100)`
`(750)/(45 × 2) = R`
Therefore, Rate = `8 1/3 %`
Example
Vinita deposited Rs. 15000 in a bank for one year at an interest rate of 7 p.c. p.a. How much interest will she get at the end of the year?
Let us suppose that the interest on the principal of Rs. 15000 is x.
On principal Rs. 100, the interest is Rs. 7.
`x/(15000) = 7/100`
`x/(15000) xx 15000 = 7/100 xx 15000`.......(Multiplying both sides by 15000)
x = 1050
Vinita will get an interest of Rs. 1050.
Example
Vilasrao borrowed Rs. 20000 from a bank at a rate of 8 p.c.p.a. What is the amount he will return to the bank at the end of the year?
Let interest on principal 20000 rupees be x rupees.
Interest on principal 100 rupees is 8 rupees.
`x/(20000) = 8/100`
`x/(20000) xx 20000 = 8/100 xx 20000`.....(Multiplying both sides by 20000)
x = 16000
Amount to be returned to the bank = principal + interest
= 20000 + 1600
= Rs. 21600
Example
Sandeepbhau borrowed 120000 rupees from a bank for 4 years at the rate of `8 1/2` p.c.p.a. for his son’s education. What is the total amount he returned to the bank at the end of that period?
Principal = 120000, P = 120000, R = 8.5, T = 4
∴ Total interest = `(P xx R xx T)/100`
= `(120000 xx 8.5 xx 4)/100`
= `(120000 xx 85 xx 4)/(100 xx 10)`
= 120 × 85 × 4
= 40800
The total amount returned to the bank = 120000 + 40800 = 160800 rupees.
