Formulae and their applications
Statement
- Those sentences that are either true or false but not both is known as a statement.
e.g.
$9-2$ $=7$ true
$4-5$ $=1$ false
$4+5$ $=10$ false
$3+6$ $=9$ true
$x+y$ $=5$ this is not a statement because we can not decide whether a sentence is true or not.
$i)$ Karachi is in Sindh. (true) statement
$ii)$ Mango is not a fruit. (False) statement
$iii)$ Thank you (neither true nor false)
Closed Statement
- Those statements can be judged true or false.
$i.$ All animals have wings (false)
$ii.$ Two plus two makes four (true)
$iii.$ $2+5$ $=8$ (false)
Open Statement
- An open statement containing a variable (unknown) is known as an open statement.
$x+2$ $=5$
If $x=3$
$3+2$ $=5$ (true)
If $x=2$
$2$ $+2$ $=5$ (false)
Equation
- A statement with the equal sign $(=)$ indicating the equality of two mathematical expressions is called an equation.
- A statement that demonstrates the equality of two quantities.
- An equation has two sides that are equal or balanced.
- There must be an equal sign.
An equation can be either numerical or algebraic
Numerical equation
- All the elements of an arithmetical equation are numbers and operations.
$2+3$ $=5$
$4÷2×4$ $=8$
Algebraic Equation
- An algebraic equation contains one or more variables and at least one mathematical operation.
- An equation that shows the relation of equality between two algebraic expressions is known as an algebraic equation.
- It may also contain numbers.
$3x+y$ $=5$, $8x+3y$ $=5x$
Formula
- A formula is an equation or rule that shows a mathematical relationship between two or more quantities.
Area of square $=s^2$
$(a+b)^2$ $=a^2$ $+2ab$ $+b^2$
Area of rectangle $=l×w$
Identity
- An algebraic equation that is true for all values of the variable occurring in the relation is called an identity.
$(x+a)$ $(x+b)$ $=x^2$ $+(a+b)x$ $+ab$
$(x-a)$ $(x+a)$ $=x^2$ $-a^2$
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