Symbols, notation and terminology
6.1 Symbols and notation
.distinguish the different roles played by letter symbols in algebra, using the
correct notational conventions for multiplying or dividing by a given number
.know that letter symbols represent definite unknown numbers in equations,
defined quantities or variables in formulae and general, unspecified and
independent numbers in identities
.know that in functions, letter symbols define new expressions or quantities by
referring to known quantities
.understand f(x) notation
6.2 Algebraic terminology
.distinguish in meaning between the words Equation, Formula, Identity and
Expression
f(x) notation may be used
So if f(x)=x2
if f(x)=2x
then f(1)=1 f(2)=4 f(3)=9 f(-5)=25
then f(1)=2 f(2)=4 f(3)=6 f(-5)=-10
if f(x)=2x+1 then f(1)=3 f(2)=5 f(3)=7 f(-5)=-9
f(x) notation may be used
if f(x)=x2
then f(1)=1 f(2)=4 f(3)=9 f(-5)=25
The f(x) notation saves time when putting values into equations.
With y=x2, to write the above, we would have to say
When y=x2 then when x is 1, y=1; when x is 2, y=4; when x is 3,
y=9; when x is -5, y=25.
f(x)=x2
We use f(x) just like we use y.
The meaning of the words Expression, Equation, Identity and Formula
An expression is used to designate a value. The determination of this
value depends on the meaning of the symbols of the expression.
A variable is a value that may change within the scope of a given
problem or set of operations. In contrast, a constant is a value that
remains unchanged, though often unknown or undetermined. In the
expression x+3, x is a variable, but 3 is a constant.
x
2
2x 1
a
3
1 1

u v
3
x
are all expressions.



The meaning of the words Expression, Equation, Identity and Formula
An equation is a mathematical statement that two expressions are
equal having the two expressions on each side of an equal sign.
3x 2  x 10
y  3x  7
x 9
2
h  a b
2
2
2
3
8 2
A  r

(x 1) 
 x  2x 1
2

2
are all equations.

2

The meaning of the words Expression, Equation, Identity and Formula
An identity is an equation which is true always.
3
20
4
5
3x  4 10 7x 10x 6

(2x 1)  4 x  4 x 1
2

2
4x
2x 
2
(x 1)  x  2x 1
2
2
are all identities.

8 2
An identity may have an equals sign, or an identity sign.
The identity sign draws to attention the fact that it is an identity.
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The meaning of the words Expression, Equation, Identity and Formula
A formula is an equation expressing some fundamental principle.
Symbols in a formula have a set meaning, eg r for radius, A for area,
and C for circumferance.
1
A  bh
2
C  2r

h  a b
2
V  lwh


1 1 1
 
f u v
4
V  r 3
3
2
A  r
2
are all formulae.


2
V  Ah