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 then f(1)=1 f(2)=4 f(3)=9 f(-5)=25

if f(x)=2x 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.

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a3

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1

u+1

v

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x3

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x 2

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2x +1

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.

are all equations.

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3x +2 = x +10

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x 2 = 9

€

a2 +1 = 82

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a2 = 52 − 32

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A =π (52 )

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(x +1)2 =100

An equation can be solved, that is a missing value can be found.€

y = 3(5) + 7

The meaning of the words Expression, Equation, Identity and Formula

An identity is an equation which is true always.

are all identities.

€

83 = 2

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(x +1)2 = x 2 +2x +1

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2x =4x

2

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(2x −1)2 ≡ 4x 2 − 4x +1€

20

5≡ 4

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3x + 4 −10 + 7x =10x −6

An identity may have an equals sign, or an identity sign.

The identity sign draws to attention the fact that it is an identity.

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 circumference.

are all formulae.

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h2 = a2 +b2

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A = πr2

€

C = 2πr

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1

f=1

u+1

v

€

A =1

2bh

€

V = lwh

€

V =4

3πr3

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V = Ah

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