The Basics (Leaving Cert Mathematics): Flashcards

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Definition: constant

A fixed value that does not change

Definition: variable

A symbol representing an unknown value (e.g., xx, yy)

Definition: coefficient

A number that multiplies a variable (e.g., 44 in 4x4x)

Definition: term

Single component of expression, separated by ++ or −-

Definition: expression

Combination of terms with variables, constants, operations

Definition: equation

Statement showing two expressions are equal (e.g., 2x+6=102x+6=10)

Definition: like terms

Terms with same variable and same degree (power)

How to add/subtract like terms

Sum their coefficients only

Simplest form of expression

When no more like terms can be added

Commutative property (addition)

Order doesn't matter: 6+4=4+66+4 = 4+6

Indices rule: multiplying same base

Add the powers: xaimesxb=xa+bx^a imes x^b = x^{a+b}

Distribution law

a(b+c)=ab+aca(b+c) = ab + ac

Indices rule: dividing same base

Subtract the exponents: xadivxb=xa−bx^a div x^b = x^{a-b}

What exponents represent

Repeated multiplication

BIMDAS order

Brackets, Indices, Mult/Div, Add/Subtract

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