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mathematicsprinted 33 · PDF 34
165 pagesrevision 46935
printed 33 · PDF 34
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33
…a number multiplied by a letter, e.g. 5x
The number in front of a letter is called a coefficient
The coefficient of x in the term 6x is 6
The coefficient of y in the term -5y is -5
Terms that are just numbers (with no letters) are called constants
Terms can include powers and more than one letter
E.g. 6xy, 4x2, ab3c, …
What is a factor?
A factor is any number or letter that divides a term exactly (with no remainder)
E.g. all the factors of 4xy are 1, 2, 4, x, 2x, 4x, y, 2y, 4y, xy, 2xy and 4xy
A term can be separated into factors that multiply together to give that term
E.g. two factors of 5x are 5 and x
To factorise means to write something as a multiplication of factors
A common factor is one that divides both terms
The highest (or greatest) common factor is 2x
E.g. the common factors of 6xy and 4x are 2, x and 2x
What is an expression?
An expression is an algebraic statement that does not have an equals sign
There is nothing to solve
An expression is made by adding, subtracting, multiplying or dividing terms
E.g. 2x + 5y, b2 – 2cd, , …
A single term can be an expression
Expressions can be simplified (made easier)
E.g. x + x + x simplifies to 3x
What is an equation?
An equation is an algebraic statement with an equals sign between a left-hand side
and a right-hand side
Both sides are equal in value
E.g. if 2x has the same value as 10, then 2x = 10
An equation can be solved by finding the missing values of the letters that make the
left-hand side equal to the right-hand side
x = 5 is called the solution
E.g. the equation 2x = 10 is solved by x = 5
What is a formula?
A formula is a worded rule, definition or relationship between different quantities,
written in shorthand using letters
The formula is w = mg
E.g. weight, w, is mass, m, multiplied by gravitational acceleration, g
It is common to substitute numbers into a formula, but a formula on its own cannot
be solved
To turn a formula into an equation, more information is needed