General algebraic forms for specific number properties

Maths

In this future unit, pupils continue to explore composite functions, thereby building on their work from this unit. Pupils need to understand function notation from this unit as this is used in iteration.

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

Functions and proof

Which of these expressions could be even if $$n$$ is an integer?

Which of these expressions must be even for any integer $$n$$?

Which of these expressions are always odd for any integer value of $$n$$?

It is always 3 less than a multiple of 6. 

Which of these statements are true for the expression $$6n + 3$$ when $$n$$ is an integer?

Which of these must represent 3 consecutive odd numbers when $$n$$ is an integer?

$$2n$$ and $$2n$$ where $$n$$ is an integer.

$$2n$$ and $$2n + 2$$ where $$n$$ is an integer.

$$2n$$ and $$2m$$ where $$n$$ and $$m$$ are integers and $$n \ne m$$.

$$2n$$ and $$12n$$ where $$n$$ is an integer and $$n \ne 0$$.

$$2n + 1$$ and $$2m + 3$$ where $$n$$ and $$m$$ are integers.

Which of these represent any 2 different even numbers?

A multiple is the product of a number and...

Which of these is an example of consecutive integers?

Which of these shows consecutive even integers?

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