Algebraic Reasoning (Edexcel GCSE Maths: Foundation)

The ^th odd number is .

The next odd number after is .

Explain why.

Write down an expression, in terms of , for the next odd number.

Here is a right-angled triangle.

Four of these triangles are joined to enclose the square  as shown below.

Show that the area of square  is .

and  are two even numbers.

Give an example to show that the value of  is a multiple of 

Show that when  and  are both even numbers, the value of  will always be a multiple of 6

Here is a rectangular wooden block.

The measurements of the diagram are in centimetres.

Three of these wooden box are put together to construct a shelf.

The perimeter of the shelf is  cm.

Show that 

Consider the statement,

'When  and  are whole numbers,  is always a multiple of ."

Is this statement correct?
You must give a reason for your answer.

The th even number is .

Write down an expression for the next even number.

and  are two consecutive odd numbers.

Give an example to show that the value of  is a multiple of 

is a positive number.

is a negative number.

For each statement, tick the correct box.

	Always true	Sometimes true	Never true
is positive
is positive
is positive
is positive

Which of these is a correct identity?

Circle your answer.