Which expression gives the greatest value

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My name is Jordan and I am from London, England.

I had a maths test the other day, and I could have a full score on the test if only I had understood this question:

'Look at these expressions'

n-2, 2n, n², n/2, and 2/n

A) Which expression gives the greatest value when n is between 1 and 2?
B) Which expression gives the greatest value when n is between 0 and 1?
C) Which expression gives the greatest value when n is negative?

As you can see, this IS ONE question split in to three parts lol!

Can you tell me how I go about tackling this question? I lost marks on the test because of not
understanding the question.

Thanks
Regards
Jordan, London

Hi Jordan.

Let's look at (A) and you can use similar logic for parts (B) and (C).

If n is between 1 and 2 then:

n-2 is between 1-2 and 2-2 which is between -1 and 0.

2n is between 2(1) and 2(2) which is between 2 and 4.

n² is between 1² and 2² which is between 1 and 4.

n/2 is between 1/2 and 2/2 which is between ½ and 1.

2/n is between 2/1 and 2/2 which is between 2 and 1.

So which of these has the greatest possible value? Both 2n and n² go up to 4, so these two expressions tie for the greatest value.

You can solve the other problems using the same approach, Jordan.

Cheers,
Stephen La Rocque.

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