Those Pesky Little Negative Signs...

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A-level Maths By: Please log in to see tutor details
Subject: Maths » A-level Maths
Last updated: 26/02/2017
Tags: a level and gcse maths, exam technique, performance boosting, using formulae

That pesky little negative sign. So small yet so significant. So easily misplaced or forgotten yet with a massive impact on the result of your calculation, the mark you get for the question and hence your grade!

By the time we get to GCSE and A level we’re all pretty confident on how to deal with arithmetic involving negative numbers, after all we’ve been chanting “a minus times a minus is a plus” and so on since year 8 probably so why does it continue to cause so many problems?

A missing or ignored negative sign is probably the most common single reason for lost marks in maths exams, especially at A level. Take the expansion below, it all seems very straightforward if x is positive as shown...but what if it isn’t?

〖 (1+x)〗^n=1+nx/1!+(n(n-1) x^2)/2!+⋯

If what you have is this : (1-x)^n and you neglect to notice and deal with the negative symbol then you’re possibly going to throw away half the marks on that question.
And what about this old favourite?

x=(-b±√(b^2-4ac))/2a

Lots of opportunities there for mislaying the negative or even putting one in when not required.

And then there’s finding the area under a curve using integration, using the quotient rule for differentiation, solving inequalities or even just simplifying algebraic fractions like this one:
(x+3)/2- (2x-5)/3

All of these examples have a potential to go horribly wrong because of an error with a negative sign.

So what can you do to avoid the pitfall?
Well firstly, don’t cut corners and secondly use brackets. If you need to substitute in a negative then write it in using brackets, don’t do it in your head because at some point you will get it wrong and you don’t want that point to be in the middle of your one chance of sitting the exam.

So for our expansion above replace the x with a (-x) as below:
(1-x)^n=1+(n(-x))/1!+(n(n-1)(〖-x)〗^2)/2!+⋯

And for the Quadratic Formula, write it out then state your values of a, b and c before substituting them in:
2x^2- 3x-5=0
a = 2, b = (-3), c = (-5) so.....
x=(-(-3)±√(〖(-3)〗^2-4(2)(-5)))/(2(2))
x=(3±√(9-(-40)))/4
x=(3±√49)/4
x=(3+7)/4= 10/4=2.5
x=(3-7)/4= (-4)/4= -1

And what about that algebraic fraction?
(x+3)/2- (2x-5)/3

How tempting is it to miss out the bracket stage ? But it’s so easy to do this.....
(3x+3-2x-10)/6
...when you should have done this......
(3(x+3)- 2(2x-5))/6

So don’t fall into the trap, keep a close eye on your negative signs and get those marks that you’ve worked so hard for.


Rachel Cave A-level Maths Tutor (Milton Keynes)

About The Author

My students call me reassuring, motivating and helpful. I will use my experience as an examiner and teacher to help you get the best grade you can, working together to iron out issues and fill gaps so that you can go into the exam full of confidence.




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