For all A-level maths students - common mistakes.

-

\sin(a+b) = \sin a + \sin b

. I still sometimes see people do it, and if you just try a few values of a and b, you'll see it's totally wrong.

- Not putting an arbitrary constant after you've integrated. I think they give you a mark (for C2 at least) just for doing this.

Reply 2

Notnek

OP

21

Glutamic Acid

- Not putting an arbitrary constant after you've integrated. I think they give you a mark (for C2 at least) just for doing this.

Thanks for reminding me - I've just edited in the constants :biggrin:

.

Reply 3

ukstudent2011

When some people see ln x they turn it into 1/x whether it is differentiation or integration.

Reply 4

Mush

(a+b)^2 = a^2 + b^2

Ermmm. A LOT of people always fail to write out things like "for x not equal to 2" before they start finding the limit of an equation like

\frac{x+1}{x-2}

.

Erm. Can't think of much else.

Reply 5

Not quite what you're looking for, but I see the equals sign used as just a general haphazard "ok I'm solving the question! Lalalalalalala!" sign nowadays. Example:

Find the normal to the curve y = x^2 at x = 5.

Correct solution:
"y = x^2
dy/dx = 2x

At x = 5, dy/dx = 10, so gradient of normal = -1/10

Normal: y - 25 = -1/10 (x - 5)"

Wrong solution:
"y = x^2
= 2x

At x = 5, gradient = 10
= -1/10

Therefore y - 25 = -1/10 (x - 25)"

It's a silly example, but I see people doing this all over the place. And they then obviously get confused and substitute the wrong numbers into the wrong equations and so on. Knowing what to do to get an answer is one thing; knowing what to do in order to produce some correct maths is something entirely different, and the former will catch you out under exam pressure.

Reply 6

qgujxj39

Good thread, I'll add a few snippets:

- Get a graphic calculator, and learn how to use it. For some reason they've not been banned, so use one in the exam to check definite integrals, derivatives, curve sketching, manipulation of complex numbers, etc.
- If you ever have time to practice one thing, make it integration. Learn all the standard integrals and make sure you can integrate absolutely anything C4 can throw at you.
- Don't become complacent after a difficult question. It's all too easy to get carried away after tackling 10 marks worth of second-order-differential-equation-by-substitution, only to lose 5 or 6 marks by getting your constants wrong because you've failed to solve some simple simultaneous equations correctly.
- The best way to practice is to use the review exercises in textbooks (preferably Heinemann). Do question after question, making sure you know exactly how to do each one you get wrong.
- Edexcel have made past papers and mark schemes freely available: http://eiewebvip.edexcel.org.uk/pastpapers/Default.aspx . Use these to your advantage.
- For M1, make sure you get your cos's and your sins correct. Also remember that cos(x) = sin(90 - x), and vice versa.
- For S1, learn the formula for calculating percentiles of a grouped frequency table.
- Linear interpolation is a bitch.
- Finally, and most importantly of all, make sure your calculator is in the correct degree/radian mode.

Why I'm doing this at 2 in the morning I have no idea. I may add more tomorrow.

Reply 7

tommmmmmmmmm

- Get a graphic calculator, and learn how to use it. For some reason they've not been banned, so use one in the exam to check definite integrals, derivatives, curve sketching, manipulation of complex numbers, etc.

Nooooope. Calculators can't do "integration, differentiation or symbolic algebra".

Reply 8

qgujxj39

generalebriety

Nooooope. Calculators can't do "integration, differentiation or symbolic algebra".

They can do numerical calculus, right?

Reply 9

Glutamic Acid

Also, use BIDMAS (or whatever it is) correctly. I've seen so many people studying maths at A Level and higher making BIDMAS errors all over the place. It'll come back to rape you when you enter it on a calculator.

Reply 10

tommmmmmmmmm

They can do numerical calculus, right?

I really don't think so. Some people on here seem to think so, but I see no reason to believe them. The Edexcel rubric says quite clearly no integration or differentiation.

Maybe the spec says something different. I don't know.

Reply 11

squeezebox

15

Glutamic Acid

- Not putting an arbitrary constant after you've integrated. I think they give you a mark (for C2 at least) just for doing this.

The constant is vital for differential equations ;yes;

EDIT:

- Forgetting to change the limits when integrating a definite integral by substitution.

-Partial Fractions
With fractions of the form:

\frac{x+2}{(x+1)^{2}}

, I've seen many people do this:

\frac{x+2}{(x+1)^{2}} = \frac{A}{(x+1)} + \frac{B}{(x+1)}

. Which is incorrect, since as you can see, when combining the fractions again, we do not get a

(x+1)^{2}

term in the denominator.

The correct form is:

\frac{x+2}{(x+1)^{2}} = \frac{A}{(x+1)} + \frac{B}{(x+1)^{2}}[br]

-Maclaurin's Series
Remember you can't just shove any value into the series, since many expansions have restrictions on the values of x for which they are valid.

e.g

ln(x+1) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - .......

is valid for :

-1< x. \leq 1

The values of x for the common series expansions are given in the formula book.

- First Order Differential Equations - Integrating Factors

To apply this method, the differential equation must be in the form:

\frac{dy}{dx} + P(x)y = q(x)

, where P(x) and q(x) are constants or functoins of x. ie the

\frac{dy}{dx}

term must be "by itself".
If it isn't, rearrange it so that it is :smile:

.
Also, once you have found the integrating factor, remember to multiply the diff. equation in the correct form by it.

Reply 12

qgujxj39

generalebriety

I really don't think so. Some people on here seem to think so, but I see no reason to believe them. The Edexcel rubric says quite clearly no integration or differentiation.

Maybe the spec says something different. I don't know.

Not even Google can tell me.

Reply 13

EvenStevens

generalebriety

I really don't think so. Some people on here seem to think so, but I see no reason to believe them. The Edexcel rubric says quite clearly no integration or differentiation.

Maybe the spec says something different. I don't know.

The Edexcel Rubric says quite clearly no symbolic algebra, integration or differentiation.

Numeric is allowed.

Reply 14

Vjyrik

10

Many (including me) do: x^2 = 4 -> x = 2, while it should actually be 2 and -2.
It always tricks you out when there's a simple C1 question that asks you to rearrange an equation to make a variable that has a power the subject itself.

Reply 15

EvenStevens

The Edexcel Rubric says quite clearly no symbolic algebra, integration or differentiation.

Numeric is allowed.

I was always under the impression that that meant "symbolic algebra", "differentiation" or "integration".

Reply 16

Vjyrik

Many (including me) do: Sqrt(4) = 2, while it should actually be Sqrt(4) = -2, Sqrt(4) = 2
It always tricks you out when there's a simple C1 question that asks you to rearrange an equation to make a variable that has a power the subject itself.

Considering we're posting this in a thread called "common mistakes", I feel the need to pick you up on this. The square root of 4 is 2 - there's no wriggle room on that. That's just how 'square root' is defined. It's always the positive answer (except, of course, when we're working in the complex numbers and there's no such thing as 'positive' and 'negative'). The equation x^2 = 4, on the other hand, has two roots: -2 and +2. Getting from that equation to those answers is not the same thing as square rooting.

Reply 17

EvenStevens

I was under the impression it meant symbolic (algebra, differentiation or integration).

Hmm...

Well, when I e-mailed Casio asking about my calculator (Fx-991ES) they said that all their scientifics were certified for UK based examinations; and that particular calculator can do numeric integration and differentiation.

Edexcel are bastards and don't seem to e-mail me back.

Also, after reading the official...calculator ...spec list, whatever it is, it states this:

Note symbolic algebra, symbolic integration, symbolic differentiation.

Reply 18

EvenStevens

I was under the impression it meant symbolic (algebra, differentiation or integration).

Hmm...

Well, when I e-mailed Casio asking about my calculator (Fx-991ES) they said that all their scientifics were certified for UK based examinations; and that particular calculator can do numeric integration and differentiation.

Edexcel are bastards and don't seem to e-mail me back.

Also, after reading the official...calculator ...spec list, whatever it is, it states this:

Note symbolic algebra, symbolic integration, symbolic differentiation.

Ah, fair enough.

Reply 19

EvenStevens