1) If the question says "using algebra", then... use algebra. cant just use
ur calc to solve polynomials,
solve using algabraic division or the quadratic formula

2) show the process of rationalising denominators. calculators may automatically
rationalise stuff, but u must still write it down to get the method mark

3) When finding an inverse function, ALWAYS write its domain. The question
may not always ask you to state the domain, but the mark scheme will still
want you to state it.

4) When calculating partial fractions, it's not enough to just find the variables.
you must write a final statement, expressing the fraction as an actual partial
fraction

5) When expressing a final answer, write it EXACTLY as it is written in the question.
eg if the question is "Show that ..... = U² sinθ cosθ", you may NOT get a mark
for writing it as "U² cosθ sinθ". You must write it exactly as printed.

6) Don't forget to write units. If it says "giving your answer to the nearest cm",
write the units. (modelling questions)

7) Give your answer to the correct number of decimal places.
if it says "giving your answer to 3 decimal places"... then give your answer
to 3 decimal places.

8) (modelling) Ensure you've expressed answers with the correct variable names.
If the question is "express H in terms of t", don't write the final answer in terms
of y or x.

9) (modelling) When it says "State one further refinement to the model", you CAN give
more than one example, BUT all of your examples must be correct otherwise
you lose the mark. Only write one answer, which you think is the best.

10) (mechanics) in SUVAT questions, (eg find the acceleration), your
final answer must be expressed to two/three sig figs. do not express the final
answer in terms of g or as a fraction (UNLESS the question asks for an exact value)


Misconceptions:

1) When showing a function has a root in an interval, where there is a change in sign,
you MUST state that f(x) is continuous along with stating the change in sign

2) when proving points of inflection, along with showing that the first
derivative is 0, you must show that the second derivative has a sign change (
ie f(x) changes from concave to convex or vice versa)

3) when solving equations, cancelling out terms, means that the term you
cancelled out can also equal 0.
eg, solve sinθcosθ = 3cos²θ
if you divide by cosθ, then cosθ = 0 is also possible.

4) if you have ∫sin²x dx, IT IS NOT EQUAL TO ⅓sin³x.
You must use the cos2x identity where cos2x = 1-2sin²x, rearranging for sin²x

5) Small angle approximation: cos3θ is equal to 1-(3θ)²/2, NOT 3(θ²)/2

6) 1-(1-5) is equal to 5, NOT -5.
1-(1-5)
= 1 -1(1-5)
= 1-1+5
= 5


7) x² + 16 = y². YOU CAN NOT SQUARE ROOT THE EQUATION TO GET x+16=y. IT IS NOT
THE SAME. you need to take the square root of the entire side.
so root(x²+16) = y.

In essence, "3² + 4² = 5²" rooted IS NOT "3 + 4 = 5"

likewise, if you have "y + eˣ = 4", if you want to ln both sides,
it IS NOT "lny + x = ln4".
You need to ln the entire side together, so it would actually be
ln(y + eˣ) = ln4

8) ln5/ln4 IS NOT ln5-ln4.
ln(5/4) IS ln5-ln4.

9) in binomial, when factorising out, make sure you apply the power.
eg, (4+x)^¹/² = 4^¹/² (4+x)^¹/². Don't forget to apply the power to the 4 that was
factorised out.

10) Don't confuse inverse functions with the first derivative of a function
inverse: f⁻¹(x)
differentiate: f'(x) [dash instead of -1]

11) Hypothesis testing - DO NOT WRITE "H₁=...."
It must be "H₁: ...." (USE A COLON INSTEAD OF THE EQUAL SIGN)


12) Hypothesis testing for correleation - use the greek letter ρ instead of r.
Ie "H₁: ρ>..."

I haven’t watched the video yet but - When doing integration, REMEMBER THE +C!!

I cant express how useful thiss video was. As someone who needs an A* in maths next year for uni and is capable of doing the harder questions in a maths paper, i often lose marks on these sort of questions which can be so frustrating since I know how easy they are to fix/I didnt put all my working down that I did in my head (reason why I can score higher marks in further maths despite finding the maths paper much easier). Thank you so much for this!

As someone who sat theirs last year, one tip is if you have extra time, always check your definite integral questions with your calculator, no matter how complex the polynomial/equation is

A level maths test in an hour, thanks for this 🙏

some of these are crazy harsh, that projectiles one is mad

It's so simple yet so deep.

I've said it before and I'll say it again you are genuinely one of the best teachers I've ever come across. You helped me at A-Level Further Maths 3 years ago and I still, 3 years into a Maths degree at a top UK uni, frequently come back to your google drive to remind myself of core principles, conceptualise new topics from old topics, or just refresh my knowledge in general. THANK YOU MR BICEN

7:06 madness 😭

omg this is so helpful! There’s LOTS of mistakes I would have made if i didn’t watch this video. Thank you so much and hopefully i’ll get an A in maths to meet my offer😭

You helped me a lot last year to clutch Maths. Im now in Uni stressing about year 1 finals. I came back for old times sake and I feel calmer now.

Could you do thus for FM?

watching this before the exam today, thank you so much Mr Bicen best maths youtuber 💪

13:07 I believe it should be 4x^3 for dy/dx

Morning of paper 1 and this video is very helpful!!

bruh i did a level maths paper 2 for 2020 and 2019 and it just lowers my confidence so much. every other paper seems to be fine

For mechanics I reccomend to give your answer as the fraction and the decimal approximation to make it as clear as possible to the examiner what ur answer is so a=6/7 =0.857 m/s²

I have paper 1 this afternoon and this vid is so useful :)

3:42 I definitely would've made that mistake 💀 Thank you Mr Bicen

Great video, how about forgetting to “+c” on an indefinite integral?