All Leaving Cert Mathematics posts
• #### Proofs davidconroy

What Proofs are there where I must have the information learned off perfectly? including Given: To Prove : Construction: Proof: etc Thanks.

1. #### maryh97

All the JC proofs plus Theorems 11,12,13. Also proof by induction, and know what proof by contradiction is. There may be a few more, look up the syllabus it'll tell you everything there.

2. #### nicolaa

Do we have to be able to prove the amortisation formula?

3. #### themathstutor.ie

There has been some confusion, even among teachers including ourselves, about which proofs are examinable. But we have double-checked with the NCCA, and for LCH you just need 11, 12 and 13. You do not need to know the proofs of the JCH theorems.

Hope that helps,

Eamonn - TheMathsTutor.ie

4. #### maryk

At ordinary level what theorems do we have to know, is it the junior cert higher level ones. Also so we have to prove them ??

5. #### josephine-gilmartin

what about the trigometric proofs and de moirve's theorem, do you need to be able to prove these?

6. #### themathstutor.ie

The original question implied that the OP was asking about synthetic geometry proofs.

If you look at the syllabus

http://www.ncca.ie/en/Curriculum_and_Assessment/Post-Primary_Education/Project_Maths/Syllabuses_and_Assessment/LC_Maths_English_2013.pdf

you will see that the following proofs are in the Number strand at LCH level:

Prove that SQRT(2) is not rational.

Also, prove by induction

- simple identities such as the sum of the first n natural numbers and the sum of a finite geometric series

- simple inequalities such as

n! > 2^n,

2^n ≥ n^2 (n ≥ 4)

(1+ x)^n ≥ 1+nx (x > –1)

- factorisation results such as 3 is a

factor of 4n –1

- prove De Moivre’s Theorem by induction

There are also trig derivations that you need to know, as mentioned in the syllabus:

- derive the trigonometric formulae 1, 2, 3, 4, 5, 6, 7, 9

Happy to help,

Eamonn - TheMathsTutor.ie

7. #### evafinn

http://resources.teachnet.ie/hpunzet/2010/lch_theorems.html

8. #### themathstutor.ie

With absolute respect to the author of that resource, we have checked directly with the NCCA and they have confirmed explicitly that you do NOT need to know the 5 JCH proofs.

[By the way, this is a point of confusion even among teachers: https://groups.google.com/forum/#!topic/project-math/i6oFcsbjODM ]

So, it's good news - as stated above, for synthetic geometry, you need to know the proofs of theorems 11, 12 and 13 only for LCH.

If anyone wants to check with the NCCA, or in the official syllabus, you will come to the same conclusion.

Happy to help.

Eamonn - TheMathsTutor.ie

9. #### evafinn

I'm sorry! Sorry for any confusion! And thank you for correcting my mistake

10. #### themathstutor.ie

No problem Eva :-)

11. #### amc3

Will there still be a choice between 6 a and 6 b this year in paper 2

No choice.