Leaving Cert Maths Higher
2001
Paper 1:
1.
8
questions Attempt 6 . Each question will in general be divided
into three sections a,b,c .The marks are as follows (a)10 marks(b) 20 marks
(c)20 marks . Part (a) is usually relatively easy and it should be possible to
do this part in no more than three or
four lines (time at most 5 minutes.
Part (b) may be divided into 2 parts it will generally a procedure i.e. a set piece of Maths like a proof Ex (1995)Prove
Sin3x = 3Sinx - 4 Sin3x or (95)Ex 
Show
or EX95Find x if 
You can see from the above examples that they all are
something that you have seen already . So to prepare for this section (a) learn your proofs or at least learn the
proofs on the topics you intend to answer questions on . The section
will be marked as follows 20 marks for a correct answer; if the answer is
incorrect you will loose three marks for each mistake (same mistake is never
penalised twice). It is interesting to note that on the 1995 paper Q2b (I)
received 20 marks while 2b(ii) received 5 marks, (2a) received 15 marks the
reason for this was that 2c was said to be "too difficult "This
happened again in Q5where 5a received 15 marks 5b 20 marks again 5c was a bit unusual
.In 6c they only gave 5 marks for the proof of the product rule .In question 7
the pattern was repeated, the difficult bit 7c(I) received only 5 marks. The
pattern on the second 95 paper was more consistent and most questions were
marked 10,20,20,In '96 and ‘97, 98,99
the marking scheme was more consistent ar 10,20,20,The
general impression is that if part A contains
2 parts then part A will be worth 10
- 15 marks! For students hoping to get a C or pass the paper it is obvious
that they can avoid the really difficult bits and get the result they want.
Those hoping for an A1 will have to do some of the difficult bits but must keep
in mind just how many marks they are worth.
Part c:
This section will definitely
be the most difficult part of each question and may contain something that you
may not have seen before Ex 
the deduce bit of this question seems
To been awarded no marks .It
is worth noting that the part C's on paper 1 seem to more difficult
Than those on paper 2 which
seem to be more mainstream maths. This was especially obvious on the,99
Points to Note for 2001
Paper 1 :
Questions 1 and 2 : The following all look likely (i)Factor Theorem
.(ii)Solving a linear and a quadratic simultaneously ,(iii)A question on
Indices (iv)a question on the properties of the roots of quadratic equations 
Inequalities of the form 
and problems on
absolute values 
Not asked since 96
when there was a near riot at the marking conference !There were a lot of
inequalities on the 1995 paper, four on paper 1 there were none on the 94 what
this means one cannot be sure but , I think it would be a good idea to get in a
bit of practice on inequalities . check what was asked in 1999 and 1998.The
inequality (which was based on a perfect square) asked in ,98 and ,99 cuold be
asked again this year see inequalities on web site .Also an index
equation was asked in 2(b),99, and 4(b)’98.
Question 3 Matrices and Complex numbers
; The matrix part can only be straightforward expect something on an inverse .
The complex number bit may involve solving a quadratic ,and using DeMoivres
theorem .This question has been upgraded since ’98 be careful !
Questions 4 . Question 4 last year was
really about Series , Binomial,AP/GP and even a part had an association with the Binomial Coefficients It is important
to note that the end part of 4c was worth very little.
.
There is plenty of scope to ask questions on the general term 
Question 5 : Arithmetic/Geometric
Series,Logs/Index equations and Induction . I
expect a Sum of a series maybe 
or an "is a multiple of "to appear . Induction has featured
prominently in this question is generally worth 20 marks . Note in ,97 there was an inequality asked
.The format for ’98 and ’99 was Binomial,Logs,Induction .
Question 6 : Differential Calculus Product /Quotient/Chain Rules . Expect a
rate of change problem in part C . Know how to find dy/dx of 
. Part c in ,97 was tricky but the good news you got 10 marks
for the dy/dx bit . Part © in 1999 required plen ty of thought ! They seem to
be using this question as a grader ie to separate the A’s from the B’s (because
everybody does this question)
Question 7: Differentiation from first
principals don't forget y=Sinx ., 
came up in ,97 Implicit functions/Parametric
differentiation Newton Raphson . Again the part c of this in ,97 was difficult
but again it was marked 10,10.
Question 8 : Integration : some basic
integrals plus Areas by integration and volumes of rotation note the only volumes you can be asked to
find are Cones Hemispheres and spheres .
Proofs asked so far on Paper 1 .
2000
1(b) The Factor theorem, 3(c) Prove
,
5(b) prove by induction
(6)bProve from first principals
1999 5©
by induction,6(b) y = Sinx from first principals.
1998(5c) a version of 
by induction.
1997(1b)The Factor theorem, (6b)
from first principals
1996(5c) Show by induction 
.
1995(6c) Prove the product rule
from first Principals ,
(see
the 
method on the website
)
1994(5b)Show by induction that 
is divisible by 7.
(7a) If 
from first principals
.
I do
not like to give tips but first principals seems to be popular with the
examiners the ones that have not been asked so far are are
y = Cosx, 
.
Last
year many students made a total mess of Question 7 c it might get another run this year in a more simple form Question 8 for the last two years has had a
difficult part c it would be a good
idea to have a question in reserve just in case this goes badly for you !.
Since
most students do Questions 1,2,3,6,7,8, these questions are often used to sort
out the A grades from the B grades
notice that the most difficult part c’s have been in the six most popular
questions ! . For the moment the two easiest questions on the first paper are
questions 4 and 5 .
A
couple of hours work on Questions 4 or 5 will bring great rewards . index.htm