Geometry revisited

Since quite a few students are interested in geometry, I've looked into whether we can cover this section of the course in the time remaining.
Basically, if you know your theorems from higher level junior cert and remember the basics of geometry, you should have few problems with LC ordinary level geometry.
We won't have time to go through each theorem individually, but they should be easy to study on your own. The geometry questions (4 and 8) usually have a part b which involves proving a theorem.
We will do the constructions and enlargements in class.
If your preference was to stick with the questions and options we have already covered, don't worry. We will spend just a few classes on geometry and you can work on other maths material during those classes.

After the mocks ...

With the mock exams completed, we have to settle on a schedule of revision.
Not including 2 weeks at Easter and the week starting May 12th, we will have 8 weeks of normal class time, give or take a day here or there.

We are currently prepared for the following.

Paper 1:
Q 1,2,3,4,6,7,8 (must do 6 of these 7 questions)
We left out Q5 Sequences and Series

Paper 2:
Section A Q 1,2,3,5,6,7 (must do 5 of these 6 questions)
We left out Q4 Theorems and Enlargements.
Section B Q 11 (must do 1, there are 3 other options)
We left out Q8 Further Geometry, Q9 Vectors and Q10 Further Sequences and Series.

Do we want to prepare for any further questions?

Linear Programming

The other topic we will cover in Friday's class is Linear Programming.
You need to know all the inequalities, simultaneous equations and co-ordinate geometry stuff for other parts of the paper anyway, so Linear Programming gives you an extra question with very little extra work.
It is the only option in Section B which we will be doing for now.
This is the 1-pager.

Perimeter, Area + Volume

Here is my 1-page overview of what you need to know.
Practice using the formulae for surface area, volume etc as they are presented in the mathematical tables.
Simpson's rule is in the tables also, but not in the form we are used to. h/3(1st+last+TOFE) is a good way to remember it, but you have to practice.

Alegbra class

Last night's homework question 2 had a simultaneous equation - one linear one quadratic - type question. Notethat it was xy and not x², but it has to be handled the same way.
x + 3 = 2y
xy – 7y + 8 = 0 <-this is the quadratic (can be x² or xy)
x = 2y -3 [rearrange linear equation]
(2y-3)(y) – 7y + 8 = 0 [sub in new value for x]
2y² – 3y -7y +8 = 0
2y² – 10y + 8 = 0 [always simplify equation if you can]
y² -5y + 4 = 0 [factor -4 x -1 = 4 and -4 -1 = -5]
(y-1)(y-4) = 0
So y = 1,4
If y= 1 then
x = 2(1) – 3, so x = -1 values: x = -1, y = 1
if y= 4 then
x = 2(4) – 3, so x = 5 values: x = 5, y = 4
And always check:
(-1)(1) – 7(1) + 8 = 0
(5)(4) – 7(4) + 8 = 0

Part c of this question works out as follows:
(i) √x + 1 [Turn them into same type of fraction ... LCM of 1 and √x is √x]
1 √x
= √x√x + 1 [multiply above and below leftmost fraction by √x]
√x √x
= x + 1 [don't forget √x√x = x]
√x

ii) ( 2√x ) • (x + 1 ) [cancel (x + 1) with (1+x) and cancel √x with 2√x ]
(1+x ) ( √x )
= 2

iii) 2 = x -3
x = 5

Tomorrow's double class will be Perimeter area + volume (1st period) and Linear Programming (2nd period) - Homework for tomorrow is 2006 Paper 2 - q1 and 11.

Leaving Cert Algebra

There are two algebra questions on Paper 1 and algebra permeates almost every question on the exam to a certain extent. It is worthwhile investing time and effort in practising algebra.

This is my 1-page overview of algebra - an outline of the basic concepts you need to master.
We will review this in Thursday's class.

Homework for Thursday is 2005 Paper 1 questions 2 and 3.

Statistics wrap-up

For the most part the statistics homework was well done.
It was question 7 on this paper.
The two difficulties seemed to be

• creating the cumulative frequency table from the original data given. Make sure that the last number in the cumulative frequency table is the sum of all the frequencies - which was 80 (already used this value in part ii)
• figuring out how many cars were priced between the mean and the median. This was an unusual question. You had to take the mean you calculated in part ii (26.25 or 26,250), find this value on the X-axis, trace a vertical line to the curve and then find the corresponding position on the Y-axis. This should be 50. That tells you that the "50th car" is priced at the mean price. The number between the mean and median is therefore 50-40= 10 cars.

Note with this question that the mean would be quite a bit higher than the median. Why do you think this is?

Thursday's class will be all algebra.

Statistics again

Today's class didn't go to plan - too many students didn't do the weekend work and we didn't get through the corrections.
We will have to do a full revision of Statistics in tomorrow's class and set the homework on Algebra.
Homework for the evening of 6th Feb will be two algebra questions: the 2005 paper I, q2 and q3.

Leaving Cert Statistics

There are lies, damned lies and statistics - attributed to Mark Twain or Disraeli depending on how you google it.
Statistics is the art of interpreting data - summarising complex data in numbers (by calculating a mean or a standard deviation) or presenting it graphically in graphs.
If you understand statistics, you'll know when someone is using their statistical knowledge to warp and twist the truth for their own advantage ... if you master statistics, you'll be able to warp and twist the truth to your own advantage.

We'll revise Statistics in class on Feb 5th.
Homework will be LC 2006 Paper 2 Q 7
Here is my 1 pager

Introduction

This blog is aimed at my Leaving Cert students who are taking Ordinary Level Maths gearing up for their Mock exams and then for the Leaving Cert exams in June.

In real-world class, we will be preparing for the Mock exams which take place during the week starting Feb 18th.

Students can keep up with the schedule of revision using this blog. Any other students who may find this blog useful are welcome to join in.

The questions we are working toward are as follows:
Paper I
Q1 Arithmetic (completed mid Jan)
Q2 Algebra (Thurs 7th Feb)
Q3 Algebra (..)
Q4 Complex Numbers (Thurs 31 Jan)
Q6 Functions (Fri 1 and Tue 5 Feb)
Q7 Calculus (Fri 1 and Tue 5 Feb)
Q8 Calculus (Fri 1 and Tue 5 Feb)
Paper II
Q1 Perimeter Area + Volume (Fri 8 Feb)
Q2 Co-ord geom of Line (Fri 25 Jan)
Q3 Co-ord geom of Circle (Mon 28 Jan)
Q5 Trigonometry (Tue 29 Jan)
Q6 Probability (Wed 30 Jan)
Q7 Statistics (Wed 6 Feb)
Q11 Linear Programming (Fri 8 Feb)

All your comments and constructive feedback are welcome!