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Algebra - How to Revise

Updated: Sep 6, 2023

There are no shortcuts or cheat "codes" to studying Algebra for the Leaving Cert.

HOWEVER, the Algebra Essentials modules on Tacit Maths might be as close as you will get.


The modules take all the "pure" Algebra questions that have come up in Part A of the LCHL Maths exam over the last few years.


This blog post goes through 5 Simple Tips on how to study Algebra and how use these modules.

Towards the end there's a few pointers on HOW TO USE the Algebra Essentials modules effectively.


Feel free to preview one of the worksheets here:

WATERMARK Algebra Essentials #1
.pdf
Download PDF • 2.58MB

Tip #1. Algebra in the Leaving Cert

The Leaving Cert is made up of three main domains:

- Calculus,

- Geometry

- Statistics.

There are also a few smaller topics (i.e. Complex Numbers, Sequences & Series, Financial Maths).

So where does Algebra fit in?

Well, Algebra permeates through all of these topics.

WARNING: If your Algebra skills aren't up to scratch, it makes all the other topics that much harder to master.






Tip #2 - Good News: Low Hanging Fruit

If you read our "12 Top Tips for Leaving Cert Maths" blog post, you will recall that there is a lot of "Low Hanging Fruit" on the Leaving Cert paper.

In Paper 1 these are predominantly made up of Algebra Questions.


NB: IT IS VITAL THAT YOU GET FULL MARKS IN THESE QUESTIONS.


If you look at Q1 from the Paper 1 (HL) shown here, these two easy questions were worth 25 Marks in total!

Before you start worrying about advanced concepts, make sure you have the basics covered.




Tip #3: Logs and Indices are Key (HL Only)

When Leaving Cert students are asked which concept bothers them the most, Logs always comes up on top.

When there is a choice on the LC Paper, Logs are often avoided.

But there's no avoiding it, Logs and Indices are everywhere in Algebra in the Higher Level course.


When solving problems related to:

- Logs,

- Indices,

- The Exponential Function (e^x),

- Natural Logs (ln), you use a very similar set of rules and approaches.


They appear multiple times almost every year (see image).


They can appear as questions on their own, or part of longer Calculus questions.

They can even come up as part of a Financial Maths questions!

Advice: It's best to just accept it now. Logs are going to feature in your Algebra life from now on.


Tip #4: Quadratic Equations - Know them inside out (OL & HL)


Are you a "Guide Number" type of person? Do you just open two sets of brackets and go mad? Or do you use the "-b formula" no matter what type of Quadratic appears??

No matter what your approach, you cannot go into a Leaving Cert Maths exams without being fully confident with Quadratic Equations.

In Ordinary Level, Quadratics can appear as standalone questions, as part of Calculus or Simultaneous Equations questions, or perhaps in the middle of a long Part B question.

Challenge: Have a look at the Quadratic Equations image above. How confident would you in solving each of these types of Quadratics?

NB: Interestingly, the bottom example here is often the worst answered of the lot!



Tip #5: How it's come up 2020-2023

If LC 2023 has taught us anything, it's dangerous to use past paper to predict what's coming up in the next Leaving CErt.

HOWEVER, sometimes it is interesting to look out for trends of some sort.


This list shows the Pure Algebra* questions that came up in recent year.

(*By Pure Algebra we mean no Calculus, Complex Numbers, Financial Maths etc.)


Higher Level Paper 1

LCHL 2023

- Q1: Modulus, Rearranging formulae, Dividing Algebra

- Q3: Logs

- Q6: Simultaneous/Quadratic Equations


LCHL 2022

- Q1: Nature of Roots & Square Form

- Q2: Factor Theorem & Dividing Algebra

- Q4: The Exponential Functions (with Sequences & Series)


LCHL 2021

- Q2: Modulus and Solving Cubic Equations/Functions

- Q3: Surds, Quadratic Equations AND Logs & Indices


LCHL 2020

- Q3: Logs


Ordinary Level Paper 1


LCOL 2023

- Q2: Linear Equations & Inequalities, Simultaneous Equations

- Q6: Simplifying, Quadratic Equations


LCOL 2022

- Q2: Linear Equations, Indices & Simultaneous Equations

- Q6: Inequalities (With Seq.& Series)


LCOL 2021

- Q3: Quadratic Equations

- Q4: Linear Equations & Simult. Eqs


LCOL 2020

- Q2: Algebra Fractions & Simult. Eqs.

- Q4: Indices Equations

- Q5: Quadratic Equations


How to use the Tacit Maths Algebra Essentials Worksheets

1. Table of Contents: Level of Difficulty

There are two important features to the Table of Contents.

  1. The topic covered in each question.

  2. The perceived difficulty level of each question.

Here's a simple guideline to the difficulty levels:

Basic: Every LCHL student needs to be getting full marks in these questions.

Medium: By the time the Leaving Cert comes, you should be aiming to be fully competent at these questions.

Advanced: If you are aiming for a H1 or H2, you need to be getting all of these out fully.

If your targets are lower, you should still be aiming to get as many attempt marks as possible in these types of questions.


2. Algebra Essentials Confidence Table

Here's a very simple tool to help you analyse which topics you are confident in.

All of the topics here correspond to the questions in the worksheet. This should paint a good picture as to where you need to focus.


3. More Focused Study


Remember, the Algebra Essentials modules cover all the topics of Algebra.


If you are looking for more focused study, don't panic.


If you find that you are struggling with Logs/Indices or the Exponential Functions, then there are more in depth modules focusing on these topics that you can use.


The key Algebra Modules you should be focusing on are:








4. Use the eLearning Modules (Interactive Solutions)

Every Tacit Maths module has eLearning Modules corresponding to the worksheets you are working on.


The Algebra Essentials worksheets have the solutions to each question, completed step by step, and explained in detail.


Feel free to fly through to simply find the solution, or go through it at your own pace to see where you are going wrong.










Algebra Essentials Video

Finally, have a look at this video, outlining in more detail how to approach Algebra in Leaving Cert Higher Level Maths


For more information on how to sign up to the modules on Tacit Maths, visit our website (www.TacitMaths.ie) or contact Diarmuid directly at: diarmuid@tacitmaths.ie




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