# Algebra - How to Revise

Updated: Sep 6

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:**

** **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

**I**f 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.

The topic covered in each question.

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:

- __Square Form & Nature of Roots__,

- __The Factor Theorem, Functions & Graphs__.

- __The Exponential Function (FREE)__.

**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