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THE Exponential Function - How to Revise

Updated: Sep 25

- What is the most common, yet under-appreciated topic on the Leaving Cert HL exam paper?

- What was the WORST ANSWERED QUESTION in Paper 1 of LCHL 2022? (watch the video in Tip #5 to find out)

THE Exponential function is one of the more fascinating concepts on the Leaving Cert course.

Interestingly, most text books don't put a huge emphasis on it.

But when you look at how often it appears in the LC, there's a case that it deserves its own chapter (see Tip #4)

Tacit Maths Module on the Exponential Function (FREE)

The Exponential Module/Worksheets/Solutions are FREE to everyone!


This worksheet/module is designed to be quite short.

The aim should be to target exam questions ASAP.

The module contains:

- Notes with corresponding eLearning module.

- 10 LCHL Exam questions

- Powerpoint solutions to all of the above.

Tips for Revising The Exponential Function

1. Exponentials V THE Exponential

Worksheet: Page 3 - 4

Powerpoint: Page 9 -18

This is an important distinction to make.

"Exponential Equations" are any equation where the unknown is a power.

Well prepared students will know that we use Logs to solve equations.

However, THE Exponential function is a special type of function.

It is critical that students understand the differences and similarities as to how you approach both of these.

2. Trouble with Decimals

Worksheet: Page 4

Powerpoint: Page 20

For some reason, many students get completely turned off when they see equations/functions with decimals in them.

A well prepared student should be fully confident in working with integers, decimals, fractions, standard notation, percentages etc.

The exercise above should help with that.

NOTE: Students should note that all the solutions to the above exercise are whole numbers...

3. Incomplete Functions

Worksheet: Page 5 - 6

Powerpoint: Page 9 -18

A complete function should only have one variable in it (usually x)

When you look at the Part B questions, you will find that a very common feature is they have two extra unknowns (see image).

The approach to solving this problem is quite straightforward as you will see.

HINT: One of the clues that will help is finding the "initial value".

It is almost always mentioned in some shape or form.

4. Appearances in Previous Leaving Certs

- LC 2023: 30 Mark Questions (with Differentiation)

- LC 2022: 50 Mark question

- LC 2022: 30 Mark question (with Sequences & Series)

- LC 2021: 50 Mark question (Calculus)

- LC 2020: 55 Mark question (Calculus)

- LC 2019: 25 Mark question (Algebra/Calculus)

- LC 2018 Q7: 50 Mark Question

- LC 2018 Q8: 50 Mark Questions

- LC 2017: 55 Mark Question (Calculus)

- LC 2016: 25 Mark Question (Functions/Algebra)

- LC 2014: 60 Mark Question (Calculus)

5. WORST Answered Question in Leaving Cert Paper 1

In 2022, students had the option of skipping some Part A questions.

The VAST MAJORITY skipped Q4, and those who attempted it did quite poorly!

TIP: Rather than simply watching the video below, why not TRY IT OUT YOURSELF FIRST.

See how you would have done and compare your solution to the video.

(Click to Download)

Q4 LCHL 2022 P1
Download PDF • 236KB

Video Solution:

For more information on how to sign up to the modules on Tacit Maths, visit our website ( or contact Diarmuid directly at:

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