Rearrange, factorise and simplify the algebra the rest of Paper 1 depends on
✓Leaving Certificate · Higher Level · Paper 1 · Strand 4
Stop practisingthe algebra you can already do.
Algebra & Complex Numbers is 66 short, guided lessons built around the question types that keep coming back. First you see the method. Then you try it. Then the help comes away.
This is Strand 4 of five, not the whole course. The other strands are still being written. Your purchase includes one year's access to Algebra & Complex Numbers only.
66guided lessons
Strand 4sold on its own
1 yearof access
Peter O'Hagan · teaching for over 20 years
Today's plan18–24 min
The Factor Theorem · Lesson 12
Turn a cubic into a route you already know.
Lesson progress3 of 5 steps
Up nextWorked example → guided attempt
CourseAlgebra & Complex Numbers
LevelLeaving Certificate Higher Level
FormatGuided self-study in the Forkhill app
Revision should expose the gap
Practise the question you need—not the one you already know.
Familiar questions make revision feel productive. They do not show you what will catch you out in the exam. The course gives you a deliberate route through these recurring question types.
Solve polynomial equations of degree 3 and higher, with or without a factor given
✓Recognise hidden quadratics and handle equations containing a square root
✓Solve simultaneous equations, including three unknowns and mixed-order pairs
✓Solve inequalities, including modulus and denominator cases
✓Move between rectangular and polar form and apply De Moivre’s theorem
✓Five stages in every lesson
Shown properly. Then the help comes away.
Every lesson begins with the working on show and ends with you applying the method somewhere less familiar. If you need help, hints arrive one at a time, so you get a nudge before you get the answer.
The app is where you find out whether you were right. The paper is where you do the working—and where the marks are earned.
Explain→Model→Imitate→Fade→Apply
Read the four-minute app guide A focused next step
Return to inequalities with an unknown in the denominator.
(x − 2)(x + 5) ≥ 0
Method mark earned. Now test the sign in each interval.
The question returns before the method has time to disappear.
“I forgot to test which intervals made the expression positive.”
One honest sentence is more useful than re-reading the whole lesson later.
Explain
Learn the method through one example worked all the way through.
Model
Watch it used on a real question, from the first line to the last.
Imitate
Take the same steps yourself before you reveal the working.
Fade
Try again with fewer prompts and more of the method left to you.
Apply
Use it in the less obvious form you are more likely to meet in an exam.
What's covered
The algebra Paper 1 keeps asking for.
Algebra comes first in the story because it supports so much of the paper. Complex numbers remains part of the strand, but the sequence is built around the algebraic fluency students repeatedly need.
Polynomial thinking
Build the habits that make higher-degree equations feel structured rather than improvised.
- The Factor Theorem
- Polynomial equations of degree 3 and higher
- Conditions on the roots of a quadratic
Algebraic fluency
Strengthen the manipulation that sits underneath almost every successful Paper 1 solution.
- Rewriting expressions and surds
- The binomial theorem
- Hidden quadratics and equations with a square root
Equations & inequalities
Build a dependable route through the cases where signs, roots and unknowns can catch you out.
- Three simultaneous unknowns
- One linear and one order-2 equation
- Modulus and denominator inequalities
Complex numbers
Connect each representation so you can choose the one the question actually needs.
- Rectangular and polar form
- De Moivre’s theorem
- Roots of a complex number and proofs
The app checks. You do the maths.
Work it on paper.Use the feedback well.
Where partial credit applies, you can see which parts earned marks. The app does not pretend to replace handwritten exam working; it helps you practise it more deliberately.
A useful next step
Today’s Plan suggests what to work on next. It is advice, not a gate, and every lesson remains open from day one.
Bring it back before it fades
Practice & Review returns questions after a gap so ‘I could follow that’ has a chance to become ‘I can do that’.
Your mistakes, in your words
Keep a private note of what caught you out and build revision around your mistakes rather than everybody else’s.
Working still happens on paper
Read the question on screen, work it as you would in the exam, then enter your answer and compare the method. Printable sheets help keep that working clear.
Built and taught by Peter O'Hagan
Professional teaching judgement, built into every next step.
I have spent 23 years teaching and preparing students for high-stakes examinations, including 21 years in a Northern Ireland grammar school and time as Head of Physics. I now teach Leaving Certificate Maths and Physics in the Republic of Ireland.
This course turns that classroom judgement into a clearer self-study route: diagnose the question, sequence the practice, revisit it before it fades and move towards independent exam working.
BSc (Hons)Physics with AstrophysicsMaster's with DistinctionEducational StudiesFormerHead of Physics
Straightforward scope and pricing
Start with the strand that makes the rest of Paper 1 easier to handle.
Algebra & Complex Numbers is sold as its own complete strand. You can see exactly what is included before you pay, with no suggestion that this is the full Higher Level Maths course.
Founding-student credit
Buy at €39 now and receive a €39 credit if you later buy the completed multi-strand course, if and when it becomes available.
Founding price
€39
First 30 students or until 30 September 2026. €49 thereafter.
- 66 guided Algebra & Complex Numbers lessons
- One year's access
- Today's Plan, feedback and spaced review
- Printable working sheets
Immediate digital access requires your express agreement before payment. A parent or guardian must arrange payment for a student under 18.
Questions, answered clearly
Before you begin.
No vague bundles and no implied future access. Here is what this purchase means.
Is this the full Leaving Certificate Higher Level Maths course?
No. This purchase is for the standalone Algebra & Complex Numbers strand only. Other strands are still being written and will be priced separately if and when they are released.
What do I get access to?
You receive one year’s access to 66 guided lessons, question practice, feedback, spaced review, the mistake notebook and printable working sheets for Algebra & Complex Numbers.
How does the €39 founding price work?
The founding price is €39 for the first 30 students or until 30 September 2026, whichever comes first. The price is then €49.
What happens if a complete multi-strand course is released later?
Students who buy this strand at the €39 founding price will receive a €39 credit if they later buy the completed multi-strand course, if and when it becomes available.
Do I need anything beside the app?
Bring a pen and paper. The app is designed to guide real exam-style working, not to be tapped through like a quick quiz.
Can a student under 18 buy the course?
A parent or guardian must set up the account and arrange payment for a student under 18.
Right work. Right order. Right time.
Know how to start the next algebra question.
You do not need another pile of questions. You need a clear next one—and a method you can still use when the numbers change.
Start the course — €39
One year's access · founding price terms apply