One named lesson instead of the vague instruction to ‘revise algebra’
✓For parents of fifth- and sixth-year Higher Level Maths students
Stop asking,“Have you done enough maths?”
Give them one clear Algebra lesson to do today, a finish line they can see and feedback that helps them take the next step—without you becoming the maths teacher.
One payment · one year's access · standalone Algebra & Complex Numbers strand. This is not the full five-strand Maths course.
66guided lessons
≈10 minfor most lessons
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
Question-by-question exam audit
Past papers are free. Knowing what to do with them is the course.
I worked through every Higher Level Paper 1 from 2007 to 2026 and the published marking schemes through 2025, grouping questions by the algebraic move they actually require.
This is not prediction. It is a teaching order built from the recurring structures in the papers and the methods the schemes reward.
A past paper can give you a question and a marking scheme can give you an answer. Neither decides what to practise next, takes the help away gradually or brings the question back later to see what the student can still do. That is the work the app adds.
Peter O'Hagan · 23 years teaching · Master's with Distinction, including research in computer-assisted formative assessment
Paper auditEvery Higher Level Paper 1, 2007–2026
Marking schemesPublished schemes through 2025 analysed
Real exam models65 of 66 lessons use a real Paper 1 question
Structure without the study police
Give the evening a clear beginning and end.
The student still has to do the maths. The app makes the work specific enough to begin, short enough to finish and useful enough to return to later—without a parent having to choose the questions.
A visible stopping point—most lessons take about ten minutes
✓Real working on paper, where the exam method has to live
✓Hints one at a time, before the full solution is revealed
✓Questions brought back after a gap, when doing them again actually tests memory
✓A private Mistake Notebook that turns ‘I got it wrong’ into ‘here is what I will do next time’
✓Every lesson available from day one, with Today’s Plan suggesting where to begin
✓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.
Past papers provide the raw questions. Forkhill turns them into a learning sequence: see the method, try it with support, try it with less help, then meet it again later and find out what stayed.
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.
It returns after two days, then later again when it keeps going well—so the student has to do it from memory, not simply recognise it.
“I forgot to test which intervals made the expression positive.”
Record what was asked, where the attempt went wrong and the rule to remember. The note stays private and takes you back to the exact question.
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
Algebra is the working language of both papers.
This strand is examined on Paper 1, but algebra does not stay there. Rearranging, substituting, factorising and solving equations sit underneath calculus, coordinate geometry, trigonometry and other Paper 2 work. Complex numbers remains part of the strand, while algebra is the foundation running through it.
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 successful work across both exam papers.
- 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
Private practice. Honest feedback.
Try it. Check it.Improve it.
Confidence grows when a student can try a question on paper, be wrong in private, see the correction and have another go with a little less help. Where partial credit applies, the app can show which structured parts earned marks. It does not claim to read or mark handwriting.
A useful next step
Today’s Plan suggests what to work on next. The student can follow it or choose any lesson; everything is available from day one.
Bring it back before it fades
Practice & Review brings a mastered question back after two days, then at longer gaps when it keeps going well. That is how ‘I understood it’ becomes ‘I can still do it’.
Make the mistake useful
After a real attempt, write what the question asked, where your working went off course and the rule that will help next time. The private note links back to that exact question.
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
Build the algebra that supports work across both papers.
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.
Why not just download past papers?
Past papers give you the questions. This course adds the teaching order, a worked method, guided attempts with less help each time, one-at-a-time hints, scheduled review and a private record of what to fix. It is built from the papers; it does not claim to predict the next one.
Does this algebra help with Paper 2 as well?
Yes. The course itself covers the standalone Algebra & Complex Numbers strand and its real exam models come from Paper 1. But rearranging, substituting, solving equations and handling expressions are used throughout Paper 2 in areas such as calculus, coordinate geometry and trigonometry. It supports those topics; it does not replace teaching them.
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