Leaving Cert · Higher Level

Learning Roadmap

The full course, start to finish, in the order we teach it. Work down the map one stop at a time — each builds on the one before.

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Before you start

Prerequisites

Higher Level assumes a lot of Junior Cert groundwork without ever re-teaching it — and it's usually the gaps here, not the hard topics, that cost marks. Have a quick look down this list before Algebra 1.

Fractions, decimals and percentages — including converting between them by hand
Negative numbers and order of operations (BIMDAS)
Ratio and proportion
The basic index laws — xa · xb = xa+b
Substituting values into an expression
Rearranging a simple formula to make x the subject
Rounding, significant figures and scientific notation
Pythagoras, and area and perimeter of basic shapes
📗 The Formulae & Tables booklet. You're given one in the exam and you can't bring your own. Get a copy early and learn what's actually in it — a surprising number of marks are lost looking for a formula that was on page 9 all along.
🔢 Your calculator. Know your own model properly — fractions, surds, stats mode and degrees vs radians. Exam day is a bad time to find out where a button lives.
Open the prerequisites module
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Foundations

Algebra 2

Indices, surds and logs, algebraic fractions, and inequalities — where most marks quietly get lost.

Coming soon
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Foundations

Algebra 3

Cubics and the factor theorem, the discriminant, completing the square, and the harder abstract algebra questions.

Coming soon
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Trigonometry

Trigonometry 1

Right-angled triangles, the sine and cosine rules, area of a triangle, radians and the unit circle.

Coming soon
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Trigonometry

Trigonometry 2

Identities, trig equations, graphs and transformations, double-angle formulae and 3D problems.

Coming soon
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Co-ordinate Geometry

Co-ordinate Geometry

The line and the circle — slopes, distances, equations, intersections, tangents and angle problems.

Coming soon
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Functions & Calculus

Functions

Domain and range, graph shapes and transformations, injective and surjective, limits and continuity.

Coming soon
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Functions & Calculus

Differentiation

First principles, the product, quotient and chain rules, tangents, max/min problems and rates of change.

Coming soon
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Functions & Calculus

Integration

Anti-derivatives, definite integrals, area under curves, average value and the trapezoidal rule.

Coming soon
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Geometry

Geometry

The examinable theorems and proofs, constructions, enlargements, and area and volume of solids.

Coming soon
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Number

Patterns

Sequences and series, arithmetic and geometric progressions, sums to infinity and proof by induction.

Coming soon
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Number

Complex Numbers

The Argand diagram, modulus and conjugates, polar form, de Moivre's theorem and roots of equations.

Coming soon
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Statistics & Probability

Statistics

Data types and spread, the normal distribution, confidence intervals, hypothesis tests and p-values.

Coming soon
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Statistics & Probability

Probability

Counting and arrangements, the probability rules, conditional probability, Bernoulli trials and distributions.

Coming soon
🎓 Exam ready