Paul Keogan

LCHL Maths – Indices and Logs

LCHL Indices and Logs

Your progress through this topic0 of 8 lessons

Lessons in this topic

All 8 lessons, in order — each one ticks off as you open it.

1JC revision 2Rules of logs Part 1 3Rules of logs part 2 4Changing the base 5Unknown in the power/ the natural log 6Quadratic Equations 1 7Quadratic Equations 2 8Log Problems

Laws of indices

Product law — Product lawIndices and Logs 1

Quotient law — Quotient lawIndices and Logs 1

Power of a power — Power of a powerIndices and Logs 1

Fractional index — Fractional indexIndices and Logs 1

Negative index — Negative indexIndices and Logs 1

Laws of logarithms

Log ↔ index — Log ↔ indexIndices and Logs 2

Product law — Product lawIndices and Logs 3

Quotient law — Quotient lawIndices and Logs 3

Power law — Power lawIndices and Logs 3

Change of base — Change of baseIndices and Logs 4

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Jump straight to the fully worked solution for that paper.

2023 Paper 1 Q2 →2023 Paper 1 Q3 →2023 Paper 1 Q9 →2021 Paper 1 Q3 →2020 Paper 1 Q3 →

Paul Keogan

LCHL Maths – Number Theory

LCHL Number Theory

Your progress through this topic0 of 5 lessons

Lessons in this topic

All 5 lessons, in order — each one ticks off as you open it.

1Types of numbers 2Prime Factorisation 3Number Theory 3 Proof by contradiction: Prove root 2 is irrational★ Learn off 4Number Theory 4 Construct √2★ Learn off 5Construct √3★ Learn off

Key ideas in this topic

Natural numbers (ℕ) — Natural numbers (ℕ)Number Theory 1

Integers (ℤ) — Integers (ℤ)Number Theory 1

Rational numbers (ℚ) — Rational numbers (ℚ)Number Theory 1

Irrational numbers — Irrational numbersNumber Theory 1

Real numbers (ℝ) — Real numbers (ℝ)Number Theory 1

The number sets — The number setsNumber Theory 1

Prime factorisation — Prime factorisationNumber Theory 2

√2 is irrational — √2 is irrationalNumber Theory 3

The two constructions

Construct √2 — Construct √2Number Theory 4

Construct √3 — Construct √3Number Theory 5

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2023 Paper 1 Q3 →2023 Paper 1 Q9 →2022 Paper 1 Q1 →2022 Paper 1 Q2 →2022 Paper 2 Q6 →

Paul Keogan

LCHL Maths – Algebra

LCHL Algebra

Your progress through this topic0 of 23 lessons

Lessons in this topic

All 23 lessons, in order — each one ticks off as you open it.

Key ideas in this topic

The Quadratic Formula — The Quadratic FormulaAlgebra 2

Difference of Two Squares — Difference of Two SquaresAlgebra 1

Sum of Two Cubes — Sum of Two CubesAlgebra 3

Difference of Two Cubes — Difference of Two CubesAlgebra 3

The discriminant — two distinct real roots — The discriminant — two distinct real rootscrosses the x-axis twice

The discriminant — one repeated real root — The discriminant — one repeated real roottouches the x-axis

The discriminant — no real roots — The discriminant — no real rootsdoesn’t meet the x-axis

Check it against the exam

Jump straight to the fully worked solution for that paper.

2023 Paper 1 Q1 →2023 Paper 1 Q2 →2023 Paper 1 Q4 →2023 Paper 2 Q4 →2022 Paper 1 Q2 →