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Maths

Advanced Maths 16–18

AS/A-level-style and AP Calculus AB-style maths for ages 16–18: differentiation, tangents and stationary points, integration and areas, exponentials and logarithms, trigonometric equations, binomial expansion, sequences and series, the binomial and normal distributions, and SUVAT mechanics. Typed exact answers with worked solutions.

Start the programmeTake the check-up
Ages 16–186 levels · 61 lessonsAbout 5 minutes a lessonFree to start

Level 1 · Unit 1

The first steps on the path

Lessons unlock one after another. Done lessons stay open for extra practice.

Try a sample lesson

This is how the first lesson starts. Sign in to play it and save stars.

Learn

Quadratic equations

About 5 minutes

How it works

Keep the equation balanced: whatever you do to one side, do to the other until x is on its own.

  • Example 1

    Write 3x² − 30x − 3 in the form 3(x + p)² + q. Give (p, q).

    Answer: (−5, −78)

  • Example 2

    Solve x² − 12x − 12 = 0 by completing the square. Give exact answers.

    Answer: x = 6 ± 4√3

Let’s practise

What’s inside

6 levels · 11 units · 61 lessons. Each unit ends with a check-up that unlocks the next one.

Level 1 · From GCSE-style to A-level-style

  1. From GCSE-style to A-level-style · 6 lessons

    • Quadratic equations
    • Algebraic fractions
    • Surds
    • Functions
    • Graph transformations
    • Exact values
Level 2 · AS-style start

  1. Calculus · 5 lessons

    • Differentiation
    • Tangents and normals
    • Stationary points
    • Integration
    • Areas under curves

  2. Advanced maths · 6 lessons

    • Exponentials and logarithms
    • Trigonometric equations
    • Binomial expansion
    • Sequences and series
    • Binomial and normal distributions
    • Mechanics (SUVAT, F = ma)
Level 3 · AS-style core

  1. Calculus · 5 lessons

    • Differentiation
    • Tangents and normals
    • Stationary points
    • Integration
    • Areas under curves

  2. Advanced maths · 6 lessons

    • Exponentials and logarithms
    • Trigonometric equations
    • Binomial expansion
    • Sequences and series
    • Binomial and normal distributions
    • Mechanics (SUVAT, F = ma)
Level 4 · AS/A-level-style

  1. Calculus · 5 lessons

    • Differentiation
    • Tangents and normals
    • Stationary points
    • Integration
    • Areas under curves

  2. Advanced maths · 6 lessons

    • Exponentials and logarithms
    • Trigonometric equations
    • Binomial expansion
    • Sequences and series
    • Binomial and normal distributions
    • Mechanics (SUVAT, F = ma)
Level 5 · A-level-style

  1. Calculus · 5 lessons

    • Differentiation
    • Tangents and normals
    • Stationary points
    • Integration
    • Areas under curves

  2. Advanced maths · 6 lessons

    • Exponentials and logarithms
    • Trigonometric equations
    • Binomial expansion
    • Sequences and series
    • Binomial and normal distributions
    • Mechanics (SUVAT, F = ma)
Level 6 · A-level / AP Calculus AB-style

  1. Calculus · 5 lessons

    • Differentiation
    • Tangents and normals
    • Stationary points
    • Integration
    • Areas under curves

  2. Advanced maths · 6 lessons

    • Exponentials and logarithms
    • Trigonometric equations
    • Binomial expansion
    • Sequences and series
    • Binomial and normal distributions
    • Mechanics (SUVAT, F = ma)

About this programme

Level 1 starts where GCSE-style Higher ends; the last level reaches A-level-style and AP Calculus AB-style questions (chain, product and quotient rules).

Crayonbird is not linked to any exam board. Every question is original and generated by code, and the answer keys are worked out exactly, so they are always right.

Questions grown-ups ask

How do I type answers like √12 or x ≥ 3?

A maths keypad under each answer box has √, powers, fractions, π, brackets and ≤ ≥. Answers are checked by value, and you get a nudge when the value is right but not yet in its simplest or factorised form.

How long is a lesson?

Most lessons take 5 to 10 minutes: a short learn card, practice that is marked as you go, and often a quick game. Little and often works best.

Do children need an account?

A grown-up signs up and adds a child profile; children never need an email or password. Class students sign in with their class code and PIN.

Is the practice the same every time?

No. Every practice step is generated fresh, so a child can repeat a lesson as often as they like and still get new questions.

Can I see how my child is doing?

Yes. The parent dashboard shows each programme, the level, stars, when your child last practised, and the skills that are going well or need more work.

Can I print the lessons?

Lessons are made for the screen, but every practice sheet can also be printed from the worksheet maker.

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