Additional Maths from square one, for teenagers who learn at home.

Inside the course

This is chapter 1, Functions, as a learner sees it. Every picture is a screen of the course as it is today. Chapters 1 to 4 are in testing now, and the others are being built.

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   Your teenager picks the way in

   A chapter can start with a story, with short cards, with both, or with the lesson straight away. The choice can change at any time, and no progress is lost.

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   A story asks why before any rule

   Chapter 1 opens with a comic set on an island that still has to be mapped. The hero carries the name your teenager picks. Every story page has a button to skip it.

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   Worked examples, one step at a time

   Short cards build each idea. A worked example shows its steps one by one, with the graph next to the working. In the next example, a step is left for your teenager.

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   A hint before the answer

   Each answer is checked at once. A question comes with up to three hints, opened one at a time, and a common slip gets a line that names it. A button says "This was hard for me", with no penalty.

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   How the marks are earned

   Card lessons end with exam-style questions. After the answer comes the worked solution, with a mark tag on each line (B1, M1, A1), so your teenager sees what earns a mark. The questions and mark notes are our own.

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   The full lesson says why it matters

   The Workshop is the full lesson of a chapter. Each section opens with "Why this matters", then explains, shows examples and sets practice. Chapter 1 has 14 sections, about 5.5 hours of work, cut into 6 study sessions.

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   One map for the whole course

   Each chapter is a land on one island, from Mapping Gate to Exam Summit. The map shows where your teenager is and what comes next.

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   A plan that ends at the exam

   Your teenager picks the exam series, the days of the week and a pace. The planner works out the weeks and a done-by date for each chapter. The course works without it, too.

How the course teaches

Six habits shape the course.

• Why before how

  An idea starts in a situation where it does real work: an oven, a thermometer, a locked gate. The rule comes after the question.

• Shown, then shared, then alone

  First a full worked example. Then examples with a step left open. Then questions with no help on the page, and hints one tap away.

• Checked at every step

  Answers are checked at once, so a slip is caught where it happens and not three pages later.

• Words and pictures together

  Where the maths has a shape, the graph stands beside the algebra and moves with it.

• Good places to stop

  Lessons are cut into short study sessions, and each one ends at a place to pause. There are no streaks and no leaderboards.

• Paper stays

  The exam is written by hand. Exam-style cards say what to show on paper, and the story's hero works things out on paper too.

The 15 chapters

The course follows the Cambridge IGCSE Additional Mathematics syllabus (0606), which is shared with Cambridge O Level Additional Mathematics (4037). It starts from what IGCSE Maths teaches.

Chapters 1 to 4 are in testing now. The other chapters are being built and tested in order.

1. Functions

   Mapping GateIn testing now

   Number machines: which inputs they take and which outputs can come out. Run a machine backwards, chain two together, fold a graph up with |f(x)|.

2. Quadratic functions

   Parabola HillsIn testing now

   Complete the square to find where a parabola turns and how high or low it goes. Use b² − 4ac to tell if a line cuts the curve, touches it or misses it.

3. Factors of polynomials

   Factor QuarryIn testing now

   Put one number into a polynomial and the remainder tells you if it is a factor. Split a cubic into a linear factor times a quadratic, then solve it.

4. Equations, inequalities and graphs

   Modulus CanyonIn testing now

   Solve modulus equations and inequalities, by algebra or from a careful sketch. Spot the quadratic hiding in a harder equation; sketch cubics and their folds.

5. Simultaneous equations

   CrossroadsBeing built

   Find where a straight line meets a curve by putting one equation into the other. Count the meeting points first, then pair every x with its own y.

6. Logarithmic and exponential functions

   Log ForestBeing built

   Meet eˣ and ln x, two curves that undo each other, and their asymptotes. Use the log laws to bring x down from a power and solve the equation.

7. Straight-line graphs

   Gradient CanalBeing built

   Midpoints, lengths, parallel and perpendicular lines, perpendicular bisectors. Choose axes that turn a curved law into a straight line, then read its constants.

8. Coordinate geometry of the circle

   Circle LakeBeing built

   Find a circle's centre and radius from any form of its equation. Where a line meets a circle: a chord, a tangent, or no contact at all.

9. Circular measure

   Radian OrchardBeing built

   Measure angles in radians, the way a circle measures itself. Find arc lengths and sector areas, then build harder shapes from them.

10. Trigonometry

    Sine WindmillsBeing built

    Six trig functions and their wave graphs, with amplitude and period. Solve trig equations in a given range, and prove identities line by line.

11. Permutations and combinations

    Counting MarketBeing built

    Count arrangements where order matters and selections where it does not. Use n!, ⁿPᵣ and ⁿCᵣ, with rules like "these two must stand together".

12. Series

    Series TerracesBeing built

    Expand (a + b)ⁿ and find one chosen term, such as the term without x. Arithmetic and geometric progressions, their sums, and endless sums with a total.

13. Vectors in two dimensions

    Current CoastBeing built

    Write vectors in every form, find lengths and unit vectors, solve geometry. Add velocities, track a moving point with r = r₀ + tv, see if two paths meet.

14. Differentiation

    Tangent RidgeBeing built

    Differentiate powers, trig, eˣ and ln x with the chain, product and quotient rules. Find tangents, normals, rates of change and the highest or lowest point.

15. Integration and kinematics

    Area PlainsBeing built

    Integrate by running differentiation backwards, with + c where it belongs. Find areas under and between curves; follow a particle with s, v and a.

Two more lands close the map: Proving Ground, with mixed questions from all 15 chapters, and Exam Summit, the two written papers.

Questions parents ask

Who is the course for?

For teenagers aged about 14 and up who learn Additional Maths on their own, at home or next to school. Additional Maths itself starts at square one here. It builds on IGCSE Maths, and the first section of chapter 1 refreshes what is needed.

Which exams is it for?

Cambridge IGCSE Additional Mathematics (0606) and Cambridge O Level Additional Mathematics (4037). Swirlwise is not affiliated with or endorsed by Cambridge University Press & Assessment.

Is the exam part of the course?

No. Your teenager sits the exam at an exam centre, as a private candidate. Our free guide for families on the waiting list explains how that works in the UK.

What does my teenager need?

A laptop or a tablet with a current browser, paper and a pencil. Progress is saved to the account, so it is the same on every device.

Do I have to teach?

No. The course does the teaching. An adult at home keeps an eye on the plan and the pace.

When does it open, and what does it cost?

The opening month is at the top of this page. The price is not set yet. Families on the waiting list hear both before anyone else.