Exam Mode · Further Mathematics

Your guided session, built like a tutor

Learn the essentials, test yourself immediately, then lock it in with a mini exam hit. Every topic card below is a full micro-lesson.

Focus block25 min
Recall sprint6 min
Exam hit8 min
Session progress0%

Full session map

Every topic covered in this subject, with time estimates.

Total ~192 mins

Matrices & Transformations

Paper 1 · Both

24 min
Next up
Open lesson

Proof & Algebra

Paper 1 · Both

Locked
24 min

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Functions & Graphs

Paper 2 · Both

Locked
24 min

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Advanced Vectors

Paper 2 · Both

Locked
24 min
In today’s focus

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Calculus: Differentiation

Paper 2 · Both

Locked
24 min
In today’s focus

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Inequalities & Regions

Paper 1 · Both

Locked
24 min

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Circle Theorems (Advanced)

Paper 2 · Both

Locked
24 min
In today’s focus

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Coordinate Geometry

Paper 1 & 2 · Both

Locked
24 min

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Focus topics (start here)

Each card is a full micro-lesson: learn → check → apply.

Focus 1

Advanced Vectors

Paper 2 · Both

Full notes

Teach it

  • Vector Proof

    Use vector equations to show parallel or intersection points.

  • Vector Geometry

    Show collinearity by proving vectors are scalar multiples.

Key facts

  • Parallel vectors are scalar multiples.
  • Collinear points lie on the same straight line.
  • Magnitude = √(x² + y²)
  • Midpoint of AB = (a + b)/2

Key terms

Position vector: Vector from the origin to a point.
Displacement vector: Vector representing movement from one point to another.
Collinear: Points that lie on the same straight line.
Unit vector: Vector with magnitude 1.

Quick check

Show that vectors (6,9) and (2,3) are parallel.

2 marks · Paper 2

Focus 2

Calculus: Differentiation

Paper 2 · Both

Full notes

Teach it

  • Gradient Function

    Differentiate x^n to get nx^(n-1).

  • Tangents and Normals

    Gradient of tangent = dy/dx at that point.

Key facts

  • Differentiate x^n → nx^(n-1)
  • Constant terms differentiate to 0.
  • Stationary points: dy/dx = 0
  • Tangent gradient = dy/dx

Key terms

Derivative: Rate of change of a function, written dy/dx.
Tangent: Line that touches a curve at one point with same gradient.
Normal: Line perpendicular to the tangent at a point.
Stationary point: Point where gradient is zero (maximum, minimum, or inflection).

Quick check

Differentiate y = 3x^4 - 2x^2 + 5.

2 marks · Paper 2

Focus 3

Circle Theorems (Advanced)

Paper 2 · Both

Full notes

Teach it

  • Alternate Segment Theorem

    Angle between tangent and chord equals angle in alternate segment.

  • Tangent Properties

    Tangent is perpendicular to radius at point of contact.

Key facts

  • Angle at centre = 2 × angle at circumference.
  • Angle in a semicircle = 90°.
  • Alternate segment theorem for tangents.
  • Opposite angles in cyclic quadrilateral sum to 180°.

Key terms

Alternate segment: Segment on opposite side of chord from tangent.
Cyclic quadrilateral: Quadrilateral with all vertices on a circle.
Tangent: Line that touches circle at exactly one point.
Chord: Line segment with both endpoints on circle.

Quick check

Angle at centre is 140°. Find angle at circumference on same arc.

2 marks · Paper 2

Recap prompts

6 min

Say each prompt out loud. If you can’t, revisit the focus card.

  • Explain Coordinate Geometry in three bullet points without notes.
  • Explain Functions & Graphs in three bullet points without notes.

Session checklist

1. Read the focus cards and answer the quick checks.
2. Complete the recap prompts without looking.
3. Finish one flashcard sprint or paper question.

Progress: 0/8 topics completed.

Examiner cue

Label points clearly on diagrams.

Full exam technique

Flashcard sprint

10 cards across 2 decks.

Start flashcards

Stretch topics

If you still have time, hit one of these next.

  • Coordinate GeometryOpen
  • Functions & GraphsOpen