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TMUA Flow

Course

Each lesson starts with a figure you can move, and ends with questions in the exam's own format. Take them in order, or start where you need it most.

Paper 1

Applications of Mathematical Knowledge

20 questions75 minutes22 of 22 lessons ready

1Algebra

  1. 1Complete the square, find the vertex11 minReadyNext
  2. 2The discriminant as a region12 minReady
  3. 3Factors and remainders10 minReady
  4. 4Inequalities you can see12 minReady

2Sequences and series

  1. 5Sums you can rearrange11 minReady
  2. 6Binomial coefficients as paths12 minReady
  3. 7Recurrences that settle11 minReady

3Coordinate geometry

  1. 8Gradients, parallel and perpendicular11 minReady
  2. 9Circles, tangents and angles13 minReady

4Trigonometry

  1. 10The unit circle drives everything13 minReady
  2. 11One side, one angle, two triangles12 minReady
  3. 12Radians are lengths11 minReady

5Exponentials and logarithms

  1. 13A curve and its mirror12 minReady
  2. 14Logs turn products into sums11 minReady

6Calculus

  1. 15From secant to tangent11 minReady
  2. 16Reading a graph through its gradient13 minReady
  3. 17Signed area and the integral11 minReady
  4. 18The trapezium rule11 minReady
  5. 19Why a circle's area is πr²10 minReady

7Graphs

  1. 20Transformations in order11 minReady

8Number, geometry and probability

  1. 21Probability as area13 minReady
  2. 22Exact arithmetic without a calculator12 minReady

Paper 2

Mathematical Reasoning

20 questions75 minutes11 of 11 lessons ready

1The logic of statements

  1. 1Which way does the arrow point?12 minReadyNext
  2. 2If, only if, if and only if11 minReady
  3. 3All, some, none: quantifiers and negation11 minReady

2Proof

  1. 4One counterexample is enough10 minReady
  2. 5Proof by cases11 minReady
  3. 6Proof by contradiction12 minReady
  4. 7Putting a proof in order12 minReady

3Errors in proofs

  1. 8Where did the proof break?11 minReady
  2. 9Dividing, squaring and assuming12 minReady

4Reasoning at pace

  1. 10Statements I, II and III14 minReady
  2. 11Conjecture from small cases12 minReady