Exam-style practice

Choose your method, connect the parts and explain your conclusions. These original questions include written reasoning and sketches as well as exact answer checks.

Suggested marks guide how much working to show. The site does not automatically award examination marks for proofs, diagrams or methods. Use scaffolded fluency practice when you need a hint first.

Choose a question structure

• An identity without losing solutions

  A-level prerequisite

• Parallel lines and a misleading claim

  Level 2 / FSMQ

• Recovering a point from its image

  Level 2 / FSMQ

• A sketch with roots and a turning point

  Level 2 / FSMQ

• Choosing the branch of an inverse

  Level 2 / FSMQ

• A conjugate and a rationality claim

  Level 2 / FSMQ

• Trapezium estimates and curvature

  FSMQ / prerequisite

• Conditioning on a different population

  FSMQ / statistics

• An optimum and the physical domain

  Level 2 / FSMQ

• A volume claim based on rounded data

  A-level core

• A repeated eigenvalue and a general power

  A-level extension

• A region, a boundary and membership

  A-level core

• A line meeting a complex locus

  A-level core

• Finding every complex root once

  A-level core

• Using a series to locate a different intersection

  A-level core

• A substituted series and its endpoints

  A-level prerequisite

• An unsignposted first-order initial-value problem

  A-level core

• Repeated roots and a forced equation

  A-level core

• Solving a hyperbolic equation with a restriction

  A-level core

• Choosing the interval for a polar petal

  A-level core

• An area minimum constrained by the trace

  A-level core

• A line and a plane: every case

  A-level core

• A closest point on a finite segment

  A-level core

• A full induction argument

  A-level core

• A sum, an induction proof and an application

  A-level core

• Newton iteration and an inadmissible start

  A-level core

• Signed velocities and energy in a collision

  Mechanics option

• A discrete test and its actual significance

  Statistics option

• A shortest route and a changed edge

  Decision option

• A minimum spanning tree and a route distinction

  Decision option

• Precedence, a critical path and spare time

  Decision option

• Fermat’s theorem and an excluded case

  Further Pure option

• A recurrence and its general solution

  Further Pure option

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