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Further Maths: definitions and slips flashcards

11 cards drawn from 10 lessons: 3 definitions, 2 recall prompts, 3 check-yourself questions and 3 spot-the-error cards. The wordings that earn marks and the traps that lose them. Rate each answer to set a shorter or longer interval before the card is due again.

Further Maths · all 271 maths cards

How the five kinds differ

Standard results ask for a formula or value that may need to be recalled. Definitions ask for a mathematical term to be stated precisely. Recall prompts ask for a rule, condition or method. Check yourself cards contain a short question and answer. Spot the error cards ask you to correct an inaccurate claim.

Every card in this deck

Click any card to try it in the player above; the card itself links the lesson that teaches it.

• principal argumentDefine
• invariant lineDefine
• improper integralDefine
• State the three ways to write a plane, and how to move between themRecall
• Evaluate (1 + i)⁴ without expanding four brackets.Check
• Find the distance from the origin to the plane 2x + 2y + z = 9.Check
• Find the mean value of f(x) = x³ on [0, 2].Check
• Differentiating cosh introduces a minus sign, just as cos does.Spot the error
• Polar area is the integral of r dθ, by analogy with area under a graph.Spot the error
• Once the inductive step is proved, the statement holds for all n.Spot the error
• State the trick for an induction divisibility proofRecall

The lessons these cards come from

• Areas with polar coordinates
• Calculus with hyperbolic functions
• De Moivre's theorem and trigonometric identities
• Induction: divisibility and matrices
• Intersections, angles and distances
• Lines and planes in three dimensions
• Mean values and improper integrals
• Modulus, argument and loci
• Proof by induction: sums and series
• Systems of equations and invariance

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