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AMUEEE Mathematics Flashcards
54 question-and-answer cards covering Mathematics as it is examined in AMUEEE. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the standard equation of an ellipse with a > b and its eccentricity.
x²/a² + y²/b² = 1; eccentricity e = √(1 − b²/a²), with 0 < e < 1.
State the standard equation of a hyperbola centered at origin and its eccentricity range.
x²/a² − y²/b² = 1; eccentricity e = √(1 + b²/a²), with e > 1.
What is the eccentricity of a circle and a parabola?
Circle: e = 0; Parabola: e = 1.
Give the length of the latus rectum of the parabola y² = 4ax.
Length of latus rectum = 4a.
What is the general equation of a circle with centre (h, k) and radius r?
(x − h)² + (y − k)² = r².
State the limit definition of the derivative of f at x.
f'(x) = lim_{h→0} [f(x+h) − f(x)] / h, when the limit exists.
What is the value of lim_{x→0} (sin x)/x?
1 (x in radians).
State the product rule for differentiation.
d/dx[u·v] = u'v + uv' (where u, v are functions of x).
State the quotient rule for differentiation.
d/dx[u/v] = (u'v − uv')/v².
What is lim_{x→0} (e^x − 1)/x?
1.
Give the derivative of xⁿ with respect to x.
d/dx(xⁿ) = n·x^(n−1) (power rule).
State the three conditions for a function f to be continuous at x = a.
f(a) is defined; lim_{x→a} f(x) exists; and lim_{x→a} f(x) = f(a).
State the chain rule for differentiating a composite function f(g(x)).
d/dx f(g(x)) = f'(g(x))·g'(x).
What is the relationship between differentiability and continuity?
If a function is differentiable at a point, it is continuous there; but continuity does not imply differentiability.
Give the derivative of ln x and of e^x.
d/dx(ln x) = 1/x (x > 0); d/dx(e^x) = e^x.
What is logarithmic differentiation used for?
To differentiate functions of the form [f(x)]^{g(x)} or products/quotients of many factors, by taking ln of both sides first.
In mathematical reasoning, what is a 'statement' (mathematically acceptable statement)?
A sentence that is either true or false but not both; ambiguous or opinion-based sentences are not statements.
What is the negation of the statement 'p: 2 is an even number'?
~p: '2 is not an even number' (or 'It is false that 2 is an even number').
Define a compound statement and name the common connecting words.
A statement formed by combining two or more statements using connectives: 'and', 'or', 'if-then', 'if and only if'.
Distinguish between the quantifiers 'There exists' and 'For all'.
'For all' (∀) is universal — true for every element; 'There exists' (∃) is existential — true for at least one element.
What does it mean to validate a statement of the form 'if p then q' by the direct method?
Assume p is true and show by a logical chain of steps that q must then be true.
Describe validating 'if p then q' by contrapositive.
Prove the contrapositive '~q ⇒ ~p', which is logically equivalent to 'p ⇒ q'.
How do you validate a statement using proof by contradiction (reductio ad absurdum)?
Assume the statement is false (assume ~p), then derive a logical contradiction, forcing p to be true.
How can you show a statement of the form 'for all x, p(x)' is false?
By giving a counterexample — a single case where p(x) fails — which disproves the universal claim.
What this deck covers
The Mathematics deck follows the AMUEEE Mathematics syllabus — 5 chapters and 10 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.8 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 65 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Mathematics flashcards FAQ
How many Mathematics flashcards are in this AMUEEE deck?
54 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these AMUEEE flashcards free?
Yes. The preview here is free to read with no signup, and the full 54-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the AMUEEE Mathematics syllabus — 5 chapters and 10 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.