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IAT Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in IAT. 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.
What is the standard equation of a circle with centre (h, k) and radius r?
(x − h)² + (y − k)² = r².
Give the standard equation and eccentricity range for an ellipse and a hyperbola.
Ellipse: x²/a² + y²/b² = 1, eccentricity e < 1. Hyperbola: x²/a² − y²/b² = 1, eccentricity e > 1. (Parabola e = 1.)
What is the standard equation of a parabola opening rightward, and its focus and directrix?
y² = 4ax; focus (a, 0); directrix x = −a.
State the distance formula between two points in three-dimensional space.
d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²].
What is the section formula for a point dividing the join of (x₁,y₁,z₁) and (x₂,y₂,z₂) in ratio m:n internally?
((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n), (mz₂+nz₁)/(m+n)).
State the standard limit lim(x→0) (sin x)/x.
lim(x→0) (sin x)/x = 1 (x in radians).
What are the derivatives of sin x, cos x, and tan x?
d/dx(sin x) = cos x; d/dx(cos x) = −sin x; d/dx(tan x) = sec²x.
State the product rule and quotient rule for differentiation.
Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v − uv')/v².
What three conditions must hold for a function f to be continuous at x = a?
(1) f(a) is defined; (2) lim(x→a) f(x) exists; (3) lim(x→a) f(x) = f(a).
State the chain rule for differentiating a composite function y = f(g(x)).
dy/dx = f'(g(x)) · g'(x), i.e., dy/dx = (dy/du)(du/dx).
What is the derivative of log_e x and of e^x?
d/dx(ln x) = 1/x; d/dx(e^x) = e^x.
How do you find whether a critical point gives a local maximum or minimum using the second derivative test?
At a point where f'(x)=0: if f''(x) < 0 it is a local maximum; if f''(x) > 0 it is a local minimum; if f''(x) = 0 the test fails.
What does it mean for a function to be increasing or decreasing on an interval in terms of its derivative?
f is increasing where f'(x) > 0 and decreasing where f'(x) < 0 on the interval.
State the power rule for integration: ∫ xⁿ dx.
∫ xⁿ dx = x^(n+1)/(n+1) + C, for n ≠ −1 (for n = −1, ∫ dx/x = ln|x| + C).
State the formula for integration by parts.
∫ u v dx = u ∫v dx − ∫ (u' ∫v dx) dx; commonly ∫ u dv = uv − ∫ v du.
What is the fundamental theorem of calculus (evaluation part) for a definite integral?
∫_a^b f(x) dx = F(b) − F(a), where F is an antiderivative of f.
How do you find the area bounded by a curve y = f(x), the x-axis, and lines x = a and x = b?
Area = ∫_a^b |f(x)| dx (taking absolute value where the curve is below the axis).
What is the order and degree of a differential equation?
Order: the order of the highest derivative present. Degree: the power of the highest-order derivative when the equation is polynomial in derivatives (free of radicals/fractions).
State the general solution method for a linear first-order differential equation dy/dx + Py = Q.
Use integrating factor IF = e^(∫P dx); then solution is y·(IF) = ∫ Q·(IF) dx + C.
How are the dot product and cross product of two vectors a and b defined in terms of the angle θ between them?
Dot product: a·b = |a||b|cosθ (a scalar). Cross product: |a×b| = |a||b|sinθ, directed perpendicular to both (a vector).
What is the condition for two non-zero vectors to be perpendicular and to be parallel?
Perpendicular: a·b = 0. Parallel: a×b = 0 (or a = λb for some scalar λ).
What are direction cosines of a line, and what relation do they satisfy?
Direction cosines l, m, n are the cosines of angles the line makes with the x, y, z axes; they satisfy l² + m² + n² = 1.
In linear programming, what is the corner point theorem for finding the optimal solution?
If the feasible region is bounded, the objective function attains its maximum and minimum at corner (vertex) points of the feasible region.
In mathematical reasoning, what is the contrapositive of the statement 'if p then q', and how does its truth relate to the original?
The contrapositive is 'if not q then not p'. It is logically equivalent to the original statement (both have the same truth value).
What this deck covers
The Mathematics deck follows the IAT Mathematics syllabus — 7 chapters and 22 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 7.1 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 80 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 IAT deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these IAT flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the IAT Mathematics syllabus — 7 chapters and 22 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.