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🇺🇸 ACT (American College Testing) · flashcards
ACT (American College Testing) Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in ACT (American College Testing). 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.
For a quadratic in form y = ax^2 + bx + c, what is the x-coordinate of the vertex?
x = -b/(2a). Substitute back to find the y-coordinate of the vertex.
What does the leading coefficient's sign tell you about a parabola y = ax^2 + bx + c?
If a > 0 the parabola opens upward (vertex is a minimum); if a < 0 it opens downward (vertex is a maximum).
What causes a vertical asymptote and a hole in a rational function?
A vertical asymptote occurs where the denominator equals zero (and the factor does not cancel); a hole occurs where a factor cancels from both numerator and denominator.
What is the domain restriction for a square-root function sqrt(g(x))?
The radicand must be non-negative: g(x) >= 0. The domain is all x satisfying that inequality.
What does the exponential function y = a*b^x model, and what determines growth vs decay?
It models exponential growth/decay with initial value a. If b > 1 it grows; if 0 < b < 1 it decays.
How are logarithms and exponents related (definition of log)?
log_b(x) = y means b^y = x. A logarithm answers 'to what power must the base be raised to get x?'
State the three main logarithm rules (product, quotient, power).
log(mn) = log m + log n; log(m/n) = log m - log n; log(m^p) = p * log m.
How does y = f(x) + k versus y = f(x - h) transform a graph?
f(x) + k shifts the graph vertically (up if k > 0, down if k < 0); f(x - h) shifts horizontally (right if h > 0, left if h < 0).
What transformation does y = -f(x) versus y = f(-x) produce?
y = -f(x) reflects the graph across the x-axis; y = f(-x) reflects it across the y-axis.
What is the sum of the interior angles of a triangle, and of an n-sided polygon?
A triangle's interior angles sum to 180 degrees; an n-sided polygon's interior angles sum to (n - 2) * 180 degrees.
What are complementary and supplementary angles?
Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees.
What does it mean for two triangles to be similar, and what follows about their sides?
Similar triangles have equal corresponding angles; their corresponding sides are proportional (same ratio).
What are the circumference and area formulas for a circle of radius r?
Circumference C = 2*pi*r (or pi*d); Area A = pi*r^2.
How is an inscribed angle related to the central angle subtending the same arc?
An inscribed angle is half the measure of the central angle (and half the intercepted arc) that subtends the same arc.
What is the equation of a circle with center (h, k) and radius r?
(x - h)^2 + (y - k)^2 = r^2.
State the area formulas for a triangle, rectangle, and trapezoid.
Triangle: (1/2)*base*height. Rectangle: length*width. Trapezoid: (1/2)*(b1 + b2)*height.
What are the volume formulas for a rectangular box, a cylinder, and a sphere?
Box: l*w*h. Cylinder: pi*r^2*h. Sphere: (4/3)*pi*r^3.
What is the distance formula between points (x1, y1) and (x2, y2)?
d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
What is the midpoint formula for the segment from (x1, y1) to (x2, y2)?
Midpoint = ((x1 + x2)/2, (y1 + y2)/2) — average the x-coordinates and the y-coordinates.
How are the slopes of parallel lines and perpendicular lines related?
Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (their product is -1).
State the Pythagorean theorem and the side ratios of 30-60-90 and 45-45-90 triangles.
a^2 + b^2 = c^2 (c = hypotenuse). 45-45-90 sides: 1 : 1 : sqrt(2). 30-60-90 sides: 1 : sqrt(3) : 2.
How do you find the mean, median, and mode of a data set?
Mean = sum of values divided by count. Median = middle value when ordered (average of two middle values if even count). Mode = most frequently occurring value.
What is the range of a data set, and what does standard deviation measure?
Range = maximum value minus minimum value. Standard deviation measures the spread/dispersion of values about the mean (larger means more spread out).
What is the basic probability formula, and how do you find the probability of independent events both occurring?
P(event) = (favorable outcomes)/(total outcomes). For independent events A and B both occurring, multiply: P(A and B) = P(A)*P(B). The SOH-CAH-TOA ratios are sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
What this deck covers
The Mathematics deck follows the ACT (American College Testing) Mathematics syllabus — 5 chapters and 23 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 101 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 ACT (American College Testing) 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 ACT (American College Testing) 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 ACT (American College Testing) Mathematics syllabus — 5 chapters and 23 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.