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🇺🇸 High School Diploma · flashcards
High School Diploma Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in High School Diploma. 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 a function, and what does the vertical line test determine?
A relation where each input (x) has exactly one output (y). The vertical line test confirms a graph is a function if no vertical line crosses it more than once.
What are the domain and range of a function?
Domain is the set of all valid inputs (x-values); range is the set of all resulting outputs (y-values).
What is a vertical asymptote of a rational function, and where does it occur?
A vertical line the graph approaches but never touches; it occurs where the denominator equals zero (and the numerator does not).
State the Remainder Theorem and the Factor Theorem.
Remainder Theorem: dividing a polynomial f(x) by (x − a) gives remainder f(a). Factor Theorem: (x − a) is a factor of f(x) if and only if f(a) = 0.
What is the general form of an exponential function, and what distinguishes growth from decay?
f(x) = a·b^x (a ≠ 0, b > 0, b ≠ 1). Growth when b > 1; decay when 0 < b < 1.
How are logarithms and exponents related (definition of log)?
log_b(x) = y means b^y = x. A logarithm is the inverse of exponentiation.
State the three main logarithm laws (product, quotient, power).
log(xy) = log x + log y; log(x/y) = log x − log y; log(x^n) = n·log x.
Define the imaginary unit i and state i².
i = √(−1), so i² = −1.
How do you add complex numbers, and what is the complex conjugate of a + bi?
Add real and imaginary parts separately: (a+bi)+(c+di) = (a+c)+(b+d)i. The conjugate of a + bi is a − bi.
What is the explicit formula for the nth term of an arithmetic sequence?
a_n = a_1 + (n − 1)d, where d is the common difference.
What is the explicit formula for the nth term of a geometric sequence?
a_n = a_1 · r^(n−1), where r is the common ratio.
What is the sum of a finite arithmetic series of n terms?
S_n = n(a_1 + a_n)/2, or equivalently n/2 · [2a_1 + (n−1)d].
What is the sum of an infinite geometric series, and when does it converge?
S = a_1 / (1 − r), valid only when |r| < 1.
Define mean, median, and mode.
Mean: the arithmetic average. Median: the middle value when data is ordered. Mode: the most frequently occurring value.
What does standard deviation measure, and how does it relate to variance?
It measures the spread of data around the mean. Standard deviation is the square root of the variance.
State the probability formula for the union of two events, P(A or B).
P(A or B) = P(A) + P(B) − P(A and B). For mutually exclusive events, P(A and B) = 0.
What is the formula for conditional probability P(A | B)?
P(A | B) = P(A and B) / P(B), for P(B) ≠ 0.
What is the difference between a population and a sample, and what is random sampling?
A population is the entire group of interest; a sample is a subset studied. Random sampling gives every member an equal chance of selection to reduce bias.
In experimental design, what is the difference between an observational study and a controlled experiment?
An observational study records data without intervention; a controlled experiment imposes a treatment to establish cause-and-effect, using control and treatment groups.
What is the correlation coefficient r, and what range of values can it take?
A measure of the strength and direction of a linear relationship between two variables, ranging from −1 (perfect negative) to +1 (perfect positive); 0 means no linear correlation.
What does the slope of a least-squares regression line represent in bivariate data?
The predicted change in the response variable (y) for each one-unit increase in the explanatory variable (x).
Define the six trigonometric ratios using SOH-CAH-TOA and reciprocals.
sin = opp/hyp, cos = adj/hyp, tan = opp/adj; csc = 1/sin, sec = 1/cos, cot = 1/tan.
State the Pythagorean trig identity and the definition of one radian.
sin²θ + cos²θ = 1. One radian is the angle subtending an arc equal in length to the radius; 180° = π radians.
What is the intuitive meaning of the limit of f(x) as x approaches a?
The value f(x) gets arbitrarily close to as x approaches a (from both sides), regardless of whether f(a) itself is defined.
What this deck covers
The Mathematics deck follows the High School Diploma Mathematics syllabus — 5 chapters and 24 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 99 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 High School Diploma 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 High School Diploma 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 High School Diploma Mathematics syllabus — 5 chapters and 24 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.