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Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling Flashcards
51 question-and-answer cards covering Mathematics: High School Geometry, Statistics, and Modeling as it is examined in Partnership for Assessment of Readiness for College and Careers (PARCC). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics: High School Geometry, Statistics, and Modeling deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What are the volume formulas for a prism/cylinder and for a pyramid/cone?
Prism/cylinder: V = B·h (base area times height). Pyramid/cone: V = ⅓·B·h. For a cylinder V = πr²h; for a cone V = ⅓πr²h.
What are the volume and surface area formulas for a sphere?
Volume = (4/3)πr³; surface area = 4πr².
What is the surface area formula for a cylinder?
Surface area = 2πr² + 2πrh (two circular bases plus the lateral rectangle of height h and width 2πr).
What is Cavalieri's Principle?
If two solids have the same height and equal cross-sectional areas at every level, then they have the same volume.
What two-dimensional shapes result from cross-sections of a cylinder cut parallel versus perpendicular to its base?
A cut parallel to the base yields a circle (congruent to the base); a cut perpendicular to the base (through the axis) yields a rectangle.
What solid is generated by rotating a right triangle about one of its legs, and a rectangle about one of its sides?
Rotating a right triangle about a leg generates a cone; rotating a rectangle about a side generates a cylinder.
What is population density, and how is it modeled with geometry?
Population density = number of people / area (or per unit volume). It is a ratio used to model and compare how concentrated a quantity is over a region, e.g., people per square mile.
In a frequency distribution, what does the shape (skew) tell you about mean vs. median?
In a right-skewed (positive) distribution the mean is greater than the median; in a left-skewed (negative) distribution the mean is less than the median; in a symmetric distribution mean ≈ median.
When should you use the mean and standard deviation versus the median and IQR to summarize data?
Use mean and standard deviation for roughly symmetric data with no outliers; use median and interquartile range (IQR) for skewed data or data with outliers, since they are resistant to extreme values.
How is the interquartile range (IQR) computed, and what is the 1.5·IQR outlier rule?
IQR = Q3 − Q1. A value is an outlier if it is below Q1 − 1.5·IQR or above Q3 + 1.5·IQR.
In a two-way frequency table, what is the difference between a joint, marginal, and conditional relative frequency?
Joint: a cell count relative to the grand total. Marginal: a row or column total relative to the grand total. Conditional: a cell relative to its own row or column total (probability given a category).
What does the correlation coefficient r measure, and what is its range?
r measures the strength and direction of a linear relationship between two quantitative variables; it ranges from −1 to +1, where ±1 is a perfect linear relationship and 0 is no linear relationship.
What is the key distinction between correlation and causation?
Correlation indicates that two variables are associated, but it does not establish that one causes the other; causation can only be inferred from a well-designed randomized experiment, not from observational correlation.
In the empirical (68-95-99.7) rule for a normal distribution, what percent of data falls within 1, 2, and 3 standard deviations of the mean?
About 68% within 1 SD, about 95% within 2 SD, and about 99.7% within 3 SD of the mean.
What is the difference between a sample survey, an experiment, and an observational study?
A sample survey estimates a population characteristic from a sample; an experiment imposes a treatment to test cause and effect; an observational study records data without imposing treatments and cannot establish causation.
Why is random assignment important in an experiment, and random selection in a survey?
Random assignment balances confounding variables across treatment groups so differences can be attributed to the treatment (causation). Random selection makes a sample representative so results generalize to the population.
What is the purpose of using simulation to evaluate whether a result is statistically significant?
Simulation generates the distribution of outcomes expected by chance under a model; if the observed result is rare (in the tails) of that simulated distribution, it is statistically significant and unlikely due to chance alone.
What is the addition rule for the probability of A or B?
P(A or B) = P(A) + P(B) − P(A and B). If A and B are mutually exclusive, P(A and B) = 0, so P(A or B) = P(A) + P(B).
What is the formula for conditional probability P(A | B)?
P(A | B) = P(A and B) / P(B), provided P(B) > 0. It is the probability of A given that B has occurred.
What is the multiplication rule for P(A and B), and how does it simplify for independent events?
P(A and B) = P(A)·P(B | A). If A and B are independent, P(B | A) = P(B), so P(A and B) = P(A)·P(B).
What condition defines two events A and B as independent?
A and B are independent if P(A | B) = P(A) (equivalently P(B | A) = P(B), or P(A and B) = P(A)·P(B)). Knowing one occurred does not change the other's probability.
What is the complement rule in probability?
P(not A) = 1 − P(A). The probability that an event does not occur is one minus the probability that it does.
What does it mean for two events to be mutually exclusive (disjoint)?
They cannot occur at the same time, so P(A and B) = 0. Mutually exclusive events with nonzero probability are necessarily dependent.
How can a two-way table be used to determine whether two categorical variables are independent?
Compare conditional relative frequencies: if the conditional distribution of one variable is the same across all categories of the other (e.g., P(A|B) = P(A|not B) = P(A)), the variables are independent; if they differ, the variables are associated.
What this deck covers
The Mathematics: High School Geometry, Statistics, and Modeling deck follows the Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling syllabus — 5 chapters and 15 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.2 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 152 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: High School Geometry, Statistics, and Modeling flashcards FAQ
How many Mathematics: High School Geometry, Statistics, and Modeling flashcards are in this Partnership for Assessment of Readiness for College and Careers (PARCC) deck?
51 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these Partnership for Assessment of Readiness for College and Careers (PARCC) flashcards free?
Yes. The preview here is free to read with no signup, and the full 51-card deck is free inside the Examius app.
What do the Mathematics: High School Geometry, Statistics, and Modeling cards cover?
They follow the Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling syllabus — 5 chapters and 15 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.