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CAT Quantitative Aptitude: Modern Mathematics Flashcards
50 question-and-answer cards covering Quantitative Aptitude: Modern Mathematics as it is examined in CAT. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Aptitude: Modern Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the addition rule of probability for any two events.
P(A∪B) = P(A) + P(B) - P(A∩B). For mutually exclusive events, P(A∩B) = 0, so P(A∪B) = P(A) + P(B).
Define mutually exclusive events.
Two events are mutually exclusive if they cannot occur simultaneously; their intersection is empty, so P(A∩B) = 0.
Define independent events and give the multiplication rule for them.
Two events are independent if the occurrence of one does not affect the other. For independent events, P(A∩B) = P(A) x P(B).
What is the difference between mutually exclusive and independent events?
Mutually exclusive events cannot both happen (P(A∩B)=0). Independent events can both happen and one does not influence the other (P(A∩B)=P(A)P(B)). Two events with nonzero probability cannot be both.
Define conditional probability and give its formula.
The probability of A given B has occurred: P(A|B) = P(A∩B) / P(B), provided P(B) > 0.
State the general multiplication rule of probability using conditional probability.
P(A∩B) = P(A) x P(B|A) = P(B) x P(A|B).
State Bayes' Theorem for two hypotheses.
P(A|B) = [P(B|A) P(A)] / P(B), where P(B) = P(B|A)P(A) + P(B|A')P(A'). It updates the probability of A after observing B.
State the Law of Total Probability.
If B1, B2, ..., Bn partition the sample space, then P(A) = sum over i of P(A|Bi) x P(Bi).
Define a random variable.
A random variable is a function that assigns a numerical value to each outcome of a random experiment. It can be discrete (countable values) or continuous (values over an interval).
Define expected value (mean) of a discrete random variable.
E(X) = sum of [xi x P(xi)] over all values; it is the long-run average value weighted by probabilities.
Give the formula for the variance of a random variable.
Var(X) = E(X^2) - [E(X)]^2 = E[(X - mean)^2]. Standard deviation is the square root of the variance.
What conditions define a binomial probability distribution?
A fixed number n of independent trials, each with only two outcomes (success/failure), with constant success probability p across trials.
Give the binomial probability formula for k successes in n trials.
P(X = k) = nCk x p^k x (1 - p)^(n - k), where p is the probability of success.
What are the mean and variance of a binomial distribution?
Mean = np; Variance = np(1 - p) = npq, where q = 1 - p.
Define a sample space and an event in probability.
The sample space is the set of all possible outcomes of an experiment. An event is any subset of the sample space.
Define the union, intersection, and difference of two sets.
Union A∪B = elements in A or B; Intersection A∩B = elements in both A and B; Difference A - B = elements in A but not in B.
Define the complement of a set and the empty set.
The complement A' is all elements in the universal set not in A. The empty set (null set) has no elements and is a subset of every set.
State De Morgan's Laws for sets.
(A∪B)' = A' ∩ B' and (A∩B)' = A' ∪ B'.
How do you find the number of elements in exactly one of two sets A and B?
Exactly one = |A| + |B| - 2|A∩B| = |A∪B| - |A∩B|.
Define a power set and give its cardinality.
The power set is the set of all subsets of a set. For a set with n elements, the power set has 2^n elements.
State the Binomial Theorem for (a + b)^n.
(a + b)^n = sum from k=0 to n of [nCk x a^(n-k) x b^k]. The coefficients nCk are the binomial coefficients.
Give the formula for the general (r+1)th term in the expansion of (a + b)^n.
T(r+1) = nCr x a^(n-r) x b^r.
How many terms are in the expansion of (a + b)^n, and what is the sum of its coefficients?
There are (n + 1) terms. The sum of all binomial coefficients is 2^n (set a = b = 1).
How do you find the middle term(s) in the expansion of (a + b)^n?
If n is even, there is one middle term: the (n/2 + 1)th term. If n is odd, there are two middle terms: the ((n+1)/2)th and ((n+3)/2)th terms.
What this deck covers
This deck covers the Quantitative Aptitude: Modern Mathematics portion of the CAT syllabus in question-and-answer form. Browse the full CAT syllabus to see how it fits with the rest.
Answers are written to be recallable, not just readable — averaging about 102 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.
Quantitative Aptitude: Modern Mathematics flashcards FAQ
How many Quantitative Aptitude: Modern Mathematics flashcards are in this CAT 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 CAT 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 Quantitative Aptitude: Modern Mathematics cards cover?
They follow the Quantitative Aptitude: Modern Mathematics portion of the CAT syllabus, in question-and-answer form.
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.