CogAT Grades 9-12 flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Analogy bridge sentence

A full sentence stating the exact relationship between the first pair, such as "a hammer is used to drive a nail." Applying the same sentence to each answer choice reveals which pair matches.

Classification odd-one-out

A verbal item giving five words where four share a single defining property. The answer is the one word that fails that property, so the rule must fit exactly four words.

Sentence completion polarity

The direction a blank takes, positive or negative, set by signal words. Contrast words like although or despite flip the expected meaning; cause words like because or therefore continue it.

Double-blank completion rule

Both blanks must be satisfied by the same answer choice at once. An option fitting only one blank is incorrect no matter how natural that single blank reads.

Degree relationship

An analogy link based on intensity, such as warm is to hot as cool is to cold. The correct answer must match both the direction and the relative magnitude of the stem pair.

Part-to-whole analogy

A relationship where one term is a component of the other, such as branch to tree. Nested versions exist, like tree to branch as branch to twig, and the hierarchy level must match.

Connotation versus denotation

Denotation is a word's literal meaning; connotation is its emotional charge. Two options may share meaning but differ in tone, and the sentence's attitude selects between them.

Necessary inference

A conclusion that must be true given the stated text alone. Any answer requiring one additional unstated assumption lies outside the passage and is incorrect.

Scope words in answers

Qualifiers such as all, never, only, and must create strong claims needing strong support, while some, may, and often are weaker and easier to justify from a passage.

Prefix direction clues

Word beginnings that signal meaning, such as bene and mal for good and bad, pre and post for before and after, and inter and intra for between and within.

Consecutive difference method

Subtract each term from the next in a number series. A constant result means linear growth; a changing result requires differencing again to expose a quadratic pattern.

Interleaved number series

A series built from two alternating subsequences, often at odd and even positions. Split the terms into two lists and solve each pattern separately before recombining.

Arithmetic sequence formula

For a sequence with constant difference d, the nth term equals the first term plus (n minus 1) times d. The sum of n terms is n times the average of first and last.

Geometric sequence ratio

A series where each term is multiplied by a fixed ratio. Divide consecutive terms to confirm the ratio, then multiply the last term by it to find the next.

Fibonacci-type series

A series where each term equals the sum of the two preceding terms. Test it by adding the first two terms and checking whether the result equals the third.

Harmonic mean for speeds

For equal distances traveled at speeds a and b, average speed equals 2ab divided by (a plus b). It is always lower than the simple average of the two speeds.

Percentage change formula

Change equals new minus old, divided by old, times 100. Successive percentage changes multiply rather than add, so a 20 percent rise then fall is a net 4 percent loss.

Set union formula

Total equals group A plus group B minus the overlap, plus any members in neither group. It solves two-group counting problems without listing individual members.

Contrapositive logic rule

If P then Q is logically equivalent to if not Q then not P. The reversed statement, if Q then P, is not valid and appears frequently as a distractor.

Divisibility shortcuts

A number is divisible by 3 or 9 if its digits sum to a multiple of 3 or 9, by 4 if the last two digits form a multiple of 4, and by 6 if divisible by both 2 and 3.

Ratio part-to-whole conversion

A part-to-part ratio such as 3 to 5 has 8 total parts. Divide the given total by the number of parts to find one part's value, then scale each share.

Weighted average formula

The sum of each value multiplied by its weight, divided by the total of all weights. A simple average is correct only when every weight is equal.

Pythagorean triples

Whole-number right triangle sets including 3-4-5, 5-12-13, and 8-15-17, plus their multiples. Recognizing them lets you find a missing side without computation.

Scale factor area rule

When a figure's lengths are multiplied by k, its area multiplies by k squared and its volume by k cubed. This applies to similar figures and scale drawings.

Matrix row and column rule

In a figure matrix, the transformation must hold both across each row and down each column. The correct answer satisfies both directions simultaneously.

Rotation versus reflection test

Rotating a figure preserves its handedness, while mirroring reverses it. An asymmetric feature such as a dot or notch reveals which transformation occurred.

Paper fold hole count

Each fold doubles the layers at the punched point, so a punch through all layers yields two to the k holes for k folds crossed. Unfold in reverse order, mirroring across each crease.

Cube net opposite faces

In a cube net, opposite faces never share an edge. Identify the three opposite pairs first, then eliminate any answer showing two opposite faces adjacent.

Superposition with cancellation

A figure rule where overlapping parts of two figures cancel while non-overlapping parts remain. Compare where lines disappear, not only where new lines appear.

Symmetry classification

Grouping figures by their number of lines of symmetry and rotational symmetry order. Figures sharing the same symmetry profile belong to the same class.

Enclosed region count

The number of bounded areas inside a figure, distinct from its number of lines or sides. It is a frequent discriminating attribute in figure classification and series items.

Embedded figure scanning

Locating a target shape hidden inside a larger drawing by searching first for its most distinctive corner or angle, since that feature is hardest to disguise.