CogAT Level 12 cheat sheet

Verbal Analogies follow A : B :: C : D; the relationship between A and B must hold in the same direction and same category between C and D (function, part-whole, degree, category, or antonym).

Sentence Completion: cover the blank, predict a word from context clues, then test each option; a word that fits grammatically but reverses the sentence's logic is wrong.

Verbal Classification (Odd One Out): three or more words share a category or a common attribute; the answer is the word that lacks that shared attribute, not the least familiar word.

Antonym items reward the opposite in the same part of speech and intensity; a related-but-not-opposite word (e.g., a synonym) is a common trap.

Degree relationships (warm : hot :: cool : cold) differ from category relationships (rose : flower); naming the exact relationship type before choosing prevents near-miss errors.

Part-to-whole items can run either direction (wheel : car vs car : wheel); match the direction used in the stem, not the more natural-sounding one.

When two options seem to fit an analogy, prefer the one that keeps the same grammatical form and same specificity level as the stem pair.

Number Series: compute consecutive differences first; if differences are constant it is arithmetic, if ratios are constant it is geometric, and if differences themselves form a pattern, apply that second-level rule.

Alternating series interleave two sequences (positions 1,3,5 and 2,4,6); check each subsequence separately before concluding the series is irregular.

Number Analogies: find the operation linking the first pair (e.g., x3, +12, square), then apply the identical operation to the third number to get the answer.

Number Puzzles supply a rule such as a total, a product, or a relationship between two unknowns; translate each sentence into an equation and solve for the single unknown asked.

Quantitative Comparison: you may add, subtract, multiply, or divide both sides by the same positive number; multiplying or dividing by a negative flips the comparison.

Estimate before computing: rounding to the nearest ten or hundred usually eliminates all but one answer in CogAT-style multiple choice, saving time on multi-step items.

Perimeter and area of rectangles: P = 2(l + w) and A = l x w; when the perimeter is fixed, area is largest when the rectangle is a square.

Average (mean) = sum of values / number of values; total = mean x count, which solves most missing-value and combined-group questions.

Figure Analogies: identify the transformation from the first figure to the second (rotation, reflection, size change, shading, added or removed part), then apply exactly that transformation to the third figure.

Figure Classification: find the attribute shared by the majority of figures (number of sides, symmetry, open vs closed, curved vs straight lines, filled vs outlined) and exclude the figure that breaks it.

Paper Folding: unfold step by step in reverse order; each unfold mirrors the hole pattern across the fold line, so the number of holes doubles with each fold that crosses the hole.

Punch-hole counts: a hole punched through one layer after n folds produces up to 2^n holes when fully unfolded, fewer if the hole lies on a fold line.

Figure matrices (2x2 or 3x3): the rule across rows equals the rule down columns; verify a candidate answer against both directions before selecting.

Rotation preserves shape and orientation of features; reflection reverses left-right orientation, so a mirrored figure is never the same as a rotated one.

Cube counting and cube folding: opposite faces never appear adjacent, so eliminate any answer showing two faces that are opposite on the net.

Symmetry checks: a line of symmetry maps the figure onto itself; counting symmetry lines is often the fastest discriminator among similar-looking options.