CogAT Level 11 cheat sheet

Analogy format is A : B :: C : D; the relationship between A and B must hold in the same direction and same logical type between C and D.

Common analogy relationships: synonym, antonym, part-to-whole, whole-to-part, category-to-member, member-to-category, function, cause-to-effect, degree, and sequence.

Classification items present three or four words sharing one hidden category; the answer is the option that does NOT belong, so test each option against the shared category before choosing.

Sentence completion: read the whole sentence first, predict a word for the blank, then match the prediction to options; a two-blank item requires both words to fit, and one wrong word eliminates the option.

Signal words flip meaning: 'although', 'despite', 'except', and 'unlike' indicate contrast, so the blank likely takes an antonym of the stated idea; 'because', 'since', and 'and' indicate continuation or sameness.

Degree relationships (warm : hot :: cool : cold) and sequence relationships (first : second :: third : fourth) are frequently confused with synonym pairs; check whether intensity or order matters.

Verb analogies often encode function (knife : cut :: pen : write); noun analogies more often encode category or part-whole (wheel : car :: petal : flower).

If two options seem correct, prefer the one whose relationship is narrower and more specific, since broad relationships (both are living things) fit too many pairs.

Number series: compute consecutive differences first; constant difference means arithmetic, constant ratio means geometric, and changing differences mean look at second differences or alternating rules.

Alternating series split into two interleaved sequences (positions 1,3,5 and 2,4,6); each subsequence follows its own rule, so check odd and even positions separately.

Square and cube patterns: 1, 4, 9, 16, 25 is n squared; 1, 8, 27, 64 is n cubed; 2, 4, 8, 16, 32 is doubling; 1, 1, 2, 3, 5, 8 is the Fibonacci rule (each term is the sum of the two before).

Number analogy format is A : B :: C : ?; identify the operation linking A to B, then apply the identical operation to C, keeping order of operations the same.

Number puzzle (equation) items give a rule such as a + b = c built from the two given numbers; test candidate rules on every row before applying the rule to the row with the unknown.

Order of operations: multiplication and division before addition and subtraction; when a puzzle rule is ambiguous, prefer the simplest rule that fits all given examples.

Divisibility shortcuts: by 2 last digit even; by 3 digit sum divisible by 3; by 5 last digit 0 or 5; by 9 digit sum divisible by 9; by 4 last two digits divisible by 4.

Percent and fraction benchmarks: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/10 = 10%, 1/8 = 12.5%; use these to compare quantities without full computation.

Figure analogy format is A : B :: C : ?; describe the change from A to B as a transformation (rotation amount, reflection axis, size change, shading change, added or removed element) and apply it to C.

Rotation must be tracked by direction (clockwise vs counterclockwise) and amount (90, 180, 270 degrees); a reflection looks similar but reverses orientation, so compare a landmark feature such as a notch or dot.

Figure classification: find the attribute shared by the given figures (number of sides, symmetry, open vs closed, straight vs curved lines, shading pattern, number of internal regions) and choose the option matching it.

Matrix items are grids with a rule across rows and down columns; check the row rule first, then confirm it holds down the column before selecting the missing cell.

Paper folding: trace the punch through each unfold step; the number of holes doubles at each unfold, so a single punch through n folds can produce up to 2^n holes.

A fold along a vertical line mirrors holes left-right; a fold along a horizontal line mirrors holes up-down; holes on the fold line itself are not duplicated.

Counting rules: closed polygons have the same number of sides and vertices; a figure with n straight lines can form at most n(n-1)/2 intersection points.

Symmetry check: a figure has line symmetry if a fold maps it onto itself, and rotational symmetry if a turn of less than 360 degrees maps it onto itself; use these to separate otherwise similar options.