IQ test practice questions, with worked answers
One worked example of every question type used on this site, with the reasoning spelled out. None of these are among the 30 scored questions, so working through them will not distort your result.
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A word about practice. Practising a format reliably improves your score on that format, which is a practice effect rather than a change in ability. That is worth knowing in both directions: it means a bit of familiarity stops the format itself from being the obstacle, and it means a score obtained after heavy practice on the same test is inflated. Everything below is a demonstration of how each type works, not a coaching drill.
Figural matrices
A three-by-three grid of figures with the bottom-right cell missing. One or more rules govern how the figures change across each row; your job is to work out every rule and apply them all at once. Difficulty is driven mainly by how many rules run simultaneously - one is easy, three is hard.
Example 1: two rules at once
Which figure completes the matrix?
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Answer: B
Two rules are running. Size steps up along each row - small, medium, large - wrapping back round at the end. Shading is arranged so that each of the three shadings appears exactly once in every row and every column. The missing cell has to satisfy both at the same time. A useful habit: work out one attribute at a time and eliminate options as you go, rather than trying to hold the whole figure in mind at once.
Boolean figure logic
A variant where each cell is a grid of marks, and the third cell in a row is produced by combining the first two. The combination is one of: keep marks in either cell (union), keep only marks in both (intersection), keep marks in exactly one (exclusive-or), or start from the first and remove anything in the second (subtraction).
The trick is to check the top two rows first to identify which operation is in play, then apply it to the third. Test the operations in order and stop when one explains both complete rows.
Example 2: find the operation, then apply it
In each row, the third figure is derived from the first two. Which figure completes the bottom row?
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Answer: B
This one is exclusive-or: the third cell keeps only the marks that appear in exactly one of the first two cells. Marks present in both cancel out and disappear. If you assumed union (keep everything from both), you would end up with too many marks - and one of the distractors is exactly that answer, which is how these items catch a half-formed rule.
Number and letter series
A sequence follows a generating rule; you supply the next term. With numbers, the reliable opening move is to write down the differences between consecutive terms. If the differences are constant, it is a simple arithmetic series. If the differences themselves form a pattern, you have a second-order rule. If neither, check for multiplication, a recurrence (each term built from the two before it), or two sequences interleaved.
Example 3: differences of differences
What comes next in the series?
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Answer: 53
The differences are 4, 7, 10, 13 - and those rise by a constant 3 each time. So the next difference is 16, giving 37 + 16 = 53. Whenever a series grows faster than linearly but not by a constant multiplier, take differences twice.
Example 4: an alternating step through the alphabet
What comes next in the series?
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Answer: N
Convert letters to positions first - that turns the problem back into a number series. C=3, F=6, G=7, J=10, K=11. The steps are +3, +1, +3, +1, so the next step is +3, giving position 14: N. Letter series are almost always number series in disguise.
Spatial rotation
You are shown a figure and must pick the option that is the same figure rotated - not reflected. The distractors are mirror images, and they are genuinely hard, because a reflection has the same outline, the same number of cells and the same overall shape. It is only the handedness that differs.
The technique that works: pick one distinctive feature - a protruding arm, a corner notch - and track where it must end up relative to the rest of the figure after the turn. If an option has that feature on the wrong side, it is a reflection, and no amount of rotation will fix it.
Example 5: rotation versus reflection
Which figure is a rotation of the figure on the left?
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Answer: C
This figure is chiral: its mirror image cannot be produced by any rotation, however far you turn it. Every wrong option here is that mirror image at some angle, or a figure with one cell moved. Turning the page - or your head - is a legitimate strategy and genuinely helps.
Verbal analogies
Two words stand in some relation; you must complete a second pair standing in the same relation. The discipline that makes these tractable is to name the relation explicitly before looking at the options. Vague feelings of association lead straight to the distractors, which are chosen to be associated with the right answer without standing in the right relation to it.
Example 6: name the relation first
Archipelago is to island as constellation is to ___
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Answer: star
The relation is collection to member. An archipelago is a group of islands, so a constellation is a group of stars. "Galaxy" is another kind of collection, but it is not what a constellation is made of. Naming the relation - "a collection and the thing it is made of" - settles it before the options can mislead you. "Sky" and "telescope" are merely associated with constellations; association is not the relation being tested.
General strategy
- Answer everything. On this test and most others, unanswered items count as wrong and there is no penalty for guessing. Even a blind guess on a five-option item is worth 20%.
- Eliminate before you choose. Distractors are built to be wrong in one specific way. Finding that way is usually faster than verifying the right answer from scratch.
- Do not stall. A hard item costing five minutes can cost you three easy items at the end. Mark your best guess, move on, come back if time allows.
- State the rule in words. On matrices and series, saying the rule aloud - "shading moves one place right each row" - catches errors that silent pattern-matching does not.
- Take differences. For any number series, this is the first move, every time.
- Sit somewhere quiet. Interruptions cost more than most people expect on timed reasoning tasks, and the test conditions are part of what the score assumes.
Common questions
Do these practice questions appear on the real test?
No. They are generated by the same engine but with ids that are not in the scored bank, specifically so that full worked answers can be published here without compromising the test.
Does practising improve your IQ score?
It improves your score on the practised format, which is a practice effect rather than a change in underlying ability. Familiarity with the format does help by stopping the format itself from being an obstacle, but repeated practice on the same items produces an inflated score that means less, not more.
What is the hardest type of IQ question?
It varies by person, which is the point of reporting a domain profile. Statistically, three-dimensional rotation items tend to have the lowest proportion correct of the common formats, and multi-rule figural matrices become very demanding once three rules run at once.
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