Raven's matrices practice test

A short background on Raven's matrices

John C. Raven developed his matrices in the 1930s, and they were first published in 1938. They are non-verbal matrix puzzles and are widely used as a measure of fluid, culture-reduced reasoning (Wikipedia: Raven's Progressive Matrices). Fluid reasoning is Raymond Cattell's term for working with novel problems rather than recalling learned knowledge (Wikipedia: Fluid and crystallized intelligence), and a well-made matrix is about as novel as a problem can be: no words, no numbers, just a pattern and a gap.

This page is practice in that style. The ten grids are original items from the IQ Octopus engine, not items from any Raven's form, and IQ Octopus is not affiliated with or endorsed by the publisher of Raven's Progressive Matrices. The classic test comes in Coloured, Standard and Advanced forms; the Standard form has 60 items in five sets of twelve (Bilker et al., 2012), and Pearson lists the forms as untimed (Pearson: Raven's brochure). The full guide is Raven's Progressive Matrices, explained.

What “progressive” means in this set

The set climbs steadily. The first two grids use a single rule. The middle four combine two. The last four combine up to three, and they include the trickier rule types. That climb is the point of progressive matrices: everyone solves the early items, and the later ones separate a quick reasoner from a careful and quick one.

The rule types, from easiest to hardest

1. Constant. Something stays the same in every tile, such as size. Easy to see, easy to forget when you pick.
2. Progression across a row. Count, size or direction steps along each row the same way.
3. One value per row. Each row has its own fill or shape, set by the row, not the column.
4. Distribution of three. Three values appear once in every row and every column, shuffled. The missing tile has the value its row and column lack.
5. Arithmetic. Counts climb by a fixed amount along each row, and each row starts higher than the one above. A variant moves a dot a set number of places around the edge, with each row starting further along.
6. Line overlay. Each tile is a set of edges and corner ticks. The third tile of a row keeps only the lines that appear in exactly one of the first two. Shared lines cancel.

Any of these can be turned on its side, running down columns instead of across rows. If the rows look like noise, read the columns.

A routine for every grid

Experienced solvers tend to use the same routine on every item, which is what keeps them fast on the hard ones:

• Scan the first row and list every attribute that changes and every one that does not.
• Check that list against the second row. Drop anything that does not hold.
• Look down the columns for a distribution of three or an arithmetic step.
• Say the missing tile out loud, attribute by attribute.
• Find it among the eight options, then confirm it breaks no rule.

The confirmation step is not wasted time. Wrong options are each one rule away from correct, so a quick check against every rule catches the near twins.

Mistakes that cost points on the late items

• Hunting for a progression that is not there. When three values appear in a different order in each row, nothing is moving forward. It is a distribution of three, and looking for “the next one” wastes time.
• Treating overlays as addition. On line grids, lines that appear in both of the first two tiles do not double up; they disappear. The third tile shows only the lines unique to one of them.
• Checking rows only. If a grid is transposed, every rule runs downward. Time spent on rows that make no sense is a sign to read the columns instead.

Pacing ten grids

Each grid has a 30-second ring. When it empties, the grid counts as unanswered and the next one appears. The easy grids should take well under that, and the hard ones will feel short. On the final four, use elimination: take your surest rule, cross off what breaks it, then the next rule. If the clock is nearly out with two options left, pick one; a blank never scores.

What your practice score means

At the end you see a count out of ten and a plain description of that practice performance. It is not a Raven's score, and it is not an IQ. Published tests convert raw scores using norms from large samples; this practice set has none. Use it to see which rule types you handle and where the clock bites.

Matrices do sit close to the center of intelligence testing. Charles Spearman proposed in 1904 that a single general factor, g, runs through performance on all mental tests (Wikipedia: g factor), and matrix reasoning is one of the more direct ways tests tap it. Even so, ten items are a glimpse, not a measurement.

Practice effects

Knowing the rule list above will make you better at matrices. Across many studies, retaking a cognitive ability test raised scores by about a quarter of a standard deviation on average, roughly 4 IQ points, and more when the same form was reused (Hausknecht et al., 2007). That is real, and it is about familiarity with the format. Practice on fresh grids, such as the matrix puzzle library, rather than replaying the same ten.

From matrices to an estimated IQ

Matrices make up the largest section of the full IQ Octopus test, alongside sequences, spatial items, number series and analogies. Every attempt uses fresh items, and the result is an estimated IQ with a confidence range. For more on the format, read the matrix reasoning guide, or try the abstract reasoning test for a gentler set of grids.