How to Answer 11+ NVR Matrices Questions

A matrix question shows you a grid — usually three squares by three — with one cell missing. The figures change in a fixed way along each row and down each column. Your job: work out both patterns and pick the figure that fits the gap.

A grid of nine shapes can look like a wall of noise the first time you see one. It isn't. A matrix is just two series questions stacked on top of each other — one running across, one running down — and every rule inside it comes from the same six-item checklist: shape, size, shading, number, position, direction. Check those one at a time and the grid turns from noise into two tidy patterns.

Better still, a matrix marks your own work: when your answer fits the row and the column, you know you're right before you've looked at the options.

The method

1. Read the grid like a book: along the row, then down the column. The missing square has to obey BOTH.
2. Test each feature on its own — does the row change the shape? The shading? The size? Fix one at a time; don't try to see everything at once.
3. Ask what changes and what stays the same. In many grids each row keeps one thing (its shape) while the columns change another (the fill). The split is the rule.
4. Build the missing figure in your head before looking at the options. Then find your figure in the list — don't let the options suggest ideas to you.
5. Cross out the clearly wrong answers first, and if two remain, find the one detail that differs between them — the question is really testing that detail.

A worked example

Which figure completes the grid?

1. Read the top row: circle, circle, circle — white, then grey, then black. The row keeps its shape and darkens its fill.
2. Check the middle row: squares doing exactly the same — white, grey, black. The rule holds.
3. Bottom row: white triangle, grey triangle, gap. So the gap needs a black triangle.
4. Now check the column too: the third column is black circle, black square… so a black triangle fits the column as well. Row and column both agree.
5. Options: A is the black triangle. B is grey — a repeat of the middle cell. C is white. D is a black square — right fill, wrong row.

Answer: A

The rules you'll meet

Every matrix in the bank runs on one (or two) of these families:

• Rows own one feature, columns own another — each row keeps its shape while the fill darkens down or across: white, grey, black. The classic.
• A steady change across the row — the figure grows small, medium, large; or gains a dot each cell: 0, 1, 2.
• Every variant appears exactly once — each row and each column contains each shape, each fill or each size exactly once, like a mini sudoku. Find what the row and column are both missing.
• A turn across the grid — each cell rotates a step more than its neighbour: 45° or a quarter turn each time, sometimes coming full circle.
• Counting in two directions — one more dot than the cell to the left and the cell above; or rows keep their own count while columns keep their own kind of mark.
• Checkerboard alternation — two versions of the figure alternate like the squares of a chessboard. The gap takes whichever its neighbours are not.
• A swap at every step — two shapes trade places, trade sizes or trade fills as you move along the row, then trade back.
• The middle cell combines the ends — the centre of each row shows both end shapes shrunk: stacked up, side by side, or one placed inside the other.
• A mirror across the row — the figure is flipped left-to-right (or top-to-bottom) as you cross the row, so a dot swaps sides.
• Two rules at once — size grows across while shading darkens down. Solve each direction separately, then combine.
• A built-in decoy — something appears in every cell unchanged. It codes nothing: ignore it and the real rule stands out.

The traps

The one-direction answer. The most tempting wrong option obeys the row but breaks the column — the right fill on the wrong shape. Always run both checks.

The neighbour copy. One option repeats the cell next to the gap. A matrix cell is almost never a straight copy of its neighbour — something must move on.

Feature overload. Trying to hold shape, fill and size in your head at once scrambles all three. The method is strict: one feature, checked everywhere, then the next.

The decoy detail. If a mark appears identically in every cell, it is scenery, not signal. Children lose minutes hunting for a rule in a feature that never changes.

Related

• The complete 11+ question-type guide
• NVR: Series & Sequences — a matrix row on its own
• NVR: Shape Codes — features mapped to letters instead of grid positions

All example questions come from the Brainblox question bank — practise this question type inside 15 arcade games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.