Non-Verbal Reasoning · Matrices

Matrices 11+ practice

Find a rule that works across every complete row and column of a visual matrix.

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The key idea

Understand the rule first

Compare the first two cells with the third: features may combine, cancel, rotate or change count. Confirm the same operation in another complete line before applying it.

Worked example

In each row, the third cell contains the combined dots from the first two. A row has 2 dots, then 3 dots. What is third?

The rule is addition of dot counts.
Check that no dots overlap or cancel.
2 + 3 = 5.

5 dots

Watch for this

A common misconception

Choosing an option that fits one row but contradicts a complete column.

Reusable method: Test the proposed rule in two complete lines.

Question 1 of 10
Non-Verbal Reasoningcore
In every row, cell 3 shows the shapes present in cell 1 but not cell 2. Cell 1 has a circle and square; cell 2 has a square. What remains?
- Aboth shapes
- Ba square
- Ca circle
- Dnothing
Need a hint?
Remove the shared shape.
Show worked answer
Answer C: a circle
The square cancels, leaving the circle.
Quick method: Test the proposed rule in two complete lines.
Question 2 of 10
Non-Verbal Reasoningcore
In each row, the third box contains the total number of dots in the first two boxes. The first row is 1, 2, 3. The second row is 2, 4, ?. How many dots belong in the missing box?
- A4
- B5
- C6
- D8
Need a hint?
Add the counts in the first two boxes.
Show worked answer
Answer C: 6
The stated rule is addition: 1 + 2 = 3, so 2 + 4 = 6.
Quick method: Test the proposed rule in two complete lines.
Question 3 of 10
Non-Verbal Reasoningcore
Across a row, arrows turn 90° clockwise: left, up, __. What completes the row?
- Aright
- Bdown
- Cleft
- Dup
Need a hint?
Apply the same turn from the second arrow.
Show worked answer
Answer A: right
Left turned clockwise becomes up; up turned clockwise becomes right.
Quick method: Test the proposed rule in two complete lines.
Question 4 of 10
Non-Verbal Reasoningexam-style
In each row, the third cell overlays the first two and shared marks disappear. One cell has marks at top and left; the next has marks at left and bottom. What remains?
- Aleft only
- Btop and bottom
- Ctop, left and bottom
- Dnothing
Need a hint?
The shared left mark cancels.
Show worked answer
Answer B: top and bottom
Left appears twice and disappears, leaving top and bottom.
Quick method: Test the proposed rule in two complete lines.
Question 5 of 10
Non-Verbal Reasoningexam-style
Column rule: the bottom shape has the total number of sides in the two shapes above. A triangle is above a square. How many sides should the bottom shape have?
- A5
- B6
- C7
- D12
Need a hint?
Add the side counts of the two shapes.
Show worked answer
Answer C: 7
A triangle has 3 sides and a square 4; 3 + 4 = 7.
Quick method: Test the proposed rule in two complete lines.
Question 6 of 10
Non-Verbal Reasoningcore
In each row of a matrix, the third cell contains the total number of dots in the first two cells. A row begins with 3 dots and 4 dots. What belongs in the third cell?
- A1 dot
- B4 dots
- C6 dots
- D7 dots
Need a hint?
Add the dot counts in the first two cells.
Show worked answer
Answer D: 7 dots
3 + 4 = 7, so the third cell contains 7 dots.
Quick method: Test the proposed rule in two complete lines.
Question 7 of 10
Non-Verbal Reasoningcore
In each row, any shape appearing in both first cells disappears from the third. The first cell has a circle and square; the second has a circle. What is left?
- Aa square
- Ba circle
- Ca circle and square
- Dnothing
Need a hint?
Cancel the shape that occurs in both cells.
Show worked answer
Answer A: a square
The circle appears twice and disappears, leaving only the square.
Quick method: Test the proposed rule in two complete lines.
Question 8 of 10
Non-Verbal Reasoningcore
In a 2×2 matrix, the top-left cell is a triangle and the top-right is the same triangle with a dot added. The bottom-left is a square. What should the bottom-right contain?
- Aa triangle with a dot
- Ba square with a dot
- Ca plain square
- Da dot only
Need a hint?
Apply the same left-to-right change to the bottom row.
Show worked answer
Answer B: a square with a dot
The rule adds a dot without changing the shape, so the missing cell is a square with a dot.
Quick method: Test the proposed rule in two complete lines.
Question 9 of 10
Non-Verbal Reasoningexam
A 2×2 matrix has: top-left black circle, top-right white circle, bottom-left black triangle. Which cell completes the pattern?
- Ablack circle
- Bwhite circle
- Cwhite triangle
- Dblack triangle
Need a hint?
Shapes match down columns and shading changes across rows.
Show worked answer
Answer C: white triangle
The bottom row must repeat the black-to-white change while keeping its triangle shape, giving a white triangle.
Quick method: Test the proposed rule in two complete lines.
Question 10 of 10
Non-Verbal Reasoningstretch
In each row, the third cell shows shapes that appear in exactly one of the first two cells. One cell has a circle, triangle and square; the next has a triangle and square. What belongs in the third cell?
- Atriangle and square
- Ball three shapes
- Cno shapes
- Da circle only
Need a hint?
Cancel every shape found in both cells.
Show worked answer
Answer D: a circle only
Triangle and square occur in both and cancel. Only the circle appears in exactly one cell, so a circle remains.
Quick method: Test the proposed rule in two complete lines.

Understand the rule first

In each row, the third cell contains the combined dots from the first two. A row has 2 dots, then 3 dots. What is third?

A common misconception

In every row, cell 3 shows the shapes present in cell 1 but not cell 2. Cell 1 has a circle and square; cell 2 has a square. What remains?

In each row, the third box contains the total number of dots in the first two boxes. The first row is 1, 2, 3. The second row is 2, 4, ?. How many dots belong in the missing box?

Across a row, arrows turn 90° clockwise: left, up, __. What completes the row?

In each row, the third cell overlays the first two and shared marks disappear. One cell has marks at top and left; the next has marks at left and bottom. What remains?

Column rule: the bottom shape has the total number of sides in the two shapes above. A triangle is above a square. How many sides should the bottom shape have?

In each row of a matrix, the third cell contains the total number of dots in the first two cells. A row begins with 3 dots and 4 dots. What belongs in the third cell?

In each row, any shape appearing in both first cells disappears from the third. The first cell has a circle and square; the second has a circle. What is left?

In a 2×2 matrix, the top-left cell is a triangle and the top-right is the same triangle with a dot added. The bottom-left is a square. What should the bottom-right contain?

A 2×2 matrix has: top-left black circle, top-right white circle, bottom-left black triangle. Which cell completes the pattern?

In each row, the third cell shows shapes that appear in exactly one of the first two cells. One cell has a circle, triangle and square; the next has a triangle and square. What belongs in the third cell?

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