TestAS Preparation

Figure Sequences

As of: 30 October 2026

What it is about

You see a series of matrices, that is, grids of squares. There are figures in the squares. From matrix to matrix, the figures change by fixed rules. You have to work out the next two matrices. These are two separate questions, each with its own answer options.

20 tasks, 25 minutes. So about 75 seconds are left per task for both sub-questions. Source: testas.de: structure of the digital TestAS.

The rules

In the preparation PDF (as of April 2022), g.a.s.t. names these kinds of changes. We summarise them in our own words:

  • Movement: A figure moves vertically, horizontally or diagonally.
  • Step size: It can stay the same or grow by 1 with each step.
  • Rotation: A figure turns around itself.
  • Colour: A figure changes colour, often in a fixed cycle.
  • Edge: Figures do not leave the grid. At the edge they bounce back or run along the edge.
  • Figures do not disappear and do not overlap.

Several figures can change by different rules at the same time. The harder the task, the more figures and rules.

An example from our Trainer

Our own generator created this example. It is easy: one figure, one rule.

Sequence shown: Matrix 1: circle (green) in row 3, column 3. Matrix 2: circle in row 3, column 2. Matrix 3: circle in row 3, column 1. Matrix 4: circle in row 3, column 2. Matrix 5 and 6 are to be found.
Four matrices. Matrix 5 and matrix 6 are to be found.

Which matrix comes next (matrix 5)?

Option A
A
Option B
B
Option C
C
Show solution

The correct answer is B. The circle moves one square to the left per step. In matrix 3 it reaches the left edge and bounces back. From then on it moves to the right: matrix 4 column 2, matrix 5 column 3, matrix 6 column 4.

  • Option A is wrong: There the step size grows, although it stays the same.
  • Option C is wrong: There the circle turns 90 degrees.

How to proceed

  1. One figure after the other. Follow each figure on its own across all four matrices.
  2. Three questions per figure: Where does it move? Does it turn? Does it change colour?
  3. Check the edge. Most mistakes happen there. Does the figure bounce back or does it run along the edge?
  4. Rule out options. The wrong options usually differ in only one figure. Check the figure with the hardest rule first.
  5. Matrix 6 builds on matrix 5. Once you have the rule, the second question costs hardly any time.

Common mistakes

  • Overlooking the growing step size (1, 2, 3 squares instead of always 1).
  • Reversing the direction wrongly when bouncing back.
  • Skipping a colour in a colour cycle with three colours.

Open

We cannot check whether the digital test uses exactly the same kinds of rules as the 2022 PDF. The demo version in the g.a.s.t. portal is only accessible after registration.