Figure Series
🔒 Log in to trackAdding, removing and changing elements
🔒 Log in to trackSome series change the number of elements: strokes grow 1, 2, 3, …; a new shape appears in the next corner each step; or shapes disappear one by one.
Others alternate: an arrow flips up/down, a shape switches between two kinds. Count carefully, and check whether each new element is added at a fixed rotation (clockwise) from the previous one.
Detailed notes
What changes here
Instead of moving, the figures add or remove something: more strokes each frame, one new dot per frame, or a growing count together with a small extra detail that alternates. The rule is about how many, not about where a mark slides.
Counting strokes
Many series draw 1, 3, 5... simple strokes inside the square. Count them in every frame and write the row of numbers: 1, 3, 5 → the step is +2, so the next frame has 7. The step can be negative (4, 3, 2 → 1) - subtraction is as common as addition.
Dots added round the frame
A very frequent series adds one dot per frame at the next corner, going clockwise: top-left; then top-right; then bottom-right; then the last corner. After the fourth frame the answer holds one dot in every corner. Watch the starting corner and the direction - both can change between questions.
A second rule
Often the count grows while a small detail alternates: an arrow flips up, down, up, down, or a mark swaps between two shapes. Two rules never interact - find the count rule, find the alternating rule, and the answer must satisfy both. Options usually break exactly one of the two: right count with wrong detail, or right detail with wrong count.
Method in the exam
- Count the main element in every frame; write the number row.
- Find the step (+1, +2, −1...). Apply it once more.
- If any detail differs between frames (arrow, shading, shape), write its row too - it usually alternates.
- Choose the option that fits every row.
Worked example
Strokes: 1, 3, 5 - two more each step, so the next frame has 7. With a second rule, say the arrow alternates up, down, up: the answer would need 7 strokes and a downward arrow. An option with 7 strokes and an upward arrow breaks the second rule; an option with 5 strokes and a downward arrow breaks the first.
Common mistakes
- Reading +1 when the real step is +2 (count every frame, don't guess).
- Missing a stroke hidden behind the frame border.
- Taking an option that fits the count but ignores the alternating detail.
- In dot series, forgetting which corner comes next and adding the dot at the wrong one.
Quick revision
- Write the count row: 1, 3, 5 → step +2 → next 7.
- Steps can be negative: 4, 3, 2 → 1.
- Dot series: one new dot at the next corner clockwise; four corners then full.
- Second rule (alternating arrow or shape) must hold along with the count.
- Options break exactly one rule each - check both before answering.
Types of questions asked
Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.
Type 1: Growing countvery common2 practice Q
Frames show 1, 2, 3... simple strokes or marks; the options differ only in how many.
Count in every frame, find the constant step (+1, +2 or −1), apply it once more.
Example: Q. Strokes: 1, 3, 5. What comes next?
Step +2: next frame has 7 strokes.
Type 2: Dots added round the framecommon2 practice Q
Each frame adds one dot at the next corner of the square.
Note the starting corner and the direction; each frame the new dot appears at the next corner; the fourth frame has all four corners.
Example: Q. Dots at TL; TL and TR; TL, TR and BR. Next?
4 dots, one in every corner (the new one at the bottom-left).
Type 3: Count plus alternating detailcommon2 practice Q
The count grows while an arrow or mark alternates (up/down, or two shapes).
Two independent rules: continue the count row, continue the alternation; the answer satisfies both.
Example: Q. Strokes 1, 2, 3, 4 with an arrow alternating up, down, up, down. Next?
5 strokes with the arrow up.
Type 4: Shrinking count with a moving markeroccasional2 practice Q
The stroke count falls each frame while a dot or ring slides round the border.
Continue the count row downwards; read the marker's border step separately; combine both.
Example: Q. Strokes 5, 4, 3, 2 and a dot moving one place clockwise. Next?
1 stroke, with the dot at the next border place.
Shortcut tricks
⚡ Count first
Count the elements in each frame. If the counts go 1, 2, 3, 4, only options with 5 survive; then check positions.
Example: Q. Strokes: 1, 2, 3, 4. Next?
5 strokes.
Where students lose marks
Ignoring an alternating element because it returns to an earlier state.
Counting a shape twice when it sits on a boundary.
Practice sets — 12 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 12 questions
Suggested time 8 min · wrong answers go to your mistake notebook automatically.