Figure Series
🔒 Log in to trackMovement and rotation
🔒 Log in to trackMost figure series move an element step by step:
- Around the border: a dot/shape jumps a fixed number of positions (1, 2, 3 …) clockwise or anticlockwise. Border positions: 4 corners + 4 edge mid-points = 8 places.
- Rotation: an arrow or line turns by a fixed angle (45°, 90°, 135°) each step.
- Shading: a shaded quarter moves round the square.
Track one element at a time across all frames, write its step (e.g. +1 clockwise), then predict its next place. Do the same for each element and pick the option that agrees on all of them.
Detailed notes
What the series asks
Four figures follow one after another by a fixed rule of movement or rotation. You must pick the fifth figure from the options. Nothing is counted or added here - something only turns or slides from frame to frame.
Number the positions
Many frames place a small mark (a dot, a ring, a square) on the border of a square. Number the 8 border places clockwise starting from the top-left corner: 0 top-left corner, 1 top-middle, 2 top-right corner, 3 right-middle, 4 bottom-right corner, 5 bottom-middle, 6 bottom-left corner, 7 left-middle. A movement "one place clockwise" then means 0 → 1 → 2; "two places anticlockwise" means 0 → 6 → 4. With numbers, the answer is a small sum: next place = last place + step (mod 8).
Arrows and directions
An arrow that turns is read by its angle. The 8 likely directions are up, up-right, right, down-right, down, down-left, left, up-left - 45 degrees apart. "90° clockwise" sends up → right → down; "45° anticlockwise" sends right → up-right → up. Write the direction under each frame, find the step, and turn once more for the answer.
Shaded parts
A shaded quarter of the square moves around the four quarters: top-left → top-right → bottom-right → bottom-left is one step clockwise each time. The same numbering trick works with 4 places instead of 8.
Two or three rules together
Harder series move two or three elements at once - say a shaded quarter, an arrow and a dot. Read one element at a time across all four frames, write its rule, then combine the rules for the answer. Never try to compare whole frames; each element obeys its own small rule.
Method in the exam
- Pick one element and follow it through all frames; note its rule (step size and direction).
- Repeat for any other element.
- Apply each rule once more to get the answer's element positions.
- Match the options; reject any option that breaks even one rule.
Worked example
An arrow points up, then up-right, then right, then down-right - it turns 45° clockwise each step. One more turn of 45° clockwise points it down. In place-numbered form: a dot at place 0, 2, 4, 6 moves two places clockwise each step, so next is 6 + 2 = 8 → place 0, the top-left corner.
Common mistakes
- Mixing up clockwise and anticlockwise after the second frame.
- Reading a 45° turn as 90° (the arrowheads are small - trace one frame at a time).
- In combined series, applying one rule to the wrong element.
- Forgetting that the movement repeats around the frame: place 7 + 1 = place 0, not place 8.
Quick revision
- Border: 8 places numbered clockwise from the top-left corner; step is added mod 8.
- Arrows: 8 directions, 45° apart; note the turn per frame.
- Shaded quarter: 4 places; one quarter clockwise at a time.
- Combined series: solve one element at a time, then combine.
- The answer must satisfy every rule, not just one.
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: Rotating arrow or linevery common2 practice Q
Each frame shows an arrow or a line at a different angle.
Write the direction in each frame; find the constant turn (45, 90 or 135 degrees, clockwise or anticlockwise); turn once more.
Example: Q. An arrow points up, up-right, right, down-right. What comes next?
45° clockwise each step; one more turn points it down.
Type 2: Element moving round the bordervery common2 practice Q
A dot, ring or square sits on a different border place in every frame.
Number the 8 border places clockwise from the top-left corner; find the step; add it to the last place (mod 8).
Example: Q. A dot at 0, 2, 4, 6 - where next?
Two places clockwise each step: 6 + 2 = 8 → place 0, the top-left corner.
Type 3: Shaded part movingcommon2 practice Q
A shaded quarter (or half) of the square jumps from frame to frame.
The quarter moves around 4 places; read the direction from the first two frames and continue.
Example: Q. Shaded quarter: TL → TR → BR → BL. Next?
One quarter clockwise each step; it returns to the top-left.
Type 4: Two or three rules togethercommon2 practice Q
Each frame carries two or three elements (shading, arrow, dot), each changing.
Follow one element through all frames at a time; write each rule; apply every rule once more for the answer.
Example: Q. Shading moves anticlockwise and the arrow turns 90° clockwise. What is the fifth frame?
Combine: shaded quarter from the shading rule, arrow direction from the turn rule - the answer satisfies both.
Formulas
s = step (positive = clockwise) on the 8 border places.
Shortcut tricks
⚡ One element, one line
Write a tiny table: element → positions in frames 1-4 → step → next. Options that fail any row are out.
Example: Q. A dot sits at places 1, 3, 5, 7 (clockwise count). Next?
Step +2: 7 + 2 = 9 ≡ 1 (back to the first place).
⚡ Angles as clock hours
Treat 45° as 1.5 clock-hours; an arrow turning 90° clockwise each step goes 12 → 3 → 6 → 9 → 12.
Example: Q. Arrow: up, right, down, … next?
Left (90° clockwise each step).
Where students lose marks
Mixing up clockwise and anticlockwise because the first step looked like both.
Tracking only one element and choosing an option that is right for it but wrong for another.
Forgetting to wrap round after the 8th border position.
Practice sets — 16 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 10 questions
Suggested time 7 min · wrong answers go to your mistake notebook automatically.