9.1 Shape Sequences and Next-in-Pattern
Key Takeaways
- A next-in-pattern item is solved by naming the smallest rule that generates every given frame, then applying that same step once more — not by picking the option that merely looks similar.
- One-rule sequences change a single feature (rotation, shading, count, or position). Stacked-rule sequences run two or more clocks at once, and the next frame must satisfy every clock.
- QFD does not publish how many analytical-aptitude items appear on Core Abilities, their timing, or a percentage cut; treat this chapter as independent practice in the skill the pack names.
- OnVUE forbids pens and paper, so lock each changing feature into a short verbal checklist and kill any option that breaks one stacked clock.
- High-frequency distractors apply only one of two stacked rules, reverse the direction, or substitute a reflection for a rotation.
Analytical aptitude inside Core Abilities, not Mechanical Reasoning
The Queensland Fire Department (QFD) Recruit Firefighter process includes an Online Cognitive Ability Test delivered by Pearson VUE with OnVUE remote proctoring. The April 2024 Firefighter Recruitment Candidate Information Pack, still linked from the 2026 recruit page, names two cognitive components: Mechanical Reasoning and Core Abilities. Core Abilities evaluates knowledge, problem solving, reasoning ability, and capacity to learn new information. The pack lists four elements: literacy, numeracy, problem solving, and analytical aptitude.
This chapter trains analytical aptitude only. Mechanical items about gears, circuits, kinetic energy, and hose pressure belong in earlier chapters. Shape sequences, odd-one-out, matrix completion, and spatial rotations are figure-based reasoning: you extract a rule from pictures, then apply it. A triangle that happens to look a little like a hydrant marker is still a triangle. Do not import physics.
QFD does not publish how many analytical-aptitude items appear, how they are timed, what weight they carry inside Core Abilities, or a percentage pass mark. Independent OpenExamPrep practice in this chapter is study material for the named skill. It is not an official QFD or Pearson paper, and it does not claim that the live sitting uses any particular item count.
For the 2027 campaign, Pearson's QFD Supervised Testing page (updated 9 September 2026) listed Core Abilities registration from 23 September 2026 to 13 October 2026 as an example window. Live dates are controlled by the invitation email. OnVUE rules still matter here: no pens, pencils, note paper, calculators, or phones. You cannot doodle the next rotation. You have to hold the rule in words. The pack also states that candidates are not expected to answer every question correctly. A stacked-rule figure can consume more time than a one-rule figure. Skipping and returning is rational if review is available on the sitting you receive; follow the on-screen instructions that day.
What a next-in-pattern item is asking
A shape sequence (also called next-in-pattern or series completion) shows three, four, or five frames in order. Each frame is a figure built from simple marks: polygons, arrows, dots, shading, or a small shape sitting on a path. Your job is to choose the option that is the next frame if the same generating rule continues.
Name five features on every item:
- Shape family — circle, triangle, square, pentagon, arrow, L-shape.
- Shading / fill — empty outline, hatched, fully filled, or a split fill.
- Count — number of sides, dots, ticks, or nested shapes.
- Rotation — orientation in the plane, usually in 45° or 90° steps.
- Position — where a satellite mark sits relative to a box (a side walk or a corner walk).
Invariants are features that never change. If every frame is a five-pointed star, star is not the rule; it is the canvas. The rule lives in what does change. If you change an invariant in your predicted next frame — turning an outline arrow into a filled arrow because that option otherwise looks tidy — you have already lost the item.
One rule versus stacked rules
A one-rule sequence changes a single feature on a regular clock. Everything else is invariant.
Worked example — one-rule rotation. Frame 1: an outline arrow pointing up. Frame 2: the same outline arrow pointing right. Frame 3: the same outline arrow pointing down. The invariant is outline arrow. The changing feature is orientation. The step is 90° clockwise. The next frame is an outline arrow pointing left. An option that points left but is filled breaks the invariant. An option that points up-left used a 45° clock that the series never showed. An option that points up again treated the series as a bounce rather than a cycle.
A stacked-rule sequence runs two or more clocks at once. Both must be true in the next frame. The usual stack is rotation and shading, count and position, or rotation and count.
Worked example — stacked rotation plus count. Imagine a square badge with filled dots inside, as if a station board were ticking appliances into service — still an abstract figure, not a mechanical system. Frame 1: square sitting flat (sides horizontal and vertical), one filled dot. Frame 2: square rotated 45° (now a diamond), two filled dots. Frame 3: square sitting flat again, three filled dots. Rule A: the square alternates flat / diamond (45° each step). Rule B: the dot count increases by one each step. The next frame is diamond orientation and four dots. An option with four dots but a flat square applied only the count clock. An option with a diamond but three dots applied only the rotation clock. Those two incomplete applications are the most common stacked-rule distractors.
Worked example — stacked shading plus position. A hollow circle sits at a corner of a square frame. Frame 1: circle empty, top-left corner. Frame 2: circle filled, top-right corner. Frame 3: circle empty, bottom-right corner. Rule A: fill alternates empty / filled. Rule B: the circle walks clockwise around the four corners. Next: a filled circle at bottom-left. An option with an empty circle at bottom-left kept the walk and dropped the fill clock. An option that places a filled circle at top-left reversed the walk.
Stacked rules feel unfair until you force a two-line checklist: diamond, four dots. Scan options for both lines. Do not fall in love with the first option that matches the more obvious clock.
Measuring the step, not guessing the vibe
Between consecutive frames, measure the delta on each changing feature, then confirm that the same delta holds for the whole series.
| Feature | How to measure the step | Clock that usually appears | Typical distractor |
|---|---|---|---|
| Rotation | How many degrees, and which way? | 90° clockwise, 90° anti-clockwise, 45°, or 180° | Mirror image (reflection) sold as the next rotation |
| Shading | Empty to hatch to fill, or a two-step alternate | Cycle of two or three fills | Skipping a stage or reversing the cycle |
| Count | +1, +2, doubling, or sides increasing by 1 | Linear growth is more common than doubling | Counting inner and outer marks as one pile |
| Position | Corner walk or side walk | Clockwise around four corners | Anti-clockwise walk that matches only Frame 1's neighbour |
| Shape family | Triangle (3 sides) to square (4) to pentagon (5) | +1 side per frame | Jumping to a hexagon too soon |
If Frame 1 to Frame 2 is +1 dot and Frame 2 to Frame 3 is +1 dot, the next step is +1, not it feels like it should jump. If the deltas themselves change in a regular way (+1 then +2 then +3), that changing delta is the rule — still one named clock, just a second-order clock. Confirm the second-order pattern on all given steps before you use it. A two-step look that happens to fit Frames 1 and 2 but fails Frame 2 to Frame 3 is not the rule; it is a coincidence you over-fitted.
A verbal method you can use without paper
Because OnVUE forbids scrap paper, use a silent script:
- Lock the canvas. What never changes?
- List changing features. Stop at two or three; if you list six you are over-fitting noise.
- Measure each clock from Frame 1 to Frame 2, then verify on Frame 2 to Frame 3.
- Predict the next frame as a short phrase: diamond, four dots, empty.
- Eliminate. Any option that fails one stacked clock is out, even if it looks tidy.
- Watch reflection. A figure flipped left-to-right is not the next 90° rotation unless the series already used flips. Rotation keeps handedness; a mirror swaps it. Section 9.4 treats this at length; on sequences, it is already a high-frequency trap.
Traps on next-in-pattern items
- Applying only one clock on a stacked item.
- Treating a reflection as a rotation.
- Reversing direction after Frame 3 because the figure looks like it should bounce.
- Changing an invariant (outline becomes filled) because that option is otherwise pretty.
- Counting a nested shape twice.
- Importing Mechanical Reasoning: the arrow would point the way the hose runs.
Pearson QFD pages point candidates to a Sample Demonstration for delivery feel. Use it to learn buttons and the timer. It does not publish a Core Abilities analytical blueprint. This OpenExamPrep chapter is independent practice for the aptitude the pack names.
Read that diagram as a verbal figure, not as a picture of an appliance. Frame 4 is left because the clock is 90° clockwise from up to right to down. If an option showed a filled arrow pointing left, the orientation clock would look satisfied and the invariant would be broken. If an option showed an outline arrow pointing up again, the candidate treated three steps as a bounce. Predict the phrase first — outline, left — then look at the choices.
A sequence shows an outline arrow pointing up, then right, then down. Which figure is the next frame if the same rule continues?
A square badge sits flat with one filled dot, then sits as a diamond with two filled dots, then sits flat with three filled dots. Which description is the next frame under stacked rules?
A circle sits empty at the top-left corner of a square, then filled at the top-right, then empty at the bottom-right. Which next frame applies both the fill clock and the position clock?