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Hard Items and Pacing
Pacing the Last Fifteen Questions
Summary
Three real items from the practice generator, solved end to end, then the clock. The point of the walkthroughs is not the folding — that is the whole rest of the unit. It is how little of the pattern you have to fold before the item is over.
Item 1 — one relationship, three options gone
Which cube results when the pattern is folded into the page?
Read the pattern before you read the options. A run of four squares across the middle, one capped square above it and one capped square below it, both hinged to the same square of the run. The upper cap is solid black, the lower cap is stippled, and the square between them is gray.
Two caps hinged to opposite edges of one square swing onto opposite faces of the cube, and opposite faces are never both visible in one drawing. That is the whole item. Any option showing the black face and the stippled face together is finished before you look at anything else.
B shows black and stipple. C shows black and stipple. D shows black and stipple. A shows the stippled face, the gray face and a blank one, and A is the answer. You never had to work out where the gray face went, and you never had to fold anything but two flaps.
Pick two shaded squares that share an edge on the pattern and check that they stay adjacent, in the same relative position, after folding. The tempting wrong choice shows the same shades with left and right exchanged — that is the mirror image, which folding into the page can never produce.
Item 2 — the relationship carries a direction
Which cube results when the pattern is folded into the page?
Again, the pattern first. A run of four with one square above its left end and one below its third square. Two marks, both half-shaded, and they sit on squares that share an edge: the gray half is on the upper square, the black half on the square directly below it.
Anchor on the black square, because it is the one whose mark points somewhere. The gray half is pressed against the very edge the two squares share; the black half is pressed against a different edge of its own square — the one as far from the gray square as it can be. That pair of contacts is what folding preserves, and it is the only thing worth checking.
In B the gray half is against the edge farthest from the black face. Out. In C the black half is pressed right up against the shared edge with the gray face, which is the one place the pattern says it is not. Out. Two options killed on one relationship, and neither needed the cube built.
A and D are harder, and worth being honest about. Both get every edge contact right. They differ only in the sense of the corner where the three faces meet: read clockwise, D goes black, blank, gray, and A goes blank, black, gray. Those are opposite senses of one corner, so exactly one of them is a drawing of the folded cube — A is the reflection. D is the answer.
The shading covers only part of each face, so its direction matters as much as its position. Fold the pattern edge by edge and track which edge of each shaded region touches which neighbouring face. A wrong option shows a correct face rotated — the shaded half or triangle pressed against the wrong edge — or the mirror image of the whole cube.
Note what that cost. The first relationship took two options off in a few seconds. The last pair took a handedness check, which is the slowest thing in the section. When you get to a pair like that with the clock against you, take the fifty-fifty and move.
Item 3 — a hard item, same procedure
Which cube results when the pattern is folded into the page?
This is a hard-tier layout: still a run of four, but the two caps are pushed to opposite ends of the run instead of sitting near the middle. Three marks now — a hatched half on the cap, a gray half on the run's third square, a black half on its fourth. Nothing about the method changes. There are simply three relationships available instead of one, and you still spend them one at a time.
Start with the cheapest, the two squares that are already side by side: gray and black. On the pattern, the black half is pressed against the outer edge of its square — as far from the gray square as that face allows. C draws it a quarter-turn round, touching the gray face. Out, and that took one look.
Now spend a fold. Walk the band round from the hatched cap and the gray face lands across the hatched square's top edge, while the hatching is pressed against the bottom one. So the hatched half faces away from gray. B presses it right against the gray face. Out.
A and D again differ only in sense: clockwise, D reads gray, hatch, black; A reads hatch, gray, black. D is the answer. Three marks, three relationships, and the two that decided anything were both single edge contacts.
The shading covers only part of each face, so its direction matters as much as its position. Fold the pattern edge by edge and track which edge of each shaded region touches which neighbouring face. A wrong option shows a correct face rotated — the shaded half or triangle pressed against the wrong edge — or the mirror image of the whole cube.
The hard item did not ask for a technique the easy one lacked. It asked for the same edge contacts, on a layout that took longer to read.
Ten minutes for fifteen items
Pattern folding is questions 76 through 90 — fifteen items, the last block of the test. Ninety items in sixty minutes works out to forty seconds each; Foundations does the whole-test arithmetic, and here it is just the number to beat. Your share of the hour is ten minutes.
Forty seconds is an average to manage, not a timer to obey. Item 1 above is a fifteen-second item: one relationship, three options gone, done. That is what pays for the hard shape-only item where you have to match eight wall rectangles against the profile, or the pair that comes down to handedness. If you reach question 83 with more than half your ten minutes gone, the fix is not to fold faster.
Four options, not five
Every pattern-folding item offers four figures, where keyholes and cube counting offer five. Two things follow, and they both favor you.
- A blind guess here is one in four, not one in five. The floor under a lost item is higher in this section than anywhere else on the PAT.
- Eliminating a single option moves you from one in four to one in three. That is a bigger jump than the same elimination buys in a five-option section, which is why a partial solve is never wasted here — even when the clock beats you, get one option out before you pick.
And you can almost always get one out. One edge contact, one opposite pair, one panel count: any of them usually kills at least one figure in a few seconds.
Triage on the first read
Sort every item into one of three piles as you read it, and never revisit the sorting.
- Answer it when the decisive relationship resolves it. Most items are this.
- Guess and go when the relationship leaves two survivors that differ only in handedness. Fifty-fifty at ten seconds beats sixty percent at ninety.
- Flag it when the pattern needs real decoding — an awkward layout with three marks, or a twelve-panel profile. Come back with the time your fast items saved. Never leave a flagged item blank. The flag is a bookmark, not a placeholder.
The drill loop
Work sets of ten. Generate them in the pattern folding practice generator, which builds unlimited items at easy, medium and hard. After each set, read every explanation — including the ones you got right, because a right answer reached by eliminating the wrong three is a different skill from a right answer reached by finding the relationship.
Then say each solve out loud in one breath: which relationship you picked, what it killed, and what decided the last pair. Where you stall is the step that is not automatic yet.
Log what caught you, not how many
"I got four wrong" tells you nothing you can act on. The wrong figures in this section come from a short, fixed vocabulary, so write down which one caught you — two words, every time.
- Wrong adjacency. You accepted a drawing that shows two faces together which the pattern makes opposite, or that puts a mark on the wrong face entirely. The signature is a miss on an item you solved quickly and confidently.
- Shading rotation. Right face, right shade, wrong way round: you tracked where the mark was and not which edge it touched. The signature is a miss on part-face shading — halves, diagonals, die pips — never on whole-face shades.
- Mirror. Every relationship checked out and you still took the reflection. The signature is a miss where the last two options looked identical to you.
After three or four sets the tally starts talking. Nine adjacency misses and nine rotation misses are different problems with different fixes: the first says you are not reading the pattern before the options, the second says you are not carrying edge contacts through the fold. Drilling more items without knowing which one you have feels like work and changes nothing.
Fatigue is the real opponent
These are questions 76 to 90. You have been holding shapes in your head for the better part of an hour, and the section that asks for the most careful bookkeeping arrives when you have the least left. Most points lost here are not lost to hard items. They are lost to reading the options before the pattern, to folding the whole net when one edge contact would have done, and to re-checking an item you already solved.
The takeaway
Fifteen items, ten minutes, four options each. Find one relationship the pattern fixes, test it against all four figures, and stop the moment one figure survives. When two survive and differ only in handedness, take the fifty-fifty and move — and when the clock beats you outright, still eliminate one figure before you pick, because one in three is worth more here than anywhere else on the test. Log every miss by cause, not by count.
Practice Questions
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