Question 1: Keyholes
A solid has a rectangular base, a raised central ridge, and a notch cut from the left side. Which opening must match its widest dimension, tallest dimension, and notch position?
Review approach: compare extreme dimensions first. Then check whether the notch appears on the correct side after the object is oriented toward the opening. Wrong answers often preserve the silhouette while moving or mirroring the notch.
Question 2: Top-front-end
An object has two stacked cubes on the left, one cube on the right, and a rear cube hidden from the front view. Which top view and front view are compatible?
Review approach: build the object by layers. The front view shows height and width but can hide depth; the top view shows width and depth but not height. A correct pair must explain all visible and hidden positions without inventing unsupported blocks.
Question 3: Hole punching
A square sheet is folded in half left-to-right, then in half bottom-to-top. A hole is punched near the folded corner. Where do the holes appear when unfolded?
Review approach: unfold in reverse order and reflect the hole across each fold line. Do not rotate the pattern unless the fold changes orientation.
Question 4: Cube counting and folding
- Cube counting: inventory each layer before counting exposed faces.
- Angle ranking: compare two angles at a time using a consistent reference.
- Pattern folding: identify opposite faces first, then test distinctive adjacent edges.
- Mixed PAT review: write down the exact visual rule you missed, not only the question type.