Free UA apprenticeship spatial reasoning practice
Spatial relations is listed in some UA locals' tests — Local 342's announcement names it next to math and mechanical aptitude — and prep providers describe a paper-folding section in the test many locals use. It is the section people are least likely to have practised. This section has four kinds of question: fold and punch a sheet of paper, pick a shape that has been turned rather than flipped, count the cubes in a stack, and work out which faces of a folded cube are opposite.
Read the full spatial reasoning guide →
Try a free timed sample
6 questions against a 5-minute clock. The timing is our own practice pace — UA locals set their own tests and time limits.
A square sheet of paper is folded once (left side over to the right) and then a hole is punched through every layer, as shown. Which picture shows the sheet when it is opened out flat again?
Worked examples
Two more spatial reasoning questions with the answer and explanation. Try each before opening the answer. For a longer set across every section, see our free UA aptitude sample questions.
Question 1. A square sheet of paper is folded once (left side over to the right) and then a hole is punched through every layer, as shown. Which picture shows the sheet when it is opened out flat again?
Choose A, B, C or D from the figure.
Show the answer
A: A. Unfold one step at a time, starting with the last fold. Each time you open a fold, every hole is copied as a mirror image across that fold line, so the sheet ends up with 4 holes. The holes only ever appear in mirror pairs across the fold lines, and nowhere the punched layers did not cover.
Question 2. How many cubes are in this stack? Every cube that sits on the floor or on another cube is there, even where you cannot see it.
- 16
- 14
- 9
- 15
Show the answer
D: 15. 15 cubes. Count column by column: look at each top face and count how many cubes high it sits, including the hidden ones underneath it. 3 + 2 + 2, then 2 + 2 + 1, then 1 + 1 + 1 = 15. Counting only the top faces gives 9, which misses every cube hidden underneath.
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These are original practice questions written to reflect what UA locals publicly describe about their apprenticeship aptitude tests. They are not official questions, and this site is not affiliated with or endorsed by the United Association, any UA local or any JATC. Formats vary by local — always check your local's notice.