- A circular piece of paper is folded in half three times, creating a wedge shape with 8 layers. A small square hole is punched through all layers near the outer curved edge. After unfolding completely, how many holes will appear and in what arrangement?
Answer: Eight square holes evenly distributed around the circumference of the circle
Three folds of a circle create 8 layers (2³ = 8). One punch through all 8 layers creates 8 holes. Since the circle was folded in half three times, the 8 holes distribute evenly around the circumference when unfolded. Choice B doubles the count incorrectly. Choice C undercounts by ignoring one fold. Choice D correctly counts holes but incorrectly describes the arrangement.
- A rectangular piece of paper is folded in half horizontally, then folded in half vertically. The resulting small rectangle has a star-shaped hole cut through all four layers at a position that is off-center but not touching any edges. What will the unfolded paper show?
Answer: Four identical star shapes positioned symmetrically in each quadrant of the original rectangle
Two perpendicular folds create 4 layers and 4-fold symmetry. One cut affects all 4 layers, creating 4 identical holes positioned symmetrically in each quadrant when unfolded. The off-center position ensures the stars appear in each quadrant rather than overlapping at the center. Choices B and D show only 2 holes, ignoring one fold. Choice C suggests the holes overlap, which contradicts the off-center placement.
- A circular piece of paper undergoes the following process: it is folded in half, then folded in half again perpendicular to the first fold, creating a quarter-circle with 4 layers. A diamond-shaped hole is cut through all layers near the curved edge. What is the result when unfolded?
Answer: Four diamond holes arranged symmetrically around the circular edge of the paper
Two perpendicular folds create 4 layers and 4-fold symmetry. One cut through all 4 layers produces 4 diamond holes. Since the cut was near the curved edge (circumference), the 4 holes appear symmetrically around the circle's edge when unfolded. Choice A undercounts the layers. Choice C doubles the count incorrectly. Choice D correctly counts but misplaces the location.
