- Look at the figures shown. Which answer figure shows what the target figure looks like when it is reflected across the horizontal line (flipped top to bottom)?
Answer: Figure B
A reflection across a horizontal line swaps top and bottom but leaves left and right unchanged. Figure B correctly flips vertically. Figure A is a left-right reflection. Figure C is a 180° rotation (both flips combined). Figure D is the original unchanged.
- A mirror image of an analog clock reads 2:50. What is the actual time?
Answer: 9:10
On an analog clock, a mirror reverses the face around the 12-6 axis, so the real time is 12:00 minus the reflected time. 12:00 - 2:50 = 9:10. The likely trap is 8:10, which comes from subtracting using 11:00 instead of the full 12-hour circle.
- Refer to the geometric solid. Which 2-D view is obtained when the solid is projected from the front?
Answer: C. A T-shape three units wide with one-unit stem
From the front, the tallest central column plus shorter side blocks produce a capital T silhouette—three units across the top and one-unit stem downward. Only option C describes that. The rectangle (A) ignores the missing lower corners, the L-shape (B) lacks one side, and D overstates the blocks.
- Use the scatter plot. Which statement best describes the correlation between variables X and Y?
Answer: C. Strong negative linear correlation
Points cluster closely along a downward-sloping line, indicating a strong negative correlation: as X increases, Y decreases significantly. Options A and B would imply upward slope; option D ignores the clear trend.
- Refer to the figure. The shape on the left is folded along the dotted line. Which figure on the right shows the correct result?
Answer: Figure D
Folding along a vertical dotted line reflects the right half onto the left half. The star on the right side lands on top of the circle on the left, producing an overlapping star-in-circle mark at that position. Figure A shows the star unreflected. Figure B reflects but ignores the overlap. Figure C reflects in the wrong direction.
- Use the Venn-style diagram. Which option shows the region representing (A ∪ C) ∩ B?
Answer: D. Shaded where B overlaps either A or C
The union A ∪ C is everything in circles A or C. Intersecting that with B leaves just the parts of B that overlap with A or C. That is exactly option D. Options A and B neglect portions, and option C is too limited—only the triple overlap.
- Based on the net of a cube shown, which option represents the three faces that will meet at vertex X after folding?
Answer: A. Faces numbered 1, 2, 5
In the given cross-shaped net, faces 1, 2, and 5 share edges that converge when folded, meeting at vertex X. Other sets include at least one face that lies opposite the vertex, so they cannot all meet there.
- Refer to the figure. The three views (top, front, side) of a solid made of unit cubes are shown. What is the minimum number of unit cubes needed to build a solid with these three views?
Answer: 5
Analyzing the top view shows an L-shape of 4 squares, and the front and side views each show height-2 stacks at one position. The minimum arrangement places 4 cubes on the base and 1 stacked cube where front and side both require height 2. Total = 5 cubes. Choice A misses one required stack. Choices C and D add unnecessary cubes.
- Square: dot upper-left, arrow up. Each step dot moves one corner clockwise and arrow turns 90° clockwise. After 3 steps?
Answer: Lower-left, arrow left
Starting at upper-left with arrow up, move the dot three corners clockwise: upper-left to upper-right to lower-right to lower-left. Turn the arrow 90 degrees clockwise three times: up to right to down to left. So after 3 steps you get lower-left, arrow left. The tempting wrong answer is lower-left with arrow down, which comes from moving the dot three steps but turning the arrow only twice.
- Refer to the diagram below. Five gears are connected as shown. Gear A is turned clockwise. In which direction does Gear E turn?
Answer: Clockwise
Meshed gears alternate direction. A→B reverses (counterclockwise), B→C reverses (clockwise), C→D reverses (counterclockwise), D→E reverses (clockwise). With 4 meshings between A and E, the direction flips 4 times, returning to clockwise. Choice B assumes an odd number of meshings. Choice C would require a jammed gear. Choice D has no basis in steady rotation.
- In a cross-shaped cube net, face 1 is central; 2 above, 3 below, 4 left, 5 right, 6 beyond 4. Which face is opposite 6?
Answer: Face 1
When you fold the net, face 4 becomes the left side of the cube. Face 6 is attached to the outer edge of face 4, so that edge becomes the back edge. Therefore face 6 folds around to become the back face, directly opposite the central face 1. The tempting wrong answer is Face 5, but face 5 is the right side, adjacent to face 1, not opposite face 6.
- Refer to the figure below. A paper is folded in half twice (first horizontally, then vertically), then a single triangular notch is cut from the folded corner indicated. When the paper is unfolded, how many total triangular holes appear?
Answer: 4
Each fold doubles the number of paper layers at the cut site. Two folds = 4 layers. A single cut through 4 layers produces 4 holes when unfolded. Choice A ignores the folding. Choice B accounts for only one fold. Choice C is a common off-by-one error.
- Look at the figure shown. The large shape is made by combining several smaller identical triangles. How many triangles of ANY size can be counted in the figure?
Answer: 16
Count systematically by size: 9 smallest triangles (6 upward-pointing, 3 downward-pointing), 3 medium triangles made of 4 small triangles each, 3 medium inverted triangles, and 1 large triangle encompassing the whole figure. Total: 9 + 3 + 3 + 1 = 16 triangles. Choice A counts only the smallest units. Choices B and D result from incomplete systematic counting.
- Three unit cubes form an L: two side by side, the third on top of the left cube. What is their total surface area?
Answer: 14 square units
Each cube has 6 faces, so 18 faces total before counting overlaps. The side-by-side pair hides one face from each cube, and the top cube hides one face from itself and from the left cube: 4 hidden faces total. 18 - 4 = 14. The tempting wrong answer is 18, from adding the faces without subtracting the shared faces.
- Refer to the grid below. A token starts at square S and moves according to the rules shown by the arrows: each gray square pushes the token one step in the arrow's direction, and each white square ends the token's movement. Where does the token end up?
Answer: Square R
Starting at S, follow the arrows: S (right arrow) → next square (down arrow) → next square (right arrow) → next square (down arrow) → lands on white square R, ending movement. A student tracing only 2 steps lands at P. Following only the rightward arrows without downward turns leads to Q. Overshooting one square leads to T.
- A right-facing arrow with a dot above it is rotated 90 degrees counterclockwise. What is the result?
Answer: Up arrow, dot on left
Rotate the arrow 90 degrees counterclockwise: an east-facing arrow becomes up-facing. The dot above the arrow is on top before rotation; rotating that position counterclockwise carries it to the left side. So you get an up arrow with a dot on its left. The tempting mix-up is putting the dot on the right, which is what a clockwise rotation would do.
- Look at the three overlapping circles shown with labeled regions. Which region represents items that are triangles AND shaded, but NOT large?
Answer: Region 4
Region 4 is the intersection of 'Triangles' and 'Shaded' only, excluding 'Large.' Region 2 is only Triangles. Region 5 is the center (all three). Region 7 is only Shaded. A common error is selecting Region 5 because it includes both triangles and shaded, but that region also includes 'Large,' which the question excludes.
