Figural Reasoning and Patterns Flashcards

A cube has a star on its top face and a circle on its front face. The cube is tipped backward (the front face rises upward). Which face is now on top?

Answer: The circle face

Tipping the cube backward raises the front face to become the new top, so the circle face is now on top.

A sequence shows: Figure 1 = small shape inside a large circle; Figure 2 = small circle inside a large triangle; Figure 3 = small triangle inside a large square. What is Figure 4?

Answer: Small square inside a large circle

The inner shape follows circle→triangle→square→circle and the outer shape follows circle→triangle→square→circle with a one-step offset, giving a small square inside a large circle.

In a figure analogy: a dark pentagon is to a light pentagon as a dark hexagon is to:

Answer: A light hexagon

The transformation changes fill from dark to light while the shape stays the same, so a dark hexagon becomes a light hexagon.

A grid pattern shows shapes where the number of sides increases by 1 going left to right across a row and decreases by 1 going top to bottom in a column. If the top-left cell has a hexagon (6 sides), how many sides does the shape in the bottom-right cell of a 3×3 grid have?

Answer: 6

Moving 2 steps right adds 2 sides and moving 2 steps down subtracts 2 sides: 6 + 2 − 2 = 6, so the bottom-right cell has a hexagon (6 sides).

A series of figures shows 1 shaded triangle in Figure 1, 3 in Figure 2, 6 in Figure 3, and 10 in Figure 4. How many shaded triangles are in Figure 5?

Answer: 15

The sequence is triangular numbers: each figure adds one more triangle than the previous step (1, +2, +3, +4, +5), so Figure 5 = 10 + 5 = 15.

A figure shows a large square divided into four equal quadrants. The top-left quadrant is shaded. After two reflections — first across the vertical midline, then across the horizontal midline — which quadrant is shaded?

Answer: Bottom-right

Reflecting across the vertical midline moves the shading to the top-right; then reflecting across the horizontal midline moves it to the bottom-right.

A pattern matrix has the rule: the shape in each cell equals the shape directly above it rotated 90° clockwise. The top-left cell contains an upward-pointing arrow. What does the cell two rows below the top-left contain?

Answer: A downward-pointing arrow

One row down = 90° clockwise (rightward arrow); two rows down = another 90° clockwise = downward-pointing arrow.