Figural Reasoning and Patterns Flashcards

A sequence shows figures with 1, 4, 9, 16, and 25 dots arranged in square grids. How many dots will the next figure contain?

Answer: 36

The sequence is perfect squares (1², 2², 3², 4², 5²), so the next term is 6² = 36.

A 3×3 matrix shows shapes where each row contains a circle, triangle, and square in some order, and each column also contains each shape exactly once. The top row is circle, triangle, square and the middle row starts with triangle. What shape is in the bottom-left cell?

Answer: Square

Column 1 already has circle (top) and triangle (middle), so the bottom-left must be square.

A series of circles is shown: the first is fully shaded, the second has the right half shaded, the third has the right quarter shaded. Which best describes the fourth circle?

Answer: Right eighth shaded

Each step halves the shaded area while keeping it on the right side, so the fourth circle has the right eighth shaded.

A figure sequence shows an arrow pointing right, then rotated 45° counterclockwise to point up-right, then pointing up, then pointing up-left. What direction does the fifth arrow point?

Answer: Left

Each arrow rotates 45° counterclockwise; after four 45° steps from right (0°), the fifth arrow points left (180°).

In a visual analogy, a solid black square is to a hollow square outline as a solid black triangle is to:

Answer: A hollow triangle outline

The transformation removes the fill while keeping the same shape, so a solid black triangle becomes a hollow triangle outline.

A 4×4 checkerboard pattern has the top-left square shaded black. How many black squares are in the entire grid?

Answer: 8

A 4×4 checkerboard has 16 squares split evenly, giving exactly 8 black squares.

A pattern shows alternating rows of stars: odd rows have filled stars numbering 1, 3, 5 and even rows have hollow stars numbering 2, 4, 6. What is the total number of stars across the first six rows?

Answer: 21

Rows 1 through 6 contain 1+2+3+4+5+6 = 21 stars total.