TACHS Quiz: Completing Figure Matrices
15 questions · exam conditions
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Completing Figure MatricesQuestion 1 of 15

3x3: Row1: white circle, gray square, black triangle. Row2: gray square, black triangle, white circle. Bottom-right?

gray square
black triangle
white circle
gray circle
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TACHS Quiz

TACHS Quiz: Completing Figure Matrices

Practice Completing Figure Matrices in TACHS with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Completing Figure Matrices, giving you a quick way to practice the rules, question types, and explanations that matter most for TACHS.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

3x3: Row1: white circle, gray square, black triangle. Row2: gray square, black triangle, white circle. Bottom-right?

  1. gray square (correct answer)
  2. black triangle
  3. white circle
  4. gray circle
Explanation: Each row shifts the three shapes one place to the left, wrapping the first shape to the end. Row 1 is white circle, gray square, black triangle; Row 2 is gray square, black triangle, white circle; so Row 3 is black triangle, white circle, gray square. The bottom-right cell is therefore the gray square. The tempting white circle is wrong because it belongs in the middle of the third row, not the last cell.

Question 2

Matrix: dots +1 across rows/columns; shapes down are square, circle, triangle. Top-left square, 1 dot. Bottom-right?

  1. circle with 5 dots
  2. square with 5 dots
  3. triangle with 6 dots
  4. triangle with 5 dots (correct answer)
Explanation: Moving right or down adds one dot, so from the top-left square with 1 dot, the bottom-right is two steps right and two steps down: 1 + 2 + 2 = 5. Shapes run square, circle, triangle down each column, so the bottom-right shape is triangle. Triangle with 6 dots is wrong because it overcounts the steps; the correct increase is only 4 dots.

Question 3

2x2: top-left white square, dot top; top-right white square, dot right; bottom-left gray square, dot top. Bottom-right?

  1. gray square, dot right (correct answer)
  2. gray square, dot top
  3. white square, dot right
  4. gray square, dot bottom
Explanation: Each row keeps the square color: top row is white, bottom row is gray. Each column keeps the dot position: left column has dot top, right column has dot right. So the missing cell must be a gray square with a dot right. The tempting answer, gray square with dot top, only follows the row color and ignores the column dot rule.

Question 4

Each row/column has one W/G/B and one C/S/T. Row1: WC, GS, BT. Col1: WC, GT, BS. Bottom-right?

  1. white triangle
  2. gray circle (correct answer)
  3. black square
  4. gray square
Explanation: Top row uses W/G/B and C/S/T, and the left column forces row 2 as GT, BC, WS, so row 3 starts BS. Column 2 then needs white triangle, and column 3 needs gray circle to complete each color and shape once. The tempting gray square is wrong because row 3 already has a square in column 1 and column 3 already has a square in row 2.

Question 5

Refer to the figure matrix below. Which choice correctly completes it?

  1. Two overlapping circles with the overlap region shaded black
  2. Two overlapping circles with both circles shaded black and overlap white (correct answer)
  3. Two non-overlapping circles, left one black, right one white
  4. Two overlapping circles, both unshaded with a black dot in the overlap
Explanation: Row rule: the third cell of each row is the XOR (symmetric difference) of the first two cells — regions shaded in exactly one of the first two figures become shaded in the third. In row 3, cell 1 has both circles black with overlap white, and cell 2 has only the overlap black; applying XOR leaves both circles black and overlap white. (A) is the intersection only. (C) ignores overlap structure. (D) adds an extraneous element.

Question 6

Study the figure matrix below. Which option best completes the missing cell?

  1. A clock face showing 7:30 (hands at 7 and 6) (correct answer)
  2. A clock face showing 9:00 (hands at 9 and 12)
  3. A clock face showing 8:00 (hands at 8 and 12)
  4. A clock face showing 6:30 (hands at 6 and 6)
Explanation: Moving across each row from left to right, the time advances by 1 hour and 30 minutes each step. In row 3: first cell shows 4:30, second cell shows 6:00, so the third cell should show 7:30 (advancing another 1 hour 30 minutes).

Question 7

Study the 3×3 matrix below. Which answer completes the missing cell?

  1. A square divided into 4 quadrants with the top-left and bottom-right shaded
  2. A square divided into 4 quadrants with the top-right and bottom-left shaded
  3. A square divided into 4 quadrants with all four quadrants shaded
  4. A square divided into 4 quadrants with no quadrants shaded (correct answer)
Explanation: In each row, the three shaded-quadrant patterns cover each of the four quadrants exactly once across columns 1 and 2, and column 3 shows whatever remains. In row 3, columns 1 and 2 together cover all four quadrants, so nothing remains — column 3 is blank. (A) and (B) are diagonal patterns that don't follow the rule. (C) would be the complement rule, not the remainder rule.

Question 8

Look at the figure matrix shown. Which figure completes the matrix correctly?

  1. A circle with 5 radial spokes and 2 concentric inner rings
  2. A circle with 6 radial spokes and 2 concentric inner rings (correct answer)
  3. A circle with 5 radial spokes and 3 concentric inner rings
  4. A circle with 6 radial spokes and 3 concentric inner rings
Explanation: Spokes: across each row, the spoke count increases by 1 (row 3: 4→5→6). Rings: down each column, the ring count increases by 1 (col 3: 0→1→2). So bottom-right has 6 spokes and 2 rings. (A) uses row 3 column 2's spoke count. (C) uses wrong ring count. (D) confuses the ring increment.

Question 9

Look at the 3×3 matrix of figures below. Which figure belongs in the empty cell (bottom-right) to complete the matrix according to the row and column rules?

  1. A black pentagon with 3 small white circles inside
  2. A white pentagon with 3 small black circles inside (correct answer)
  3. A black pentagon with 3 small black circles inside
  4. A white pentagon with 3 small white circles inside
Explanation: Row rule: the outer shape gains one side across each row (triangle→square→pentagon in row 3). Column rule: the outer shape's fill color rotates black→white→white down column 3, so the pentagon is white. The number of inner dots equals (row number), so row 3 has 3 dots; the inner dots' color alternates opposite the outer shape's color, so black dots. Result: white pentagon with 3 black dots. (A) inverts both colors. (C) keeps the outer shape black (ignores column color rotation). (D) makes the inner dots white (ignores the inversion rule).

Question 10

Study the 3×3 figure matrix shown. Which answer choice correctly completes the bottom-right cell?

  1. An arrow pointing up-right with 4 tick marks on the shaft (correct answer)
  2. An arrow pointing down-left with 4 tick marks on the shaft
  3. An arrow pointing up-right with 3 tick marks on the shaft
  4. An arrow pointing down-left with 3 tick marks on the shaft
Explanation: Across each row the arrow rotates 45° clockwise. Row 3 begins with an arrow pointing left, so the cells go left→up-left→up-right. Down each column the number of tick marks increases by 1 (row 1:2, row 2:3, row 3:4). So bottom-right is up-right with 4 ticks. (B) reverses the arrow direction. (C) uses column-2's tick count. (D) combines both errors.

Question 11

Examine the matrix provided. Which choice completes it?

  1. Three horizontal parallel lines with a small circle above the top line
  2. Three horizontal parallel lines with a small circle between the middle and bottom lines
  3. Three horizontal parallel lines with a small circle below the bottom line (correct answer)
  4. Three horizontal parallel lines with a small circle between the top and middle lines
Explanation: The circle moves down one level per column (column 1: above top; column 2: between top-middle; column 3: between middle-bottom) — and down one additional level per row. Row 3, column 3: start at above-top, add 2 column steps + 2 row steps = 4 downward moves, landing below the bottom line. (A) no movement applied. (B) only row movement. (D) only column movement.

Question 12

Refer to the matrix shown. Which option correctly fills the missing cell?

  1. An L-shape made of 4 squares in the bottom-left corner orientation
  2. An L-shape made of 4 squares in the top-right corner orientation (correct answer)
  3. A T-shape made of 4 squares pointing upward
  4. A T-shape made of 4 squares pointing downward
Explanation: The shape in each row is constant (row 3 uses L-tetromino). Across each row, the shape rotates 90° clockwise. Row 3 col 1 is L in standard orientation (bottom-left), col 2 rotated 90° CW (bottom-right), col 3 rotated 180° = top-right corner. (A) is the starting orientation, unrotated. (C) and (D) use the wrong shape entirely (T-tetromino).

Question 13

Look at the 3×3 figure matrix. Select the choice that completes the matrix.

  1. A hexagon with one diagonal line and a small dot in the upper-right region
  2. A hexagon with two diagonal lines forming an X and a small dot in the center
  3. A hexagon with three lines through the center (like an asterisk) and no dot (correct answer)
  4. A hexagon with three lines through the center and a small dot in the center
Explanation: Number of internal lines equals the row number (row 1:1 line, row 2:2 lines, row 3:3 lines). The dot appears only in columns 1 and 2; column 3 never has a dot. Thus bottom-right: 3 lines, no dot. (A) uses row-1 line count. (B) uses row-2 line count and adds a dot. (D) correctly has 3 lines but incorrectly adds a dot.

Question 14

Look carefully at the 3×3 matrix below. Which figure completes the matrix?

  1. A cluster of 9 small dots arranged in a 3×3 square pattern (correct answer)
  2. A cluster of 8 small dots arranged in a circular ring pattern
  3. A cluster of 9 small dots arranged in a cross/plus pattern
  4. A cluster of 7 small dots arranged in a triangular pattern
Explanation: The number of dots in each cell equals the row number multiplied by the column number. Row 3, column 3 requires 3 × 3 = 9 dots. Within each row, the dot arrangements follow a pattern: the third column uses a square/grid arrangement. Therefore, the missing cell needs 9 dots arranged in a 3×3 square pattern.

Question 15

Examine the matrix of figures below. Which figure completes the pattern in the missing cell?

  1. A large circle containing a small black square and a small white triangle
  2. A large circle containing a small white square and a small black triangle (correct answer)
  3. A large square containing a small black circle and a small white triangle
  4. A large square containing a small white circle and a small black triangle
Explanation: Row rule: the outer shape in row 3 is constant (circle). Column rule: column 3 contains the two inner shapes that did NOT appear in the first two columns of that row. Row 3 columns 1 & 2 show (square+circle) and (triangle+circle), so column 3 contains square+triangle. Color rule: the small shape that was black in column 1 becomes white in column 3, and vice versa — so white square + black triangle inside a circle. (A) flips the colors. (C) and (D) use the wrong outer shape.