PMA Graduate Course Non-Verbal Intelligence Syllabus

What is the 'superimposition' rule in pattern matrices?

The result figure is formed by overlaying the first two figures; sometimes lines common to both are kept, sometimes only non-common lines remain (the cancellation rule).

What are 'Pattern Matrices' in non-verbal intelligence tests?

Grids of figures arranged so that a logical rule operates across rows and/or columns, and the test-taker must deduce the rule to fill the missing figure.

In a pattern matrix, why check both rows and columns?

Because the governing rule may run horizontally, vertically, or both; confirming the rule in both directions prevents choosing a figure that fits one direction but breaks the other.

Define 'Mirror Reflection' in non-verbal reasoning.

The image of a figure as it would appear in a vertical plane mirror placed to its side: left and right are reversed while top and bottom stay the same.

In a vertical (lateral) mirror, which features of the figure are swapped?

Left and right are interchanged (laterally inverted); top and bottom remain unchanged.

What is the rule for the mirror image of letters and numbers in a vertical mirror?

Each character is laterally reversed; e.g., 'b' appears as 'd', and 'p' appears as 'q'. Symmetrical characters like A, H, M, O, T, U, V, W, X, Y appear unchanged.

Which capital letters look the SAME in a vertical mirror reflection?

Letters with vertical-axis symmetry: A, H, I, M, O, T, U, V, W, X, Y.

How is the angle between a figure and its mirror image related to the mirror line?

The figure and its mirror image are equidistant from the mirror line and symmetric about it; the mirror line acts as the axis of symmetry (perpendicular bisector between corresponding points).

Define 'Water Reflection' in non-verbal reasoning.

The image of a figure as seen in water (a horizontal mirror below it): top and bottom are inverted (upside-down) while left and right stay the same.

In a water reflection, which features are swapped compared to a mirror reflection?

Water reflection inverts TOP and BOTTOM (vertical flip); a vertical mirror reflection swaps LEFT and RIGHT (horizontal flip).

What is the key difference between mirror image and water image?

A mirror image is a left-right (lateral) flip about a vertical line; a water image is a top-bottom (vertical) flip about a horizontal line.

Which capital letters look the SAME in a water reflection?

Letters with horizontal-axis symmetry: B, C, D, E, H, I, K, O, X.

In a water image, how do numbers like 0, 3, and 8 behave?

0 and 8 appear unchanged (horizontal symmetry); 3 also appears symmetric, while digits like 1, 2, 4, 5, 6, 7, 9 are inverted top-to-bottom.

What are 'Paper Folding Patterns' (paper folding and punching) problems?

A problem where a sheet is folded one or more times and a hole is punched; you must determine the pattern of holes when the paper is fully unfolded.

What is the basic rule for the number of holes after unfolding a punched, folded paper?

Each fold doubles the number of holes; if a paper is folded n times and one hole is punched, unfolding generally reveals 2^n holes.

How do you locate the holes when unfolding a folded-and-punched paper?

Reverse each fold one at a time; for every fold, reflect each existing hole across that fold line to its mirror position, repeating until the sheet is flat.

If a square is folded once in half and one hole is punched, how many holes appear when unfolded?

Two holes, positioned symmetrically about the fold line (mirror images of each other).

If a square is folded twice (into quarters) and one hole is punched, how many holes appear?

Four holes, because each of the two folds doubles the count (2 then 4), arranged symmetrically across both fold lines.

What is a 'dot situation' problem in non-verbal reasoning?

A problem where dots are placed in a figure relative to specific regions; you must find another figure in which a dot can be placed satisfying the same regional conditions.

What general strategy applies to almost all non-verbal reasoning items?

Observe the figures, identify the underlying rule or relationship, apply it consistently, and eliminate answer options that violate the rule.

Why is the elimination method useful in non-verbal tests?

Because rejecting each option that breaks the detected rule narrows choices quickly and reduces the chance of error when the correct figure is hard to construct mentally.

What does 'lateral inversion' mean?

The left-right reversal of an image, as produced by a plane mirror; the defining feature of a mirror (vertical) reflection.

How can symmetry help in classification and odd-one-out problems?

Figures can be grouped by whether they have line symmetry, rotational symmetry, or none; a figure lacking the group's symmetry is often the odd one out.

In sequence/series problems, what does 'shading rotation' refer to?

A rule where the shaded portion of a figure moves to a new position (e.g., rotates clockwise) at each step while the outline stays the same.

What is the difference between 'rotation' and 'reflection' of a figure?

Rotation turns the figure about a point keeping its handedness (orientation sense) the same; reflection flips it across a line, reversing its handedness (mirror-reversed).

How do you distinguish a rotated figure from a reflected figure in the options?

A reflected figure is a mirror image (cannot be obtained by turning in the plane), whereas a rotated figure preserves the original's left-right sense; check an asymmetric detail to tell them apart.

In a 3x3 matrix, what is the 'progressive change' rule?

A feature (such as number of lines, dots, or shaded cells) increases or decreases by a fixed amount as you move along each row or column.

What should you check first in a figure-analogy when multiple options look correct?

Check the orientation/direction and the count of elements, since distractor options usually keep the right shape but change rotation, position, or number to mislead.

How is a clock or arrow direction used as a rule in non-verbal series?

An arrow or pointer rotates by a fixed angle each step (e.g., 45 or 90 degrees); tracking its direction across figures reveals the next position.

What is the relationship between the original figure and its image regarding size in mirror and water reflections?

The size and shape are unchanged in both; only the orientation is flipped (left-right for mirror, top-bottom for water), so the image is congruent to the original.

Summarise the three core flip rules a student must memorise for reflection problems.

Mirror (vertical mirror): swap left-right. Water (horizontal mirror): swap top-bottom. Rotation by 180 degrees: swap both left-right AND top-bottom together.