Section 5.1: Next in Sequence

Section 5.1: Next in Sequence

The abstract reasoning subtest of the Victoria Police Entrance Exam is designed to evaluate a candidate’s fluid intelligence—the ability to identify patterns, logical rules, and relationships in visual data, and apply this logic to solve novel problems. Administered by the Australian Council for Educational Research (ACER), this computer-based test can be sat either at the official Camberwell assessment venue in Victoria or through supervised remote proctoring. Because this subtest is highly speeded (typically allocating only 30 seconds per question), candidates must develop a structured approach to rapidly decode visual series.

The Mechanics of Next in Sequence Questions

In a next in sequence question, you are presented with a series of diagrams (typically four or five frames) that follow a logical progression from left to right. Your task is to identify the next frame in the series from a set of four multiple-choice options. The underlying patterns are governed by specific geometric and logical rules:

1. Rotations: Elements within the frame rotate around their own axes or around the centre of the frame. These rotations are usually in predictable increments:

   • 90-degree rotations (quarter turns), which can be clockwise (CW) or counterclockwise (CCW).
   • 45-degree rotations (eighth turns), which often alternate direction or follow a progressive pattern.
   • 180-degree rotations (half turns), which manifest as vertical or horizontal inversions.

2. Pattern Progression: This involves a numerical or qualitative change in the characteristics of elements. Examples include:

   • Shading progressions (e.g., moving from unshaded to striped to solid black).
   • Cardinality changes (e.g., a shape’s sides increasing from 3 (triangle) to 4 (square) to 5 (pentagon)).
   • Element count modifications (e.g., the number of dots inside a shape increasing by one, or doubling in each step).

3. Translation: The physical movement of an element from one position to another within the boundaries of the frame. This movement can be along the edges (linear translation), across diagonals (diagonal translation), or in a circular path.

4. Symmetry: Reflections across a vertical, horizontal, or diagonal axis. Often, an element will alternate between its standard form and its mirrored image in a repeating A-B-A-B pattern.

5. Size changes: The scaling up or scaling down of objects. This is frequently combined with shading or layering (e.g., a small solid circle becomes a medium striped circle, then a large hollow circle).

Systematic Solving Methodology

Under the pressure of the Victoria Police exam, guessing or trying to comprehend the entire diagram at once leads to cognitive overload. Instead, candidates should apply the Single Element Isolation (SEI) technique. This method involves breaking the diagram down into its individual components and tracking them independently.

• Step 1: Focus on a Single Element: Ignore the rest of the image. Look only at one feature—for instance, a small black dot in the corner.
• Step 2: Map the Movement: Determine how that single element changes from frame 1 to frame 2, then frame 2 to frame 3. Is it rotating, translating, changing color, or scaling? Write down or mentally note the rule (e.g., "moves clockwise to the next corner").
• Step 3: Eliminate Options: Check the four multiple-choice options. Eliminate any options that do not place this specific element in the correct position or state.
• Step 4: Repeat for the Next Element: If more than one option remains, pick another element (e.g., the orientation of the central arrow) and determine its rule. Eliminate further options until only one correct answer remains.

Real-World Victoria Police Context

The Abstract Reasoning subtest maps directly to the Australian Core Skills Framework (ACSF Level 3) cognitive standards required of modern police officers. General duties officers must rapidly assess changing environments, identify anomalies, and predict sequences of events during operations. An officer observing a vehicle's movements or a crowd's dynamics is performing real-time pattern analysis analogous to these abstract reasoning sequences.

Detailed Worked Example: The Intersecting Shapes Sequence

Consider a sequence of four frames:

• Frame 1: A large unshaded triangle containing a small black square in its top corner.
• Frame 2: A large unshaded square containing a small black square in its top-right corner.
• Frame 3: A large unshaded pentagon containing a small black square in its bottom-right corner.
• Frame 4: A large unshaded hexagon containing a small black square in its bottom corner.

Let's dissect the pattern:

• Rule 1 (Outer Shape): The outer shape is a polygon whose number of sides increases by one in each step. It goes from a triangle (3 sides) to a square (4 sides) to a pentagon (5 sides) to a hexagon (6 sides). Therefore, the next shape in the sequence (Frame 5) must be a heptagon (7 sides).
• Rule 2 (Inner Element): The small black square is translating along the corners of the outer shape. Looking closely at its position:
  • In the triangle, it is at the top corner (12 o'clock).
  • In the square, it is at the top-right corner (approx. 2 o'clock).
  • In the pentagon, it is at the bottom-right corner (approx. 5 o'clock).
  • In the hexagon, it is at the bottom corner (6 o'clock).
  • This indicates a clockwise rotation/translation along the vertices of the polygon. For a heptagon in Frame 5, the element must move to the next corner, which is the bottom-left corner (approx. 7 o'clock).

By applying the Single Element Isolation technique, we can eliminate any options that do not show a heptagon (7 sides) or do not place the small black square in the bottom-left position.

Common Pitfalls and How to Avoid Them

• Overlooking Compound Rules: Some elements are governed by two rules simultaneously. For example, a star might rotate 45 degrees clockwise while also alternating between black and white. If you only track the rotation, you might select an option with the wrong shading.
• Misidentifying the Direction of Rotation: Candidates often confuse clockwise and counterclockwise rotations, especially when shapes are complex or when the rotation angle is 135 degrees. When a shape rotates 135 degrees CCW, it is equivalent to rotating 225 degrees CW. Keeping track of the exact angles is crucial.
• Ignoring Frame Boundaries: Sometimes, the pattern involves elements moving out of the frame and wrap-around translation (e.g., an element exiting from the right side and re-entering from the left). Recognize this as a valid translation rule rather than a random disappearance.