1. Figure Series & Patterns 🔄
Find the pattern in a series of figures and predict what comes next!
Common Pattern Types
| Pattern Type | What to Look For | Example |
|---|---|---|
| Rotation | Figures turning clockwise/counter-clockwise | Arrow rotating 45° each step |
| Addition | Elements being added each frame | 1 dot, 2 dots, 3 dots, 4 dots... |
| Subtraction | Elements being removed | Full circle, 3/4, 1/2, 1/4... |
| Alternation | Pattern switches between two states | Black, white, black, white... |
| Movement | Object moving in a direction | Circle moving left to right |
| Size Change | Objects growing or shrinking | Small, medium, large, larger... |
| Shading Change | Fill patterns changing | Empty, striped, solid... |
Strategy for Figure Series
- Look at overall shape changes first
- Check for rotation (how many degrees?)
- Count elements (increasing? decreasing?)
- Note position changes (where do things move?)
- Check shading/color patterns
- Verify your pattern applies to ALL figures
2. Figure Matrices (3x3 Grids) 🔲
Find the missing figure in a 3x3 grid. Patterns work across rows AND down columns!
How Matrices Work
Row Patterns
- Each row follows a consistent rule
- Elements combine or cancel out
- Each row has all variations
- Sum/difference patterns
Column Patterns
- Same rules apply down columns
- Must be consistent with row pattern
- Check diagonal patterns too
- Missing piece satisfies both
Common Matrix Rules
- Addition: Row 1 + Row 2 = Row 3
- Subtraction: Row 1 - Row 2 = Row 3
- Unique Elements: Each element appears once per row/column
- Transformation: Same change across each row
3. Spatial Reasoning - Cube Folding 🧊
Given an unfolded cube, determine which 3D cube it makes when folded.
Cube Folding Rules
Finding Opposite Faces
In a cross-shaped pattern:
- Top face is opposite to the 3rd face down
- Faces with a gap between them are opposite
- Adjacent faces in pattern are adjacent when folded
Tips for Cube Problems
- Identify one face first
- Think about which faces touch that face
- Mentally fold step by step
- Eliminate impossible options
Common Mistakes
- Forgetting to flip/rotate faces
- Wrong orientation of symbols
- Confusing adjacent vs opposite
4. Mirror Images & Reflections 🪞
Find the correct mirror image or identify which figure is NOT a reflection.
Types of Reflections
| Type | What Happens | Example |
|---|---|---|
| Vertical Mirror (Left-Right) | Left and right swap | Letter "b" becomes "d" |
| Horizontal Mirror (Top-Bottom) | Top and bottom swap | Letter "p" becomes "d" |
| Both Combined | 180° rotation effect | Letter "b" becomes "q" |
Letters That Look Same in Mirror
Vertical mirror: A, H, I, M, O, T, U, V, W, X, Y
Horizontal mirror: B, C, D, E, H, I, K, O, X
Both directions: H, I, O, X
5. Odd One Out 🎯
Find the figure that doesn't belong in the group.
Things to Check
Visual Properties
- Number of sides/angles
- Open vs closed shapes
- Curved vs straight lines
- Shading/fill pattern
- Size relative to others
Structural Properties
- Symmetry (vertical, horizontal, rotational)
- Number of elements inside
- Direction arrows point
- Position of internal elements
- Rotation orientation
Strategy
- Scan all figures quickly first
- Look for the most obvious difference
- Check if 4 out of 5 share a property
- The one without that property is the answer
- Verify your choice doesn't fit the pattern
6. Figure Analogies 🔗
A is to B as C is to ? - Find the relationship and apply it.
Common Figure Relationships
| Relationship | A → B | So C → ? |
|---|---|---|
| Rotation | Rotates 90° clockwise | Apply same rotation to C |
| Color Inversion | Black → White | Invert C's colors |
| Size Change | Gets smaller/larger | Resize C accordingly |
| Element Addition | Line/dot added | Add same element to C |
| Reflection | Mirror image | Create mirror of C |
Steps to Solve
- Study how A transforms into B
- List all changes (rotation, color, size, elements)
- Apply the EXACT same changes to C
- Find the answer choice that matches
7. DLSUCET Abstract Tips & Practice 🎯
Exam Strategies
- Work Quickly: Abstract reasoning is time-sensitive
- Trust Your Eyes: Patterns often "jump out" at you
- Eliminate Wrong Answers: Sometimes easier than finding the right one
- Don't Overthink: Usually the simplest pattern is correct
- Skip and Return: If stuck, move on and come back
- Practice! The more patterns you see, the faster you recognize them
Practice Questions
Q1: In a series, if each figure rotates 45° clockwise, what happens after 8 figures?
8 × 45° = 360° = full rotation. Answer: Returns to original position
Q2: In a cube net, what's opposite to the face that's in the middle of a cross pattern?
Answer: The face that would be 2 squares away (not adjacent) when the pattern is folded.
Q3: What's the vertical mirror image of the letter "F"?
Answer: A backwards "F" - the arms point to the opposite direction (left instead of right).
Q4: Four shapes are circles. One is an oval. Which is the odd one out?
Answer: The oval - all others are perfect circles with equal diameter in all directions.