UPCAT Mathematics — Algebra — Sets, Exponents, Radicals, Polynomials & EquationsConcept Map
University of the Philippines loves to test Algebra — Sets, Exponents, Radicals, Polynomials & Equations through questions that span multiple sub-topics in one item. A concept map helps you see those cross-links in advance. This page will show the full Algebra — Sets, Exponents, Radicals, Polynomials & Equations concept map for UPCAT Mathematics once content generation completes.
Exam context
The University of the Philippines College Admission Test is conducted by University of the Philippines and is scheduled for Mid-2026 (announced by UP Admissions). The Mathematics subtest is marked as "25% of UPCAT items" in the official pattern, and Algebra — Sets, Exponents, Radicals, Polynomials & Equations appears in position 3rd of 9 in the UPCAT Mathematics review rotation. Passing mark: UPG ≤ 2.2 typical. Recent UPCAT 2026 papers have drawn roughly 20 questions from this subject.
Algebra — Sets, Exponents, Radicals, Polynomials & Equations - Concept map
Central Concept
Algebraic Foundations
Related Concepts
Concept
Set Theory
Sub Concepts
- Set Operations (Union, Intersection, Complement)
- Venn Diagrams
- Universal Sets and Subsets
- Cardinality and Element Relationships
Relationship To Central
Provides the fundamental language and notation for organizing mathematical objects
Concept
Exponents and Powers
Sub Concepts
- Laws of Exponents (Product, Quotient, Power Rules)
- Zero and Negative Exponents
- Scientific Notation
- Rational Exponents
Relationship To Central
Essential for expressing repeated multiplication and polynomial degrees
Concept
Radicals and Roots
Sub Concepts
- Simplifying Radical Expressions
- Rationalizing Denominators
- Operations with Radicals
- Converting between Radical and Exponential Form
Relationship To Central
Inverse operations to exponents, crucial for solving equations
Concept
Polynomials
Sub Concepts
- Polynomial Operations (Addition, Subtraction, Multiplication, Division)
- Factoring Techniques
- Special Products (Difference of Squares, Perfect Square Trinomials)
- Polynomial Classification by Degree
Relationship To Central
Building blocks for most algebraic expressions and equations
Concept
Algebraic Equations
Sub Concepts
- Linear Equations and Systems
- Quadratic Equations (Factoring, Quadratic Formula, Completing the Square)
- Higher-Degree Polynomial Equations
- Rational and Radical Equations
Relationship To Central
Applications of all previous concepts to solve real-world problems
Concept Connections
To
Algebraic Equations
From
Set Theory
Strength
moderate
Relationship
Provides notation and logical framework for solution sets
To
Radicals
From
Exponents
Strength
strong
Relationship
Inverse operations - radicals undo exponents
To
Polynomials
From
Exponents
Strength
strong
Relationship
Degree of polynomial determined by highest exponent
To
Algebraic Equations
From
Radicals
Strength
strong
Relationship
Radical equations require special solving techniques
To
Algebraic Equations
From
Polynomials
Strength
strong
Relationship
Most algebraic equations involve polynomial expressions
To
Quadratic Equations
From
Factoring
Strength
strong
Relationship
Primary method for solving quadratic equations
To
Functions
From
Set Theory
Strength
moderate
Relationship
Functions defined as special types of relations between sets
To
Scientific Notation
From
Exponents
Strength
strong
Relationship
Scientific notation is direct application of exponent rules
Previous chapter
Ratio & Proportion
Next chapter
Word Problems — Number, Age, Work, Motion, Mixture, Investment
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