AoPS

0 of 148 lessons complete (0%)
Exit Course

Exponents and Logarithms

Wizdomi AoPS Fundamentals

This is a preview lesson

Register or sign in to take this lesson.

Elite 1-on-1 Live Online Tuitions

Master the Art of Problem Solving with Wizdomi

Personalized, strategic mentorship tailored for high-achieving students in the **US, Canada, Singapore, and Australia**. Our rigorous curriculum equips students to dominate elite international math Olympiads and competitions.

Exams Powered by Our AoPS Curriculum

The Wizdomi AoPS Fundamentals curriculum provides the exact technical and conceptual foundation required to conquer the worldโ€™s most elite math competitions. Click the regions below to filter deep-dive exam guides.

AMC 8

Middle School

The premier introductory American Mathematics Competition designed to foster analytical skills and a passion for creative problem-solving.

Target Grades: Grade 8 or below (under 14.5 years old)
Format: 25 Multiple-choice questions | 40 Minutes
Scoring: 1 point per correct answer | No penalty for guessing
Core AoPS Focus: Core Integers, Fundamentals of Geometry, Linear Equations, Counting basic combinations.

AMC 10 / 12

High School

High-stakes competitions leading directly to the prestigious AIME. Tests advanced high-school level algebra, geometry, and numbers theory.

Target Grades: AMC 10 (Grades 10 or below) | AMC 12 (Grades 12 or below)
Format: 25 Multiple-choice questions | 75 Minutes
Scoring: +6 for Correct | +1.5 for Unanswered | 0 for Incorrect
Core AoPS Focus: Advanced Quadratics, Complex Numbers, In-depth Coordinate & 3D Geometry, Statistics & Advanced Probability.

AIME & USAOlympiad

Invitational

The American Invitational Mathematics Examination is open only to top performers on the AMC 10/12. Features deeply intricate, non-trivial mathematical logic.

Target Grades: Elite qualifiers via AMC 10/12 performance
Format: 15 Short-answer questions (Integers 000-999) | 3 Hours
Core AoPS Focus: Advanced Rigorous Proofs, Power of a Point, Inequalities, Complex Sequence & Series, Modular Arithmetic.

Waterloo & Caribou

Grades 3-12

University of Waterloo Math Contests (Gauss, Pascal, Cayley, Fermat, Euclid) alongside Caribou Contests emphasize structural logic, real-world word problems, and written steps.

Target Grades: Structured progressively from Elementary to Grade 12
Format: Varies (Euclid features 10 full-response and analytical questions)
Core AoPS Focus: Proportions & Percentages, Functions, Circle properties, Trigonometry, and System of Equations.

SASMO & SMO

Primary to JC

Singapore and Asian Schools Math Olympiad & Singapore Mathematical Olympiad emphasize unconventional thinking, combining rigorous local arithmetic speed with abstract proofs.

Target Grades: Primary 1 through Junior College (Grades 1-12)
Format: Section A (MCQ) & Section B (Non-routine short answers)
Core AoPS Focus: Pigeonhole Principle, Clever Manipulations, Angle Chasing, Modular Arithmetic, Divisibility.

Australian AMC & ICAS

Grades 3-12

The Australian Mathematics Competition and ICAS test critical operational data management, creative spatial and multi-dimensional analysis, and pattern optimization.

Target Grades: Year 3 to Year 12 (Divisions: Middle Primary to Senior)
Format: 30 Questions (25 Multiple-choice + 5 complex integer answers) | 60-75 Mins
Core AoPS Focus: Sets & Venn Diagrams, 3D Geometry/Surface areas, Shifts/Transforms/Dilations, and Probability trees.

Explore the Wizdomi AoPS Fundamentals Syllabus

Click on any module to view the comprehensive, structured sub-topics taught in our premium 1-on-1 sessions.

  • Integer Exponents & Extended Drafts
  • Fractional Exponents
  • Simplifying Radical Expressions
  • Rationalizing Denominators
  • Logarithms & Base Operations
  • The Square Root of -1
  • Complex Number Operations
  • Complex Planar Geometries
  • Definition of Linear Equation
  • One Equation, One Variable
  • Two Equations, Two Variables
  • Complex Strategic Word Problems
  • Direct and Inverse Proportions
  • Manipulating Analytical Proportions
  • Conversion Factors
  • Advanced Percent Computations
  • Divisibility Rules & Prime Elements
  • Varying Number Bases
  • The Last Digit Computations
  • Modular Arithmetic Tricks
  • Common and Uncommon Divisors
  • What’s a Quadratic & Factoring
  • The Quadratic Formula
  • Variations, Rearrangements & Substitutions
  • Square Roots of Irrationals and Imaginaries
  • Beyond Quadratics (Higher Polynomials)
  • Special Factorization Techniques
  • Clever Algebraic Manipulations
  • Integers, Rationals & Lowest Terms
  • Irrationals, Complex Realities and Beyond
  • An Introduction to Circles & Arc Geometries
  • Lines, Rays, Segments & Parallel Properties
  • Angles Formed By Intersecting Lines & Circle Proofs
  • Classifying Triangles & The Triangle Inequality
  • The Pythagorean Theorem, Congruency & Similarity
  • Introduction to Trigonometry & Multi-Method Triangle Areas
  • Quadrilaterals (Trapezoids, Parallelograms, Rhombi, Squares)
  • Regular Polygons & Elite Regular Hexagons
  • Strategic Angle Chasing & Complicated Area Partitioning
  • Labelling the Plane: The Distance Formula & Circle Graphs
  • Power of a Point Geometric Proofs
  • Planes, Surface Area, and Volume Mechanics
  • Spheres, Cubes, Boxes, Prisms, Cylinders, Pyramids & Cones
  • Polyhedral Analysis & Methods for Solving 3D Space Problems
  • Spatial Transformations: Translation, Rotation, Reflection
  • Distortion, Dilation, and Transformational Proof Structural Design
  • Graphing Functions, Inputs & Outputs
  • Even, Odd, and Special Custom Function Maps
  • Linear, Quadratic, and Absolute Value Inequalities
  • The Trivial Inequality Applications
  • Mathematical Operations, Properties, and Abstract Relations
  • Arithmetic, Geometric, and Infinite Complex Series
  • Advanced Counting Principles & Restriction Constraints
  • Permutations, Arrangements, and Binomial Theorem
  • Statistical Metrics, Common-Sense & Multiplied Probabilities
  • Casework Methods, Odds, and Expected Values
  • Sets Mechanics: Operations, Venn Diagrams, and Subsets
  • Direct Proofs vs. Contradiction Logic
  • Converses & Fallacies: Convincing But Wrong Dynamics
  • Mathematical Induction Mastery
  • The Pigeonhole Principle (Shooting Holes in Pigeons)
  • Parting Shots: Integrated High-Level Capstones

Ready to Unlock Elite Mathematical Capability?

Get tailored 1-on-1 expert support dynamically aligned with this AoPS framework. Prepare flawlessly for your target national exam.

Book Your 1-on-1 Free Evaluation Class