# Types of Problem

## Pure Problems

• Pure problems consider mathematical theory, abstract motivation and proof.
• Cover areas such as analysis, algebra, number theory and geometry.
• Require a thorough understanding of mathematical concepts and principles.

## Applied Problems

• Applied problems involve mathematics applied to real-world scenarios.
• Domain includes physics, engineering, economics, population dynamics, and more.
• Understanding of context and assumptions often critical to solve these types of problems.

## Open Problems

• Open problems are unsolved mathematical issues.
• Can be categorised as pure or applied problems.
• The nature of open problems requires a high level of originality and creativity.

## Recursive Problems

• Recursive problems solve something based on previous results within the problem.
• Useful in series, sequences and mathematical induction.
• Understanding recursion is fundamental to solving these types of problems.

## Geometric Problems

• Geometric problems revolve around geometric figures and properties.
• Can be purely theoretical or depend on measurements and the application of formulas.
• Familiarity with geometric terms, concepts, theorems, and postulates is crucial.

## Constraint Problems

• Constraint problems involve conditions or limitations within the problem.
• Evaluation of options within set boundaries is key to solutions.
• Understanding how to work within constraints is central to solving these problems.

## Graphing Problems

• Graphing problems involve visualising relationships between variables.
• Require understanding of coordinate geometry, functions, and calculus.
• Integration of graphical and algebraic methods often leads to solutions.

## Equation-based Problems

• Equation-based problems involve the formulation and solution of equations.
• Knowledge of various types of equations and methods to solve them is vital.
• Understanding how to interpret solutionsets is equally crucial.

## Probability Problems

• Probability problems involve predicting uncertain outcomes.
• Require understanding of probability theory, statistics, and combinatorics.
• Methods can vary from simple counting principles to sophisticated statistical techniques.