Algebra
- Investigating Patterns: Analyze number sequences, geometric shapes, or algebraic expressions to identify patterns and predict future terms.
- Solving Equations and Inequalities: Develop strategies for solving linear, quadratic, and polynomial equations and inequalities, exploring different methods and their applications.
- Function Exploration: Graph and analyze various types of functions (linear, quadratic, exponential, logarithmic) to understand their properties and relationships to each other.
Geometry
- Properties of Shapes: Explore the properties, measurements, and relationships of 2D and 3D geometric shapes, such as triangles, circles, cubes, and spheres.
- Transformations: Investigate geometric transformations (translations, rotations, reflections, dilations) and their effects on shapes.
- Area, Volume, and Surface Area: Calculate and derive formulas for the area, volume, and surface area of different geometric shapes.
Calculus
- Limits and Derivatives: Define and investigate limits and derivatives of functions, understanding their graphical and analytical interpretations.
- Integration: Explore techniques of integration, such as u-substitution, integration by parts, and partial fractions, to find antiderivatives and solve applications.
- Optimization: Apply calculus to optimize functions, finding maximum and minimum values in real-world contexts.
Statistics and Probability
- Data Analysis: Collect, organize, and analyze data using descriptive statistics (mean, median, mode, standard deviation) to draw conclusions and make predictions.
- Probability Distribution: Study different probability distributions (binomial, normal, Poisson) and apply them to solve real-world problems involving probability.
- Hypothesis Testing: Conduct hypothesis tests to determine if there is sufficient evidence to reject a claim about a population.
Other Mathematics Topics
- Discrete Mathematics: Explore topics such as sets, logic, counting principles, and graph theory, focusing on applications in computer science and engineering.
- Number Theory: Investigate properties of numbers, including prime numbers, factorization, and congruence, with an emphasis on problem-solving.
- Applied Mathematics: Apply mathematics to real-world problems in fields such as business, finance, engineering, and the sciences.