Focus Areas:

• Basic number recognition and counting
• Shapes, colors, and patterns
• Simple measurement concepts (e.g., length, weight)
• Sorting and classifying objects
• Introduction to simple addition and subtraction using visual aids

Purpose: Builds a foundation for understanding basic math concepts, enhancing cognitive and problem-solving skills for early learners.

Focus Areas:

• Basic math skills (addition, subtraction, multiplication, division)
• Word problems and real-life applications
• Measurement and data
• Geometry and algebra

Purpose: Used by many states for K-12 assessment, measuring student growth and math proficiency.

Focus Areas:

• Limits, derivatives, and integrals
• Chain rule, product rule, quotient rule
• Applications of derivatives (e.g., motion, optimization)
• Antiderivatives and area under curves
• Fundamental Theorem of Calculus
• Differential equations (basic level)

Purpose: Prepares students for advanced math in engineering, physics, and economics.

IB Math (International Baccalaureate)

IB Math Standard Level (SL)

• Focus on algebra, calculus, trigonometry, and statistics
• More accessible than HL but still provides a solid foundation in mathematical reasoning and applications

IB Math Higher Level (HL)

• More in-depth study of calculus, matrices, vectors, and advanced trigonometry
• Emphasizes rigorous problem-solving skills

Purpose: Prepares students for university-level math, particularly in fields like economics, engineering, and computer science.

GCSE Math (General Certificate of Secondary Education - UK)

• Basic arithmetic, algebra, geometry, and number theory
• Data handling and probability
• Trigonometry and transformations
• Solving linear and quadratic equations

Purpose: Fundamental math skills for students, and a standard qualification for further education or career options.

Trigonometry

• Sine, cosine, tangent, and their applications
• Unit circle and radian measure
• Pythagorean theorem and trigonometric identities
• Solving right and non-right triangles
• Graphing trigonometric functions
• Law of Sines and Law of Cosines

Purpose: Essential for students progressing to calculus, engineering, physics, and other advanced mathematics topics.

Functions (Intro and Advanced)

• Definition of a function, domain, and range
• Linear, quadratic, exponential, and logarithmic functions
• Graphing and transformations of functions
• Composition and inverse functions
• Solving function equations and systems of equations

Purpose: Foundation for calculus and advanced mathematics, focusing on the relationship between variables.

Focus Areas

AP Calculus

• AP Calculus AB: Limits, derivatives, integrals, and applications to real-life problems
• AP Calculus BC: Includes everything in AB plus more advanced topics like polar coordinates, sequences, and series
• Integration techniques, L'Hopital's Rule, and series expansions

Purpose: College-level calculus course for high school students to earn college credit through the AP exam.

SAT Math

• Algebra (linear equations, quadratic equations, systems of equations)
• Problem-solving and data analysis
• Advanced math (polynomials, rational expressions, functions)
• Geometry (angles, perimeter, volume, coordinate geometry)
• Trigonometry (basic sine, cosine, and tangent)
• Arithmetic (ratios, percentages, proportions)

Purpose: Prepares students for the SAT college entrance exam, testing fundamental and advanced math skills.

ACT Math

• Pre-Algebra and Elementary Algebra (basic operations, expressions)
• Intermediate Algebra (equations, inequalities, functions)
• Coordinate Geometry (lines, slopes, distance, midpoint)
• Plane Geometry (area, volume, angles, circles)
• Trigonometry (basic identities, right triangles)

Purpose: Prepares students for the ACT college entrance exam, emphasizing problem-solving, algebra, and geometry.

GRE Math

• Arithmetic and number theory
• Algebra and functions
• Geometry (coordinate and plane)
• Data analysis and probability
• Quantitative comparisons, problem-solving, and word problems

Purpose: Tests readiness for graduate school programs, focusing on quantitative reasoning, algebra, and geometry.

GED Math

• Basic math (operations with fractions, decimals, and percentages)
• Algebra (linear equations, inequalities, functions)
• Geometry (area, perimeter, volume, angles)
• Data analysis and probability

Purpose: Equivalency exam for high school diploma, covering basic and intermediate math skills.

Focus Areas

Higher Level (HL)

• Advanced calculus, vectors, matrices, complex numbers
• More extensive focus on mathematical proof and logic
• Extensive use of technology (graphing calculators)
• Higher-order problem-solving in real-world contexts

Standard Level (SL)

• Focus on algebra, functions, calculus, statistics
• Aimed at students pursuing non-math intensive university courses

Purpose: Rigorous math program designed to provide a strong mathematical foundation for higher education.