Genmath Study Notes: Arithmetic and Algebra

Basic Operations: Addition, subtraction, multiplication, and division.
Order of Operations: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right) - PEMDAS.
Fractions: Simplification, addition, subtraction, multiplication, and division of fractions.
Decimals: Conversion between fractions and decimals, operations with decimals.
Percentages: Calculating percentages, percentage increase/decrease, converting between percentages, fractions, and decimals.

Expressions: Variables, coefficients, constants; combining like terms.
Equations: Solving linear equations, quadratic equations, and factoring.
Functions: Understanding domain and range, function notation, and types of functions (linear, quadratic, polynomial).
Inequalities: Solving and graphing linear inequalities, systems of inequalities.
Exponents and Radicals: Laws of exponents, simplifying radical expressions.

Basic Shapes: Properties and formulas for triangles, quadrilaterals, circles, and polygons.
Angles: Types (acute, obtuse, right), angle relationships (complementary, supplementary).
Perimeter, Area, Volume: Formulas for calculating perimeter and area of 2D shapes; volume and surface area of 3D shapes (cubes, spheres, cylinders).
Pythagorean Theorem: a² + b² = c² in right-angled triangles.
Coordinate Geometry: Distance formula, midpoint formula, slope of a line.

Data Types: Qualitative vs. quantitative data.
Measures of Central Tendency: Mean, median, mode.
Measures of Dispersion: Range, variance, standard deviation.
Probability: Basic probability concepts, independent and dependent events, combinatorics.
Graphs and Charts: Bar graphs, histograms, pie charts, box plots; interpreting data visualizations.

Limits: Understanding limits, computing limits, limit properties.
Derivatives: Definition of the derivative, rules (product, quotient, chain rule), applications (tangent lines, rates of change).
Integrals: Definite and indefinite integrals, fundamental theorem of calculus, basic integration techniques (substitution, integration by parts).
Applications: Area under a curve, volume of solids of revolution, optimization problems.
Functions and Continuity: Understanding differentiability and continuity; types of discontinuities.

Basic operations include addition, subtraction, multiplication, and division, forming the foundation of arithmetic.
Order of operations follows PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Fractions require simplification and performing operations including addition, subtraction, multiplication, and division.
Decimals can be converted to fractions and vice versa; operations with decimals follow standard arithmetic rules.
Percentages involve calculating percentage values, understanding percentage increases/decreases, and converting between percentages, fractions, and decimals.

Expressions consist of variables, coefficients, and constants, and combining like terms is essential for simplification.
Equations encompass linear and quadratic types; solving includes various methods such as factoring.
Functions are defined by their domain and range, function notation, and types including linear, quadratic, and polynomial functions.
Inequalities involve solving and graphing linear inequalities as well as understanding systems of inequalities.
Exponents and radicals include laws of exponents and the process of simplifying radical expressions.

Basic shapes include triangles, quadrilaterals, circles, and polygons, each with unique properties and formulas.
Angles are categorized as acute, obtuse, or right, with angle relationships being complementary or supplementary.
Perimeter and area are calculated using specific formulas for 2D shapes, while volume and surface area calculations apply to 3D shapes like cubes, spheres, and cylinders.
The Pythagorean Theorem is a foundational principle for right-angled triangles, expressed as a² + b² = c².
Coordinate geometry involves calculating distances using the distance formula, finding midpoints, and determining the slope of lines.

Data types are divided into qualitative (descriptive) and quantitative (numerical) categories.
Measures of central tendency include mean (average), median (middle value), and mode (most frequent value).
Measures of dispersion assess how data varies through range, variance, and standard deviation.
Basic concepts of probability include understanding independent and dependent events, alongside foundational combinatorics.
Various graphs and charts (bar graphs, histograms, pie charts, box plots) aid in data visualization and interpretation.

Limits help define the behavior of functions as input approaches a specific value, with properties aiding in limit calculations.
Derivatives represent the rate of change, calculated using rules such as product, quotient, and chain rule; applications include analyzing tangent lines.
Integrals cover both definite and indefinite forms, with the fundamental theorem of calculus linking differentiation and integration.
Applications of integration include calculating the area under curves, volumes of solids of revolution, and solving optimization problems.
Functions and continuity explore differentiability, the nature of functions, and types of discontinuities affecting continuity.