[Hourly Lessons] Math, Chemistry & Biology | 1-on-1 Tutoring with Kevin Trig

Unit 1 – The Chemistry of Life

Explores the molecular foundations of biological systems.

• The chemical context of life
• Water and its biological properties
• Carbon chemistry
• Biological macromolecules

Unit 2 – The Cell

Examines cell structure, function, and energy transformation.

• Prokaryotic & eukaryotic cells
• Cell membranes and transport
• Enzymes and metabolism
• Cellular respiration
• Photosynthesis
• Cell communication & division

Unit 3 – Genetics

Studies heredity and molecular genetics.

• Meiosis
• Mendelian genetics
• Chromosomal inheritance
• Gene expression
• Viruses & biotechnology

Unit 4 – Mechanisms of Evolution

• Natural selection
• Population genetics
• Speciation
• History of life

Unit 5 – Evolutionary History of Biological Diversity

• Phylogenetic trees
• Bacteria & archaea
• Plants, fungi & animals
• Evolution of vertebrates

Unit 6 – Plant Form and Function

• Plant anatomy
• Transport systems
• Reproduction
• Hormones & environmental responses

Unit 7 – Animal Form and Function

• Nutrition
• Circulatory & respiratory systems
• Immune & excretory systems
• Nervous & endocrine systems
• Behavior

Unit 8 – Ecology

• Ecosystems
• Population ecology
• Community interactions
• Conservation biology

Unit 1 – Atomic Structure and Properties

• Moles and molar mass
• Atomic structure and electron configuration
• Mass spectra and elemental composition
• Periodic trends and valence electrons
• Ionic compounds and photoelectron spectroscopy

Unit 2 – Compound Structure and Properties

• Types of chemical bonds
• Intramolecular forces and potential energy
• Ionic and metallic structures
• Lewis diagrams and resonance
• VSEPR theory and hybridization

Unit 3 – Properties of Substances and Mixtures

• Intermolecular forces and phase properties
• Ideal and non-ideal gas laws
• Solutions and solubility
• Spectroscopy

Unit 4 – Chemical Reactions

• Net ionic equations
• Stoichiometry
• Titrations
• Acid-base reactions
• Redox reactions

Unit 5 – Kinetics

• Rate laws
• Collision model
• Reaction mechanisms
• Catalysis

Unit 6 – Thermochemistry

• Calorimetry
• Enthalpy
• Hess’s Law
• Bond enthalpies

Unit 7 – Equilibrium

• Reaction quotient
• Equilibrium constant
• Le Châtelier’s Principle
• Solubility equilibria

Unit 8 – Acids and Bases

• pH and pOH
• Weak acids and bases
• Buffers
• Titration curves

Unit 9 – Thermodynamics & Electrochemistry

• Entropy
• Gibbs free energy
• Galvanic cells
• Electrolysis

This course provides a comprehensive high school chemistry curriculum, covering everything from fundamental concepts to advanced topics commonly taught in Honors Chemistry and first-year university preparation courses.

Unit 1 – Essential Ideas

Introduces the fundamental concepts of chemistry, scientific measurement, and the classification of matter.

• Chemistry in context and classification of matter
• Physical and chemical properties
• Measurement systems and SI units
• Accuracy, precision, and uncertainty
• Mathematical treatment of experimental data

Unit 2 – Atoms, Molecules & Ions

Explores atomic theory, chemical symbols, isotopes, and the formation of compounds.

• History of atomic models
• Atomic structure and isotopes
• Chemical formulas and nomenclature
• Periodic table organization

Unit 3 – Composition of Substances and Solutions

Covers quantitative relationships in chemistry using the mole concept and solution chemistry.

• The mole and molar mass
• Empirical and molecular formulas
• Molarity and concentration calculations

Unit 4 – Stoichiometry of Chemical Reactions

Develops the quantitative analysis of chemical reactions.

• Writing and balancing chemical equations
• Reaction types
• Stoichiometric calculations
• Limiting reactants and percent yield

Unit 5 – Thermochemistry

Examines energy transfer and heat changes during chemical reactions.

• Energy and heat
• Calorimetry
• Enthalpy changes
• Thermochemical equations

Unit 6 – Electronic Structure and Periodic Properties

Studies electron arrangements and explains trends across the periodic table.

• Electromagnetic radiation
• Quantum model of the atom
• Electron configurations
• Periodic trends

Unit 7 – Chemical Bonding and Molecular Geometry

Explores how atoms bond and how molecular shape influences chemical properties.

• Ionic and covalent bonding
• Lewis structures
• Molecular geometry
• Polarity

Unit 8 – Advanced Theories of Covalent Bonding

Introduces modern bonding theories used to explain molecular behavior.

• Valence bond theory
• Hybrid orbitals
• Molecular orbital theory
• Multiple bonding

Unit 9 – Gases

Investigates the behavior of gases using mathematical models and kinetic theory.

• Gas pressure
• Ideal gas law
• Gas mixtures
• Kinetic molecular theory
• Real gases

Unit 10 – Liquids and Solids

Examines condensed phases of matter and intermolecular interactions.

• Properties of liquids
• Properties of solids
• Phase diagrams
• Crystal structures

Unit 11 – Solutions and Colloids

Studies mixtures, solution chemistry, and factors affecting solubility.

• Solution formation
• Solubility
• Colligative properties
• Colloids

Unit 12 – Kinetics

Explores reaction rates and the factors that influence chemical reactions.

• Reaction rates
• Rate laws
• Collision theory
• Catalysis

Unit 13 – Chemical Equilibrium

Examines reversible reactions and the quantitative treatment of equilibrium systems.

• Dynamic equilibrium
• Equilibrium constants
• Le Châtelier’s Principle
• Equilibrium calculations

Unit 14 – Acid–Base Equilibria

Introduces acid-base theories and quantitative analysis of aqueous solutions.

• Acid-base definitions
• pH and pOH calculations
• Buffers
• Titrations

Unit 15 – Equilibria of Other Reactions

Extends equilibrium concepts to additional chemical systems.

• Solubility product constants
• Lewis acids and bases
• Coupled equilibria

Unit 16 – Thermodynamics

Investigates spontaneity and energy changes in chemical processes.

• Entropy
• Laws of thermodynamics
• Gibbs free energy

Unit 17 – Electrochemistry

Explores oxidation-reduction reactions and electrical energy in chemistry.

• Galvanic cells
• Electrolytic cells
• Electrode potentials
• Electrolysis

Unit 18 – Representative Elements

Examines the chemistry and applications of the main-group elements.

• Periodic families
• Preparation and properties
• Industrial and laboratory applications

Unit 19 – Transition Metals and Coordination Chemistry

Studies the unique chemistry of transition metals and coordination compounds.

• Coordination complexes
• Ligands
• Colors and magnetism
• Bonding in transition metals

Unit 20 – Organic Chemistry

Introduces the structure, properties, and reactions of carbon-containing compounds.

• Hydrocarbons
• Alcohols and ethers
• Carbonyl compounds
• Carboxylic acids, amines, and amides

Unit 21 – Nuclear Chemistry

Explores radioactivity, nuclear reactions, and real-world applications of nuclear science.

• Radioactive decay
• Nuclear reactions
• Nuclear energy
• Medical and industrial applications

Algebra 1

Builds a strong foundation in algebra by developing equation-solving skills, function analysis, and mathematical modeling.

Unit 1 – Solving Linear Equations

Learn techniques for solving and verifying one- and multi-step linear equations.

Unit 2 – Solving Linear Inequalities

Represent and solve inequalities using algebraic methods and graph their solution sets.

Unit 3 – Graphing Linear Functions

Explore slope, intercepts, and graph linear relationships on the coordinate plane.

Unit 4 – Writing Linear Functions

Develop linear models from graphs, tables, data, and real-world situations.

Unit 5 – Systems of Linear Equations

Solve systems using graphing, substitution, and elimination methods.

Unit 6 – Exponential Functions and Sequences

Study exponential growth and decay, recursive sequences, and applications.

Unit 7 – Polynomials and Factoring

Perform operations on polynomials and use factoring techniques to solve equations.

Unit 8 – Quadratic Functions

Analyze parabolas, graph quadratic functions, and investigate transformations.

Unit 9 – Solving Quadratic Equations

Solve quadratic equations using factoring, completing the square, and the quadratic formula.

Unit 10 – Radicals and Data Analysis

Simplify radical expressions while developing introductory statistical reasoning and data interpretation.

Geometry

Develop logical reasoning and spatial thinking through geometric relationships, proofs, and applications.

Unit 1 – Geometry Basics

Introduce points, lines, planes, angles, and the fundamental building blocks of geometry.

Unit 2 – Reasoning and Proofs

Develop deductive reasoning skills and construct formal geometric proofs.

Unit 3 – Parallel and Perpendicular Lines

Study angle relationships, transversals, and coordinate geometry applications.

Unit 4 – Transformations

Investigate translations, reflections, rotations, dilations, and symmetry.

Unit 5 – Congruent and Similar Triangles

Apply congruence postulates and similarity criteria to solve geometric problems.

Unit 6 – Relationships Within Triangles

Explore medians, altitudes, angle bisectors, inequalities, and triangle centers.

Unit 7 – Quadrilaterals and Polygons

Classify polygons and prove their properties using geometric reasoning.

Unit 8 – Trigonometry

Apply trigonometric ratios and the Pythagorean Theorem to solve right-triangle problems.

Unit 9 – Circles and Measurement

Investigate circle theorems, arcs, sectors, circumference, area, surface area, and volume.

Algebra 2

Extend algebraic thinking with advanced functions, complex numbers, logarithms, trigonometry, and statistics.

Unit 1 – Functions

Review and extend linear, quadratic, and piecewise functions while emphasizing function notation.

Unit 2 – Complex Numbers

Perform operations with imaginary and complex numbers and solve quadratic equations with non-real solutions.

Unit 3 – Polynomial Functions

Analyze higher-degree polynomial functions, zeros, end behavior, and graphing techniques.

Unit 4 – Radical and Rational Functions

Study radical expressions, rational equations, asymptotes, and function transformations.

Unit 5 – Exponential and Logarithmic Functions

Explore exponential growth, logarithms, and real-world mathematical modeling.

Unit 6 – Sequences and Series

Investigate arithmetic and geometric sequences, recursive formulas, and summation notation.

Unit 7 – Trigonometry and Probability

Develop trigonometric concepts alongside probability models and counting techniques.

Unit 8 – Data Analysis

Interpret statistical data, regression models, and probability distributions.

Precalculus

Prepare for calculus by integrating advanced algebra, trigonometry, analytic geometry, and introductory calculus concepts.

Unit 1 – Foundations and Polynomial Functions

Review essential algebra skills, transformations, polynomial functions, and rational expressions.

Unit 2 – Exponential and Logarithmic Functions

Study exponential models, logarithms, inverse functions, and financial applications.

Unit 3 – Trigonometric Functions

Explore the unit circle, trigonometric graphs, identities, equations, and applications.

Unit 4 – Vectors and Analytic Geometry

Analyze vectors, parametric equations, and coordinate geometry in two dimensions.

Unit 5 – Polar Coordinates and Conic Sections

Investigate polar graphs along with circles, ellipses, parabolas, and hyperbolas.

Unit 6 – Matrices

Perform matrix operations and solve systems of equations using linear algebra techniques.

Unit 7 – Discrete Mathematics

Introduce mathematical induction, probability, combinatorics, and graph theory concepts.

Unit 8 – Limits and Introduction to Calculus

Develop an intuitive understanding of limits, continuity, and the fundamental ideas leading into differential calculus.