Chapter Prerequisites
Explore how high-school mathematics and physics chapters build on earlier knowledge.
Follow each arrow from prior knowledge to a chapter that uses it. Multiple incoming arrows mean you should review each connected topic. These maps suggest a study sequence; chapter names and coverage vary by school. Earlier prerequisites are inherited along each path, and independent branches can be studied in parallel.
- Foundations
- Core chapters
- Extensions
Drag or scroll to explore. Use the zoom controls or expand a diagram for a larger view. A text version is available below each map.
Mathematics
Follow algebra, geometry, and data branches from their foundations. Calculus is an extension for courses that include it.
Read chapter prerequisites
- Numbers, fractions, and ratios
- Start here. Review earlier-school basics as needed.
- Algebraic expressions and powers
- Review first: Numbers, fractions, and ratios.
- Geometry and similarity
- Review first: Numbers, fractions, and ratios.
- Equations and rearranging formulas
- Review first: Algebraic expressions and powers.
- Inequalities and intervals
- Review first: Algebraic expressions and powers.
- Functions and graphs
- Review first: Algebraic expressions and powers.
- Linear equations and functions
- Review first: Equations and rearranging formulas; Functions and graphs.
- Systems of equations
- Review first: Linear equations and functions.
- Quadratic equations and functions
- Review first: Equations and rearranging formulas; Functions and graphs.
- Polynomial functions
- Review first: Quadratic equations and functions.
- Rational functions
- Review first: Polynomial functions.
- Exponential functions
- Review first: Functions and graphs.
- Logarithms
- Review first: Exponential functions.
- Sequences and series
- Review first: Linear equations and functions; Exponential functions.
- Coordinate geometry and conics
- Review first: Geometry and similarity; Linear equations and functions.
- Right-triangle trigonometry
- Review first: Geometry and similarity; Equations and rearranging formulas.
- Unit circle and trigonometric functions
- Review first: Right-triangle trigonometry; Functions and graphs.
- Vectors
- Review first: Coordinate geometry and conics; Right-triangle trigonometry.
- Matrices
- Review first: Systems of equations.
- Geometric transformations
- Review first: Geometry and similarity; Vectors.
- Counting and combinations
- Review first: Numbers, fractions, and ratios.
- Probability
- Review first: Counting and combinations.
- Descriptive statistics
- Review first: Numbers, fractions, and ratios.
- Distributions and statistical inference
- Review first: Descriptive statistics; Probability.
- Limits and continuity
- Review first: Functions and graphs; Rational functions.
- Derivatives and applications
- Review first: Limits and continuity.
- Integrals and area
- Review first: Derivatives and applications.
Chapter coverage draws on the references below. The prerequisite arrows are our suggested connections, rather than an official curriculum or a sequence prescribed by the textbooks.
Physics
Build from measurement and mathematical tools into mechanics, thermal physics, waves, and electricity. Modern physics forms the extension branch.
Read chapter prerequisites
- Measurement, units, and uncertainty
- Start here. Review earlier-school basics as needed.
- Algebra, ratios, and graphs
- Start here. Review earlier-school basics as needed.
- Vectors and trigonometry
- Review first: Algebra, ratios, and graphs.
- Exponents and exponential decay
- Start here. Review earlier-school basics as needed.
- Motion in one dimension
- Review first: Measurement, units, and uncertainty; Algebra, ratios, and graphs.
- Motion in two dimensions
- Review first: Motion in one dimension; Vectors and trigonometry.
- Forces and Newton's laws
- Review first: Motion in one dimension; Vectors and trigonometry.
- Work, energy, and power
- Review first: Forces and Newton's laws.
- Momentum and collisions
- Review first: Forces and Newton's laws.
- Circular motion
- Review first: Forces and Newton's laws; Motion in two dimensions.
- Rotation and angular momentum
- Review first: Circular motion; Momentum and collisions; Work, energy, and power.
- Gravitation and orbits
- Review first: Circular motion; Work, energy, and power.
- Torque and static equilibrium
- Review first: Forces and Newton's laws; Vectors and trigonometry.
- Fluids and pressure
- Review first: Torque and static equilibrium; Work, energy, and power.
- Temperature, heat, and heat transfer
- Review first: Measurement, units, and uncertainty.
- Gas laws and kinetic theory
- Review first: Temperature, heat, and heat transfer; Work, energy, and power.
- Thermodynamics
- Review first: Gas laws and kinetic theory; Work, energy, and power.
- Oscillations and springs
- Review first: Forces and Newton's laws; Work, energy, and power.
- Waves and superposition
- Review first: Oscillations and springs.
- Sound and resonance
- Review first: Waves and superposition.
- Light and reflection
- Review first: Waves and superposition.
- Refraction, lenses, and ray optics
- Review first: Light and reflection; Vectors and trigonometry.
- Interference and diffraction
- Review first: Light and reflection; Waves and superposition.
- Electric charge and force
- Review first: Forces and Newton's laws.
- Electric fields and potential
- Review first: Electric charge and force; Work, energy, and power.
- Current, resistance, and DC circuits
- Review first: Electric fields and potential.
- Magnetic fields and forces
- Review first: Current, resistance, and DC circuits; Vectors and trigonometry.
- Electromagnetic induction
- Review first: Magnetic fields and forces; Work, energy, and power.
- Electromagnetic waves
- Review first: Electromagnetic induction; Waves and superposition.
- Photons and quantum ideas
- Review first: Light and reflection; Work, energy, and power.
- Atomic models and spectra
- Review first: Photons and quantum ideas; Electric fields and potential.
- Nuclear physics and radioactivity
- Review first: Atomic models and spectra; Exponents and exponential decay.
- Special relativity
- Review first: Motion in one dimension; Electromagnetic waves.
Chapter coverage draws on the references below. The prerequisite arrows are our suggested connections, rather than an official curriculum or a sequence prescribed by the textbooks.