REFERENCE & RESOURCES

Quick answers for the basics.
Trusted places for the rest.

Use Edvora’s reference sheets to refresh a rule or formula, then move to an authoritative learning source when you need depth.

QUICK REFERENCE

Keep the essentials close.

MATH

Core formulas

Slope
m = (y₂ − y₁) / (x₂ − x₁)
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Pythagorean theorem
a² + b² = c²
Circle
A = πr² · C = 2πr
Distance
√((x₂−x₁)² + (y₂−y₁)²)
Open Math hub →
SCIENCE

Common relationships

Density
ρ = m / V
Newton’s second law
F = ma
Kinetic energy
KE = ½mv²
Gravitational PE
PE = mgh
Ohm’s law
V = IR
Open Science hub →
WRITING

Revision checklist

  • Does the thesis answer the prompt?
  • Does each paragraph make one clear contribution?
  • Is evidence introduced and analyzed?
  • Are quotations integrated into your own sentences?
  • Did you check sentence boundaries and citations?
Open English hub →
RESEARCH

Source credibility

  • Who created the source?
  • What evidence does it provide?
  • When was it published or updated?
  • What is the purpose or incentive?
  • Can important claims be checked elsewhere?
Research with ChatCTM →

TRUSTED LEARNING SITES

Useful places worth bookmarking.

These links go directly to the listed organizations. Edvora does not proxy or embed them.

KKhan Academy

Free lessons and practice across math, science, economics, history, and test preparation.

khanacademy.org ↗DDesmos

Graphing calculators and classroom-ready math tools.

desmos.com ↗GGeoGebra

Interactive geometry, graphing, algebra, and statistics tools.

geogebra.org ↗PPhET

Interactive science and math simulations from the University of Colorado Boulder.

phet.colorado.edu ↗PPurdue OWL

Writing, research, grammar, and citation guidance.

owl.purdue.edu ↗PProject Gutenberg

Public-domain books and primary texts.

gutenberg.org ↗NNASA STEM

Science, engineering, and space learning resources.

nasa.gov ↗MMIT OpenCourseWare

Open course materials for advanced independent learning.

ocw.mit.edu ↗GGoogle Scholar

Search scholarly literature; evaluate sources and access carefully.

scholar.google.com ↗CCollege Board

Official SAT, AP, and college-planning information.

collegeboard.org ↗

RESEARCH WORKFLOW

Search is the beginning, not the evidence.

When a topic matters, move from a search result to the original source, identify who published it, and compare important claims across credible sources.

  1. 1
    Define the question

    Make the topic specific enough that you know what evidence would answer it.

  2. 2
    Find candidate sources

    Use library databases, official organizations, reputable publications, or scholarly search tools when appropriate.

  3. 3
    Evaluate before quoting

    Check authorship, date, evidence, purpose, and whether the source actually supports the claim you need.

  4. 4
    Record citation details

    Save title, author, publisher or site, date, and URL while the source is open.

Ask ChatCTM