Logiq Space

Master STEM with Expert Resources

Your comprehensive library of formulas, guides, and learning materials for Math, Physics, Chemistry, Engineering, and Biology.

Formula LibraryStudy Guides

Formula Library

Quick reference to essential STEM formulas organized by subject and topic.

Algebra
Fundamental algebraic formulas

Quadratic Formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Difference of Squares

a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)

Perfect Square

(a±b)2=a2±2ab+b2(a \pm b)^2 = a^2 \pm 2ab + b^2
Calculus
Derivatives and integrals

Power Rule

ddx(xn)=nxn−1\frac{d}{dx}(x^n) = nx^{n-1}

Product Rule

(fg)′=f′g+fg′(fg)' = f'g + fg'

Chain Rule

ddx[f(g(x))]=f′(g(x))⋅g′(x)\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)
Trigonometry
Angles and triangles

Sine Rule

asin⁡(A)=bsin⁡(B)=csin⁡(C)\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}

Cosine Rule

c2=a2+b2−2abcos⁡(C)c^2 = a^2 + b^2 - 2ab\cos(C)

Pythagorean Identity

sin⁡2(θ)+cos⁡2(θ)=1\sin^2(\theta) + \cos^2(\theta) = 1
Statistics
Data analysis formulas

Mean

μ=Σxn\mu = \frac{\Sigma x}{n}

Standard Deviation

σ=Σ(x−μ)2n\sigma = \sqrt{\frac{\Sigma(x - \mu)^2}{n}}

Variance

σ2=Σ(x−μ)2n\sigma^2 = \frac{\Sigma(x - \mu)^2}{n}
Linear Algebra
Matrices and vectors

Dot Product

a⋅b=∣a∣∣b∣cos⁡(θ)\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos(\theta)

Matrix Determinant (2×2)

∣A∣=ad−bc|A| = ad - bc

Vector Magnitude

∣v∣=x2+y2+z2|\mathbf{v}| = \sqrt{x^2 + y^2 + z^2}
Physics
Motion, energy, and forces

Newton's Second Law

F=maF = ma

Kinetic Energy

KE=12mv2KE = \frac{1}{2}mv^2

Ohm's Law

V=IRV = IR
Chemistry
Reactions and molecular properties

Ideal Gas Law

PV=nRTPV = nRT

pH Formula

pH=−log⁡[H+]pH = -\log[H^+]

Molarity

M=nVM = \frac{n}{V}
Engineering
Mechanics and design principles

Stress

σ=FA\sigma = \frac{F}{A}

Strain

ε=ΔLL0\varepsilon = \frac{\Delta L}{L_0}

Power

P=Wt=FvP = \frac{W}{t} = Fv
Biology
Life sciences and genetics

Hardy-Weinberg Equation

p2+2pq+q2=1p^2 + 2pq + q^2 = 1

Population Growth

dNdt=rN\frac{dN}{dt} = rN

Photosynthesis

6CO2+6H2O→C6H12O6+6O26CO_2 + 6H_2O \rightarrow C_6H_{12}O_6 + 6O_2

Study Guides & Cheat Sheets

Comprehensive guides to help you understand and master key STEM concepts across all subjects.

Algebra Essentials
Master fundamental algebraic concepts
  • •Solving linear and quadratic equations
  • •Factoring polynomials and expressions
  • •Working with exponents and radicals
  • •Understanding functions and graphs
Try Practice Problems
Calculus Fundamentals
Build a strong calculus foundation
  • •Understanding limits and continuity
  • •Derivatives: rules and applications
  • •Integration techniques and methods
  • •Applications in real-world problems
Try Practice Problems
Geometry & Trigonometry
Spatial reasoning and angle relationships
  • •Properties of shapes and solids
  • •Trigonometric functions and identities
  • •Solving triangles and circles
  • •Coordinate geometry applications
Try Practice Problems
Statistics & Probability
Data analysis and chance
  • •Descriptive statistics and measures
  • •Probability rules and distributions
  • •Hypothesis testing basics
  • •Correlation and regression analysis
Try Practice Problems
Physics Fundamentals
Master mechanics, energy, and electromagnetism
  • •Newton's laws of motion and dynamics
  • •Energy conservation and thermodynamics
  • •Electricity, magnetism, and circuits
  • •Waves, optics, and modern physics
Try Practice Problems
Chemistry Essentials
Understand reactions and molecular structures
  • •Atomic structure and periodic trends
  • •Chemical bonding and molecular geometry
  • •Stoichiometry and reaction equations
  • •Acids, bases, and equilibrium
Try Practice Problems
Engineering Principles
Apply math and physics to design
  • •Statics and dynamics of structures
  • •Material properties and stress analysis
  • •Fluid mechanics and thermodynamics
  • •Circuit analysis and control systems
Try Practice Problems
Biology Foundations
Explore life sciences and genetics
  • •Cell structure and function
  • •DNA, RNA, and protein synthesis
  • •Mendelian genetics and inheritance
  • •Ecology and population dynamics
Try Practice Problems

Tips & Tricks

Expert advice to improve your problem-solving skills and study efficiency.

Using the AI Solver Effectively

Learn how to phrase your questions and interpret step-by-step solutions for maximum learning benefit.

  • ✓Be specific with your problem statement
  • ✓Review each step carefully
  • ✓Try solving similar problems independently
Common Math Mistakes

Avoid these frequent errors that trip up students at all levels.

  • ✗Forgetting to distribute negative signs
  • ✗Mixing up order of operations
  • ✗Canceling terms incorrectly
Study Techniques

Proven methods to improve retention and understanding of mathematical concepts.

  • ✓Practice regularly, not just before exams
  • ✓Explain concepts to others
  • ✓Work through problems without looking at solutions

External Resources

Curated links to high-quality learning platforms and tools.

Educational Platforms
Free and premium learning resources
Math Tools & Calculators
Interactive tools for visualization and computation
Math Communities
Get help and discuss with other learners
Recommended Books
Essential reading for math students

  • How to Solve It

    by George Pólya

  • The Art of Problem Solving

    by Richard Rusczyk

  • Calculus Made Easy

    by Silvanus P. Thompson

  • Linear Algebra Done Right

    by Sheldon Axler

Ready to Start Solving?

Put your knowledge to the test with our AI-powered math solver.

Try the Solver Now
Free STEM Resources: Math, Physics, Chemistry, Engineering & Biology Formulas | Logiq Space | Logiq Space