How-To Guides
Step-by-step guides that teach you how to perform calculations manually.
How to Calculate Complex Roots of Polynomials: Step-by-Step Guide
Learn to manually calculate complex roots of quadratic and polynomial equations. Understand formulas, see a worked example, and avoid common pitfalls.
Read guideHow to Calculate Partial Fraction Decomposition: Step-by-Step Guide
Master partial fraction decomposition with this step-by-step guide. Learn manual calculation, formulas, worked examples, and common pitfalls.
Read guideHow to Calculate Synthetic Division: Step-by-Step Guide
Learn to perform synthetic division manually. Divide polynomials by linear factors, understand the steps, formula, and avoid common pitfalls with a worked example.
Read guideHow to Calculate Normal Distribution Probabilities Manually: Step-by-Step Guide
Learn to manually calculate normal distribution probabilities using z-scores and a z-table. Understand the formula, work through examples, and avoid common pitfalls.
Read guideHow to Calculate Roots of Polynomials (Up to Degree 4): Step-by-Step Guide
Master finding polynomial roots up to degree 4 by hand. Learn the Rational Root Theorem, synthetic division, and quadratic formula with a worked example.
Read guideHow to Calculate Roots of Polynomial Equations (Up to Degree 4): Step-by-Step Guide
Learn to manually find roots of polynomial equations up to degree 4. Master rational root theorem, synthetic division, and quadratic formula.
Read guideHow to Calculate Logarithms Manually: A Step-by-Step Guide
Learn to calculate logarithms in any base by hand using the change of base formula. Understand the underlying principles with a detailed example and common pitfalls.
Read guideHow to Solve Exponential Equations: Step-by-Step Guide
Learn to solve exponential equations like aˣ = b manually using logarithms. Understand the formula, apply base conversion, and see a worked example.
Read guideHow to Manually Solve a Cubic Equation: Step-by-Step Guide
Learn to solve cubic equations ax³+bx²+cx+d=0 by hand using Cardano's method. Understand discriminant analysis and find real and complex roots.
Read guideHow to Solve Quadratic Inequalities: Step-by-Step Guide
Learn to manually solve quadratic inequalities. Find critical points, test intervals, and express solutions in interval notation. Understand the underlying math.
Read guideHow to Calculate a Row of Pascal's Triangle: Step-by-Step Guide
Learn to manually calculate any row of Pascal's Triangle using the binomial coefficient formula. Understand the pattern, common pitfalls, and worked examples.
Read guideHow to Calculate Binomial Expansion: Step-by-Step Guide
Master manual binomial expansion using the Binomial Theorem. Learn the formula, Pascal's Triangle, and see a worked example. Avoid common pitfalls.
Read guideHow to Find the Inverse of a Function: Step-by-Step Guide
Learn to find the inverse of any function algebraically using the swap-and-solve method. Master the formula, see worked examples, and avoid common pitfalls.
Read guideHow to Calculate Exponential Growth: Step-by-Step Guide
Calculate exponential growth manually
Read guideHow to Apply the Chain Rule: A Step-by-Step Guide
Learn to differentiate composite functions
Read guideNewton's Method Calculator: A Step-by-Step Guide
Approximate roots of any function using Newton's method
Read guideTrapezoidal Rule Calculator: A Step-by-Step Guide
Calculate definite integrals using the trapezoidal rule
Read guideHow to Calculate Riemann Sums: Step-by-Step Guide
Approximate area under curves with Riemann sums
Read guideHow to Calculate Limits: Step-by-Step Guide
Evaluate limits of functions manually
Read guideHow to Calculate Integrals: Step-by-Step Guide
Learn to calculate definite and indefinite integrals manually
Read guideHow to Calculate Derivatives: A Step-by-Step Guide
Master calculus with our guide
Read guideHow to Calculate Euler's Totient Function: Step-by-Step Guide
Calculate φ(n) manually
Read guideHow to Calculate Great-Circle Distance using the Haversine Formula: Step-by-Step Guide
Calculate distance between GPS coordinates manually
Read guideHow to Calculate Derivatives Using Common Rules: Step-by-Step Guide
Master manual derivative calculations using fundamental rules like Power, Constant, and Sum/Difference rules. Includes a worked example and common pitfalls.
Read guideHow to Calculate the Collatz Sequence: Step-by-Step Guide
Learn to manually calculate the Collatz sequence for any starting number. Understand the 3n+1 conjecture, track steps, and identify peak values.
Read guideHow to Calculate the Digit Sum and Digital Root: Step-by-Step Guide
Learn to manually calculate the digit sum and digital root of any integer with this step-by-step guide. Includes formulas, examples, and common pitfalls.
Read guideHow to Classify Numbers as Perfect, Abundant, or Deficient: Step-by-Step Guide
Learn to manually classify any positive integer as perfect, abundant, or deficient by finding and summing its proper divisors. Includes examples and common pitfalls.
Read guideHow to Convert Numbers Between Bases (2-16): Step-by-Step Guide
Master manual number base conversion (binary, octal, decimal, hexadecimal) with formulas, examples, and common pitfalls. Learn to convert any base 2-16.
Read guideHow to Manually Check Divisibility Rules (2-13): A Step-by-Step Guide
Learn to manually check divisibility for numbers 2-13. Understand rules, apply formulas, and avoid common pitfalls. Master integer divisibility.
Read guideHow to Perform Basic Number Theory Calculations: A Step-by-Step Guide
Master manual number theory calculations: list primes, check divisibility, find GCD/LCM, and understand integer properties with this comprehensive guide.
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