7 min read
How to Solve Quadratic Equations: 3 Methods with Examples
Learn how to solve quadratic equations using the quadratic formula, factoring, and completing the square. Step-by-step worked examples with clear explanations.
Maths Tutorials and Guides
Step-by-step tutorials with worked examples, formulas, and links to our free calculators.
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7 min read
How to Find the Slope of a Line: Formula, Methods, and Examples
Learn how to find the slope of a line using the slope formula, rise over run, and slope-intercept form. Covers parallel and perpendicular slopes with worked examples.
8 min read
How to Calculate Probability: Formulas, Rules, and Examples
Master probability calculations with clear explanations of basic probability, conditional probability, independent events, and combinations. Includes real-world worked examples.
6 min read
How to Calculate Percentages: A Complete Guide with Examples
Learn how to calculate percentages step by step. Covers the core formula, percentage increase and decrease, finding a percentage of a number, and common mistakes to avoid.
8 min read
How to Find the Derivative: Rules, Formulas, and Worked Examples
Master differentiation with this guide to derivative rules. Covers the power rule, product rule, quotient rule, and chain rule with step-by-step KaTeX examples.
7 min read
How to Calculate Standard Deviation: Step-by-Step Guide
Understand standard deviation from the ground up. Learn the difference between population and sample standard deviation with a full worked example using a real dataset.
8 min read
How to Calculate Compound Interest: Formula and Worked Examples
Learn the compound interest formula A = P(1 + r/n)^(nt) with three fully worked examples. Understand how compounding frequency affects your returns.
9 min read
Understanding Z-Scores and Normal Distribution
Learn what z-scores mean, how the bell curve works, and how to use z-score tables. Includes worked examples and links to our standard deviation calculator.
10 min read
How to Solve Systems of Equations: 3 Methods with Examples
Master three methods for solving systems of linear equations: substitution, elimination, and matrices. Step-by-step worked examples for each approach.
9 min read
The Complete Guide to Logarithms: Rules, Examples, and Applications
Master logarithms from the basics to advanced rules. Covers log properties, change of base formula, and real-world applications in science and finance.
8 min read
How to Calculate the Area and Perimeter of Triangles
Learn multiple methods for calculating triangle area and perimeter, including base times height, Heron's formula, and trigonometric methods with worked examples.
10 min read
Understanding Eigenvalues and Eigenvectors: A Practical Guide
Learn what eigenvalues and eigenvectors are, how to compute them for 2x2 and 3x3 matrices, and why they matter in data science and engineering.
9 min read
Understanding Integrals and Antiderivatives: A Complete Guide
Learn how integrals work, from basic antiderivatives to definite integrals. Covers the power rule for integration, substitution, and the Fundamental Theorem of Calculus.
8 min read
How to Calculate Limits: Methods, Rules, and Examples
Learn how to evaluate limits using direct substitution, factoring, rationalisation, and L'Hopital's rule. Covers one-sided limits and limits at infinity.
9 min read
Taylor Series Explained: Formula, Examples, and Applications
Understand Taylor and Maclaurin series from scratch. Learn the formula, compute series for common functions, and see how they are used in science and engineering.
10 min read
A Guide to Matrix Operations: Addition, Multiplication, and Inverses
Master matrix operations including addition, scalar multiplication, matrix multiplication, determinants, and inverses with step-by-step examples.
7 min read
Mastering Fractions: How to Add, Subtract, Multiply, and Divide
A complete guide to fraction arithmetic. Learn how to find common denominators, simplify fractions, and perform all four operations with worked examples.
7 min read
Understanding Exponents and Powers: Rules, Laws, and Examples
Learn exponent rules including the product rule, quotient rule, power rule, and negative exponents. Covers scientific notation and real-world applications.
9 min read
Probability Distributions Explained: Normal, Binomial, and More
Understand the most important probability distributions: normal, binomial, Poisson, and uniform. Learn when to use each and how to calculate probabilities.
7 min read
Unit Conversion Guide: Methods, Formulas, and Common Conversions
Learn how to convert between metric and imperial units for length, mass, temperature, and more. Includes dimensional analysis and conversion factor tables.
8 min read
Ratios and Proportions: A Complete Guide with Examples
Learn how to work with ratios and proportions, including simplification, cross multiplication, direct and inverse proportion, and real-world applications.
10 min read
Understanding Complex Numbers: A Complete Guide
Learn about complex numbers from basics to advanced topics. Covers arithmetic, polar form, Euler's formula, De Moivre's theorem, and applications in engineering.
9 min read
Permutations and Combinations Explained: Formulas and Examples
Understand the difference between permutations and combinations. Covers factorials, the counting principle, Pascal's triangle, and probability applications.
9 min read
GCD and LCM Explained: Methods, Formulas, and Applications
Learn how to find the greatest common divisor and least common multiple using prime factorisation, the Euclidean algorithm, and their key relationship.
10 min read
Partial Derivatives Explained: A Guide to Multivariable Calculus
Learn how to compute partial derivatives, understand the gradient vector, and apply multivariable calculus to optimisation, physics, and economics with worked examples.
10 min read
Understanding Series and Summation: Sigma Notation and Beyond
Master series and summation from arithmetic and geometric series to convergence tests. Covers sigma notation, telescoping series, power series, and practical applications.
8 min read
How to Calculate Percentage Change: Formulas, Examples, and Common Mistakes
Learn how to calculate percentage change, percentage increase, percentage decrease, and percentage difference. Covers successive changes, reverse problems, and common pitfalls.
11 min read
Understanding Correlation and Regression: A Practical Guide
Learn the Pearson correlation coefficient, simple linear regression, the least squares method, and R-squared. Full numerical examples and common pitfalls explained.
9 min read
Compound Interest Explained: How Your Money Grows Exponentially
Understand how compound interest works with the core formula, simple vs compound comparisons, monthly contributions, loan calculations, and the Rule of 72.
10 min read
Mastering the Quadratic Formula: Discriminant, Graphing, and Real-World Uses
Master the quadratic formula with tips on the discriminant, graphing parabolas, Vieta's formulas, and real-world applications in physics, economics, and engineering.
10 min read
Statistics Basics: Mean, Median, Mode, and Measures of Spread
A complete guide to fundamental statistics. Covers mean, median, mode, range, variance, standard deviation, IQR, z-scores, and when to use each measure.
8 min read
Fraction Shortcuts and Tricks for Faster Maths
Speed up your fraction calculations with the butterfly method, cross-cancellation, the benchmark method, and quick conversion tricks. Practical shortcuts with examples.
9 min read
Understanding Slope: Real-World Applications in 6 Fields
See how slope applies beyond the classroom in road engineering, economics, medicine, meteorology, physics, and population growth. Worked examples for each application.
8 min read
Exponent Rules Cheat Sheet: All 8 Rules with Examples
Every exponent rule in one place: product, quotient, power of a power, zero, negative, and fractional exponents. Quick-reference formulas, worked problems, and common mistakes.
10 min read
Integration Techniques: A Practical Guide to Finding Antiderivatives
Learn the key integration techniques including substitution, integration by parts, partial fractions, and trigonometric substitution with worked examples.
9 min read
Real-World Uses of Matrices: From Google to Computer Graphics
Discover how matrices power real-world applications in computer graphics, machine learning, Google PageRank, economics, cryptography, and quantum computing.
8 min read
Probability in Daily Life: How Maths Shapes Your Decisions
See how probability influences everyday decisions from weather forecasts and medical tests to insurance, games, and investing. Practical examples with calculations.
7 min read
Unit Conversion Tips: Shortcuts and Tricks for Faster Conversions
Speed up your unit conversions with practical tips, mental shortcuts, and tricks for metric/imperial, temperature, speed, and cooking measurements.
10 min read
Trigonometry Basics: Sin, Cos, Tan, the Unit Circle, and Key Identities
A complete introduction to trigonometry covering sine, cosine, tangent, the unit circle, radians, Pythagorean identity, angle addition formulas, and the laws of sines and cosines.
11 min read
Introduction to Differential Equations: Types, Methods, and Applications
Learn what differential equations are, how to classify them, and how to solve first-order ODEs using direct integration, separation of variables, and integrating factors.
8 min read
How to Calculate Coefficient of Variation (Step by Step)
Learn the coefficient of variation formula (CV = σ/μ × 100), when to use CV vs standard deviation, and how to compare variability across datasets with different units.
9 min read
Chi-Square Test Explained: When and How to Use It
Learn how to perform chi-square goodness of fit and independence tests. Covers the formula, degrees of freedom, p-value interpretation, and worked examples.
9 min read
P-Value Explained: What It Means and How to Calculate It
Understand what p-values really mean, how to calculate them from z-scores and t-scores, significance levels, and the most common misconceptions researchers make.
8 min read
How to Find Outliers Using IQR and Z-Score Methods
Learn three methods for detecting outliers: the IQR method, Z-score method, and Modified Z-score. Includes worked examples and guidance on when to remove outliers.
9 min read
Sample Size Calculator: How Many Responses Do You Need?
Learn how to calculate the right sample size for surveys, A/B tests, and research studies. Covers the formula, margin of error, confidence level, and finite population correction.
10 min read
ANOVA Explained: One-Way Analysis of Variance Guide
Learn how to perform one-way ANOVA to compare means across multiple groups. Covers the F-statistic, SS/MS calculations, assumptions, and post-hoc tests.
9 min read
Bayes' Theorem Explained with Real-World Examples
Understand Bayes' theorem with the formula P(A|B) = P(B|A)×P(A)/P(B). Covers prior vs posterior probabilities, tree diagrams, and real-world applications.
8 min read
Cross Product vs Dot Product: When to Use Each
Understand the difference between cross products and dot products. Covers formulas, geometric interpretations, the right-hand rule, and physics applications.
8 min read
How to Complete the Square (Step-by-Step Guide)
Learn the completing the square method step by step. Convert quadratics to vertex form, derive the quadratic formula, and solve equations with worked examples.
8 min read
Synthetic Division Made Easy: Step-by-Step Method
Learn synthetic division step by step. Compare with long division, apply the Remainder and Factor Theorems, and find polynomial zeros with worked examples.
9 min read
Confidence Intervals Explained: What They Actually Mean
Understand confidence intervals correctly. Learn the z and t interval formulas, how to choose confidence levels, the effect of sample size, and common misinterpretations.
10 min read
Linear Regression: Finding the Line of Best Fit
Learn how to find the line of best fit using least squares regression. Covers slope and intercept formulas, R-squared, residuals, and assumptions with a full hand-computed example.
9 min read
Implicit Differentiation: The Chain Rule Trick
Learn implicit differentiation step by step. Understand why we need it, how the chain rule applies, and how to find tangent lines and second derivatives implicitly.
10 min read
Laplace Transform Table and Examples
Learn Laplace transforms with a common transforms table, key properties, and step-by-step examples solving first and second order differential equations.
8 min read
Poisson Distribution: When Events Are Random
Learn the Poisson distribution for modelling rare events. Covers the PMF formula, mean and variance, cumulative probabilities, and comparison with the binomial distribution.
8 min read
How to Calculate Density (Mass, Volume, and Formula)
Learn the density formula ρ = m/V, measurement techniques, common material densities, and applications in buoyancy and material identification with worked examples.
9 min read
Understanding Percentiles, Quartiles, and Box Plots
Learn how to calculate percentile ranks, quartiles (Q1, Q2, Q3), IQR, and construct box plots. Covers outlier detection and applications in standardised testing.
8 min read
Kinetic vs Potential Energy: Formulas and Examples
Understand kinetic energy (KE = ½mv²) and potential energy (PE = mgh). Covers conservation of energy, elastic potential energy, and the work-energy theorem with worked examples.
9 min read
Ohm's Law Explained with Calculator and Examples
Learn Ohm's law (V = IR) with the three formula forms, the Ohm's law triangle, power calculations, and series vs parallel circuit analysis with worked examples.
9 min read
Momentum and Impulse: Physics Formulas Explained
Learn momentum (p = mv) and impulse (J = FΔt). Covers conservation of momentum, elastic vs inelastic collisions, rocket propulsion, and real-world applications.
10 min read
GCSE Maths Calculator Guide 2026 — What You Need to Know
Everything you need to know about calculators for GCSE Maths: which papers allow them, recommended models, exam board rules, and essential calculator skills to practise.
11 min read
SAT Math Calculator Tips — How to Maximise Your Score
Master the digital SAT Math calculator strategy. Learn how to use the built-in Desmos, when to use vs skip the calculator, and the top 10 strategies for maximising your score.
11 min read
Best Calculators for A-Level Maths 2026
Find the best calculator for A-Level Maths. Covers Edexcel, AQA, and OCR policies, recommended models (Casio fx-991EX, TI-84), required features, and how to use them effectively.
12 min read
AP Calculus Calculator Policy Explained — AB and BC
Understand the AP Calculus calculator policy for both AB and BC exams. Section-by-section breakdown, approved graphing calculator models, essential techniques, and practice tips.