How to Find the Inverse of a Matrix (2×2 and 3×3)
Find the inverse of a 2×2 matrix with the quick formula and of a 3×3 matrix by Gauss–Jordan elimination, and check it with A × A⁻¹ = I.
Maths guides – page 2
Step-by-step guides, worked examples and study tips.
How to Solve Cubic Equations Using the Factor Theorem
Solve cubic equations by finding a root with the rational root theorem, dividing it out, and solving the remaining quadratic. Worked examples.
How to Solve Linear Inequalities (and When to Flip the Sign)
Solve linear inequalities step by step, learn the one rule that flips the sign, and show answers on a number line and in interval notation.
Line of Best Fit: Linear Regression and Correlation Explained
How to find the least-squares line of best fit, what the correlation coefficient r and r² mean, and why correlation is not causation.
Newton's Method Explained: Finding Roots with Tangent Lines
How Newton's method finds roots of equations by following tangent lines, the formula, worked examples for √2 and cos x = x, and when it fails.
Percentages When Shopping: Discounts, Tax and Tips
Work out sale prices, stacked discounts, VAT or sales tax (adding and removing it) and tips quickly, with the multiplier method.
Probability Basics: And, Or, Not and Dice
Learn the basic probability rules for 'and', 'or' and 'not', independent and mutually exclusive events, and how to count dice outcomes.
Ratios and Proportions Made Simple
Simplify ratios, share an amount in a ratio, and solve proportions by cross-multiplying, with recipe and map examples.
Riemann Sums Explained: Left, Right, Midpoint and Trapezoid
How Riemann sums approximate the area under a curve with rectangles, how left, right, midpoint and trapezoid rules compare, and why they lead to integrals.
Roman Numerals Explained: How to Read and Write Them
Learn the seven Roman numeral symbols, the subtraction rule, and how to convert years like 2026 and 1994 to and from Roman numerals.