Rounding and Significant Figures: Rules and Examples
How to round to decimal places, significant figures and the nearest 10, 100 or 1000, plus the rules for counting significant figures.
Maths guides – page 3
Step-by-step guides, worked examples and study tips.
Scientific Notation (Standard Form) Explained
Write very large and very small numbers in scientific notation, convert back, and multiply and divide numbers in standard form.
Speed, Distance and Time: The Formula Triangle Explained
Use speed = distance ÷ time to find any of the three, convert units, work with hours and minutes, and read distance–time graphs.
Taylor Series Explained: Approximating Functions with Polynomials
What Taylor and Maclaurin series are, how to build them from derivatives, and why sin x ≈ x − x³/6 + x⁵/120 near zero. Clear examples.
The Binomial Distribution Explained Step by Step
When to use the binomial distribution, the formula for exactly k successes, at-most and at-least probabilities, and the mean and standard deviation.
The Poisson Distribution Explained with Examples
When to use the Poisson distribution, how to calculate P(X = k) from an average rate λ, and how it compares with the binomial distribution.
Vectors Explained: Magnitude, Dot Product and Cross Product
Learn what vectors are, how to find magnitude, the dot product and the angle between vectors, and how the 3D cross product works.
Arithmetic vs Geometric Sequences: Formulas and Examples
Tell arithmetic and geometric sequences apart, find the nth term and the sum of each, and see when a geometric series has a sum to infinity.
Compound Interest Explained (with the Formula and Examples)
How compound interest works, the formula A = P(1 + r/n)^(nt), how compounding frequency changes the result, and the rule of 72.
Degrees and Radians: How to Convert and Why It Matters
What a radian is, how to convert between degrees and radians in exact π form, a table of common angles, and why calculus uses radians.