27 docs tagged with "Maths"

A-Level General diagnostic test: Instructions; Pure Mathematics; Algebra and Functions; Sequences, Series, and Binomial Expansion for targeted revision.

A-Level Mathematics notes on Algebraic Expressions: Board Coverage; 1. Surds; 1.1 Laws of Surds; 1.2 Irrationality of $\sqrt{2}$.

A-Level Mathematics notes on Binomial Expansion: Board Coverage; 1. Pascal's Triangle; 2. Binomial Coefficients; 2.1 Properties of Binomial Coefficients.

A-Level Mathematics notes on Coordinates and Geometry: Board Coverage; 1. The Coordinate Plane; 2. Straight Lines; 2.1 Gradient.

A-Level Mathematics notes on Correlation and Regression: Board Coverage; 1. Pearson's Product Moment Correlation Coefficient (PMCC); 1.1 Definition; 1.2 Prop.

A-Level Mathematics notes on Data Representation: Board Coverage; 1. Measures of Central Tendency; 1.1 Mean; 1.2 The mean minimises the sum of squared deviat.

A-Level Mathematics notes on Differentiation: Board Coverage; 1. The Derivative from First Principles; 1.1 Definition; 2. Derivative of $x^n$ from First Prin.

A-Level Mathematics notes on Energy and Work: Board Coverage; 1. Work Done; 1.1 Definition and derivation; 2. Kinetic Energy.

A-Level Mathematics notes on Equations and Inequalities: Board Coverage; 1. Linear Simultaneous Equations; 2. Linear-Quadratic Simultaneous Equations.

A-Level Mathematics notes on Exponentials and Logarithms: Board Coverage; 1. The Number $e$; 1.1 Definition of $e$; 1.2 Alternative characterisations.

A-Level Mathematics notes on Forces and Newton's Laws: Board Coverage; 1. Newton's Laws of Motion; 1.1 Newton's First Law (Law of Inertia); 1.2 Newton's Seco.

A-Level Mathematics notes on Functions: Board Coverage; 1. Definitions; 4. The Modulus Function; 4.1 Solving Modulus Equations.

A-Level Further Maths notes on Further Mathematics: Board Coverage for comprehensive revision and examination preparation.

A-Level Mathematics notes on Hypothesis Testing: Board Coverage; 1. Hypotheses; 1.1 Null and alternative hypotheses; 1.2 One-tailed and two-tailed tests.

A-Level Mathematics notes on Integration: Board Coverage; 1.1 Definition; 2. The Fundamental Theorem of Calculus; 2.1 Sketch proof of Part 2.

A-Level Mathematics notes on Kinematics: Board Coverage; 1. Fundamental Quantities; 1.1 Definitions; 1.2 Relationships via calculus.

A-Level Mathematics notes on Mathematics: Board Coverage; Course Structure; Statistics; Mechanics with worked examples and exam-style questions.

A-Level Mathematics notes on Moments: Board Coverage; 1. Definition of a Moment; 1.1 Real-world examples; 1.2 Sign convention.

A-Level Mathematics notes on Momentum: linear momentum, conservation of momentum, impulse, and collisions with worked examples and exam-style questions.

A-Level Mathematics notes on Numerical Methods: Board Coverage; 1. Locating Roots: Sign Change; 1.1 Sign change theorem; 1.2 Limitations.

A-Level Mathematics notes on Probability: Board Coverage for comprehensive revision and examination preparation. and examination prepar.

A-Level Mathematics notes on Proof: Board Coverage; 1.1 Method; 1.2 Example: the sum of an arithmetic series; 1.3 Example: the difference of squares.

A-Level Mathematics notes on Quadratics: Board Coverage; 1. The Quadratic Function; 2. Completing the Square; 3. The Quadratic Formula.

A-Level Mathematics notes on Sequences and Series: Board Coverage; 2. Arithmetic Sequences; 2.1 The $n$th Term; 2.2 Sum of an Arithmetic Series.

A-Level Mathematics notes on Statistical Distributions: Board Coverage; 1. Discrete Random Variables; 1.1 Definition; 1.2 Expectation and variance.

A-Level Mathematics notes on Trigonometry: Board Coverage; 1. The Unit Circle Definitions; 1.1 Radian Measure; 2. Fundamental Identities.

A-Level Mathematics notes on Vectors: Board Coverage; 1.1 Definition; 2.1 Magnitude; 2.3 Direction cosines with worked examples and exam-style questions.