87 docs tagged with "ALevel"

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

Rigorous A Level revision notes covering Mathematics, Physics, Computer Science, and Economics across AQA, Edexcel, OCR, and CIE boards.

A-Level General diagnostic test: A Level Physics — Diagnostic Test; Section A: Mechanics (Questions 1–5) 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 Physics notes on Astrophysics: 1. Astronomical Distances and Measurements; Astronomical Units of Distance; Stellar Parallax.

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

A-Level Physics notes on Capacitance: 2. Parallel Plate Capacitor; Derivation of $C = arepsilon_0 A/d$; 3. Energy Stored in a Capacitor.

A-Level Further Maths notes on Centres of Mass and Elastic Collisions: Board Coverage; 1. Centre of Mass of a Uniform Lamina; 1.1 Centre of mass by integration.

A-Level Further Maths notes on Chi-Squared Tests: Board Coverage; 1. The Chi-Squared Distribution; 1.1 Definition; 1.2 Properties.

A-Level Further Maths notes on Circular Motion: Board Coverage; 1. Angular Quantities; 1.1 Definitions; 1.2 Relationship with linear quantities.

A-Level Physics notes on Circular Motion: 1. Angular Quantities; 2. Centripetal Acceleration — Derivation; Method 1: Calculus; Method 2: Geometry.

A-Level Further Maths notes on Complex Numbers: Board Coverage; 1.1 The Argand Diagram; 1.2 Modulus and Argument; 2. De Moivre's Theorem.

A-Level Further Maths notes on Complex Numbers (Extended): Complex Numbers (Extended Treatment); 1. Modulus-Argument Form; 1.1 Polar representation.

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 Correlation and Regression (Extended): Correlation and Regression (Extended Treatment); 1. Scatter Diagrams; 1.1 Interpretation.

A-Level Physics notes on Current and Resistance: 1. Electric Current; Current as Charge per Unit Time; Derivation of $I = nAev_d$.

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 Physics notes on DC Circuits: 1. Kirchhoff's Laws; Kirchhoff's First Law (Current Law); Kirchhoff's Second Law (Voltage Law).

A-Level Further Maths notes on Differential Equations: Board Coverage; 1. First-Order ODEs: Separable Equations; 1.1 Definition; 1.2 Method.

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 Physics notes on Dynamics: 1. Newton's Laws of Motion; Newton's First Law (Law of Inertia); Newton's Second Law; Newton's Third Law.

A-Level Mathematics notes on Dynamics (Extended): Dynamics (Extended Treatment); 1. Newton's Laws of Motion; 1.1 Statement of the laws.

A-Level Physics notes on Electric Fields: 1. Coulomb's Law; Comparison with Gravity; Inverse Square Law Parallels; 2. Electric Field Strength.

A-Level Physics notes on Electric Fields: 1. Coulomb's Law; Superposition Principle; Comparison with Gravitational Force; 2. Electric Field Strength.

A-Level Physics notes on Electromagnetism Unification: 1. Maxwell's Equations (Integral Form); Gauss's Law for Electricity; Gauss's Law for Magnetism.

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 Energy and Work (Extended): Energy and Work (Extended Treatment); 1. Work Done by a Force; 1.1 Definition.

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

A-Level Physics notes on Experimental Design: Independent, Dependent, and Control Variables; Identifying Variables: Worked Examples; Control Variables in Depth.

A-Level Further Maths notes on Exponential Distribution and Continuous Random Variables: Board Coverage; 1. Continuous Random Variables.

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 Algebra: Board Coverage; 1. Polynomial Division and the Remainder Theorem; 1.1 Polynomial long division.

A-Level Further Maths notes on Further Calculus: Board Coverage; 1. Integration by Parts (Advanced); 1.1 The formula — proof from the product rule.

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

A-Level Physics notes on Gravitational Fields: 1. Newton's Law of Universal Gravitation; Geometric Origin of the Inverse Square Law.

A-Level Physics notes on Gravitational Fields: 1. Newton's Law of Gravitation; 2. Gravitational Field Strength; 3. Gravitational Potential.

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

A-Level Further Maths notes on Hyperbolic Functions (Extended): Hyperbolic Functions (Extended Treatment); 1. Definitions for thorough revision and examinati.

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 Hypothesis Testing (Extended): Hypothesis Testing (Extended Treatment); 1. The Hypothesis Testing Framework.

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 Physics notes on Kinematics: 1. Fundamental Definitions; 2. Derivation of the SUVAT Equations; Equation 1: $v = u + at$.

A-Level Mathematics notes on Kinematics (Extended): Kinematics (Extended Treatment); 1. Equations of Motion (SUVAT) -- Rigorous Derivation.

A-Level Further Maths notes on Maclaurin and Taylor Series: Board Coverage; 1. Maclaurin Series; 1.1 Definition; 1.2 Derivation from the Taylor series.

A-Level Physics notes on Magnetic Fields: 1. Magnetic Force on a Current-Carrying Wire; Magnetic Force on a Moving Charge.

A-Level Physics notes on Magnetic Fields: 1. Magnetic Flux Density; 2. Force on a Moving Charge; 3. Circular Motion in a Magnetic Field.

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

A-Level Further Maths notes on Matrices: Board Coverage; 1. Matrix Notation and Operations; 1.1 Matrix Addition and Scalar Multiplication; 1.2 Matrix Multipl.

A-Level Further Maths notes on Matrices and Transformations (Extended): Matrices and Transformations (Extended Treatment); 1. Matrix Operations; 1.1 Definiti.

A-Level Physics notes on Measurements and Error Analysis: 1. Systematic and Random Errors; Systematic Errors; Random Errors; 2. Uncertainty Analysis.

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 Physics notes on Momentum: Proof from Newton's Laws for comprehensive revision and examination preparation. and examination pre.

A-Level Physics notes on Nuclear Energy: 1. Mass Defect and Binding Energy; Mass Defect; Einstein's Mass-Energy Equation; Derivation of Mass-Energy Equivalence.

A-Level Physics notes on Nuclear Physics: 1. Rutherford Scattering; The Experiment; Interpretation; Closest Approach Distance.

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

A-Level Physics notes on Oscillations: 1. Simple Harmonic Motion — Definition; 2. The SHM Equation and Its Solutions; Derived Quantities.

A-Level Physics notes on Particle Physics: 1. The Standard Model; The Four Fundamental Interactions; 2. Quarks; The Six Flavours.

A-Level Physics notes on Physics: Board Coverage; Course Structure; Core Modules; Assessment with worked examples and exam-style questions.

A-Level Further Maths notes on Poisson and Geometric Distributions: Board Coverage; 1. The Poisson Distribution; 1.1 Definition.

A-Level Further Maths notes on Polar Coordinates: Board Coverage; 1. Converting Between Cartesian and Polar; 1.1 Definitions; 1.2 Converting from polar to Ca.

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

A-Level Mathematics notes on Probability (Extended): Probability (Extended Treatment); 1. Conditional Probability; 1.1 Definition; 1.2 Multiplication rule.

A-Level Further Maths notes on Projectile Motion: Board Coverage; 1. Equations of Motion; 1.1 Setting up the problem; 1.2 Horizontal motion (constant velocity).

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 Physics notes on Properties of Materials: 1. Hooke's Law; Springs in Series and Parallel; 2. Stress and Strain; 3. Young's Modulus.

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

A-Level Physics notes on Quantities and Units: 1. Physical Quantities and the SI System; The Seven SI Base Units; Derived Units; 2. Dimensional Analysis.

A-Level Physics notes on Quantum Physics: 1. The Photoelectric Effect; Observations; Einstein's Explanation (1905); Derivation of the Photoelectric Equation.

A-Level Physics notes on Radioactivity: 1. Nuclear Structure; 2. Types of Radioactive Decay; Alpha Decay ($lpha$); Beta Decay ($eta^-$).

A-Level Physics notes on Refraction and Total Internal Reflection: 1. Refractive Index; Dispersion and the Refractive Index; 2. Snell's Law.

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 Statics (Extended): Statics (Extended Treatment); 1. Moments; 1.1 Definition; 1.2 Moment of a force at an angle.

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 Statistical Distributions (Extended): Statistical Distributions (Extended Treatment); 1. The Binomial Distribution; 1.1 Definition.

A-Level Physics notes on Superposition and Interference: 1. The Principle of Superposition; Constructive and Destructive Interference.

A-Level Physics notes on Thermal Properties: 1. Temperature Scales; The Kelvin Scale; Triple Point of Water; Brownian Motion as Evidence for the Particle Model.

A-Level Physics notes on Thermodynamics: 2. Work Done by a Gas; Derivation of Work Done by Gas at Constant Pressure for thorough revision and examination pre.

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.

A-Level Further Maths notes on Vectors in 3D: Board Coverage; 1. Review of A Level Vectors; 2.1 Notation; 2.2 Position vectors and displacement.

A-Level Physics notes on Wave Properties: 1. Progressive Waves; Key Definitions; The Wave Equation; Real-World Application: Seismic Waves.

A-Level Physics notes on Work, Energy and Power: 1. Work Done by a Force; 2. Kinetic Energy; 3. Gravitational Potential Energy; 4. Elastic Potential Energy.