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Maths
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Types of number
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Real numbers
Arithmetic
Order of operations
Rounding
Rounding to decimal places
Rounding to nearest integer
Rounding to significant figures
Representing fractions
Converting percentages to decimals
Converting decimals to percentages
Converting fractions to decimals
Converting decimals to fractions
Converting fractions to percentages
Converting percentages to fractions
Converting recurring decimals to fractions
Divisibility
Prime numbers
Composite numbers
Prime factor decomposition
Highest common factor
Lowest common multiple
Fractions
Simplifying fractions
Multiplying fractions
Dividing fractions
Adding fractions
Subtracting fractions
Algebraic fractions
Percentages
Converting percentages to decimals
Converting decimals to percentages
Percentage of a quantity
Percentage increase
Percentage decrease
Ratio
Ratio meaning
Simplifying ratios
Algebra
Indices and surds
Laws of indices
Multiplying indices
Dividing indices
Raising an index to an index
Power of 0
Power of 1
Fractional powers
Negative powers
Changing the base of a power
Surds
Simplifying surds
Adding surds
Subtracting surds
Multiplying surds
Dividing surds
Rationalising the denominator
Linear functions
Equation of a straight line
Finding the equation of a straight line
Modulus of a linear function
Inequalities
Inequality signs
Solving linear inequalities
Quadratic inequalities
Polynomial arithmetic
Expanding brackets
Expanding single brackets
Expanding double brackets
Expanding triple brackets
Expanding brackets with surds
Factorising quadratics
Polynomial division
Difference of two squares
The factor theorem
Quadratics
Quadratic functions and their graphs
The discriminant of a quadratic equation
Completing the square
Solving quadratic equations by completing the square
Quadratic formula
Solving disguised quadratics
Sequences
Arithmetic sequences
Simultaneous equations
Solving simultaneous equations by elimination
Solving simultaneous equations by substitution
Number of intersections between graphs
Logarithms
The logarithm function
Laws of logarithms
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Subtracting logarithms
Multiplying logarithms by a constant
Proportionality
Direct proportion
Inverse proportion
Binomial expansion
Binomial expansion
Binomial expansion by factorial
Graphs
Coordinates
Cartesian coordinates
Graph transformations
Translating graphs
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Parallel line equations
Perpendicular line equations
Real-world graphs
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Exponential graphs
Exponential function
Exponential function gradient
Logarithm function gradient
Logarithm graph equation
Geometry
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Midpoint of points
Straight line equation
Circle-line intersection
Intersection of circles
Circles
Equation of a circle
Vectors
Position vectors
Triangles
Sine rule
Trigonometric identities
Finding all sine angles
Finding all cosine angles
Finding all tangent angles
Calculating tangent
Sine-cosine square identity
Sine-cosine offset identity
Differentiating sine
Differentiating cosine
Inverse trigonometry
Radians
Radian
Arc length from radians
Sector area from radians
Small angle approximation
Arcs and sectors
Arc
Sector
Calculus
Differentiation
Definition of differentiation
Derivative notation
Power rule for differentiation
Differentiation from first principles
Second derivative
Point of inflection
Turning point
Classifying stationary points
Tangent from differentiation
Normal from differentiation
Integration
Definition of integration
Integration formula
Integration of other expressions
Common calculus results
Further
Complex numbers
Adding complex numbers
Subtracting complex numbers
Multiplying a complex number by a real number
Complex conjugate
Complex numbers
Complex solutions to polynomials
Dividing complex numbers
Factorising polynomials with complex roots
The imaginary constant
Multiplying a complex number by its conjugate
Coefficient and root relationships
Quadratic roots and coefficients
Cubic roots and coefficients
Matrices
Matrix definition
Matrix addition
Matrix scalar multiplication
Matrix multiplication
Identity matrix
Matrix determinant
Inverse matrix
Singular matrix
Matrix transformations
Matrix transformations about the origin
Solving simultaneous equations using matrices
General rotation matrix
Vectors
Vector line equation
Cartesian line equation
Converting vector-form to cartesian-form line equations
Converting cartesian-form to vector-form line equations
Converting vector-form to cartesian-form line equations in 3D
Converting vector-form to cartesian-form line equations in 3D
Scalar product of vectors
Distance from point to line
Distance between two lines
Series
Series
Summation
Standard summation results
Method of differences
Maclaurin series standard results
Creating Maclaurin series
Proof by induction
Proof by induction
Hyperbolic functions
sinh
cosh
tanh
Hyperbolic functions of zero
Hyperbolic square difference identity
Hyperbolic square sum identity
sinh2x identity
Discrete
Graphs
Graph vertex
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Graph tree
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Adjacency matrix
Graph complement
Graph subdivision
Bipartite graph
Isomorphic graph
Networks
Network node
Network arc
Distance matrix
Minimum spanning tree
Prim's algorithm
Kruskal's algorithm
Network route inspection
Activity networks
Network flows
Network flows
Game theory
Pay-off matrices
Play safe strategy
Dominating strategies
Optimal mixed strategy
Linear programming
Linear Programming
Unsorted
Common function graphs
Inequality of Arithmetic and Geometric Means
Vector translation
Physics
Measurements
Base units
Unit prefixes
Energy conversions
Errors
Random error
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Precision
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Accuracy
Repeatability
Reproducibility
Electricity
Basics of electricity
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Electrical current
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Electrical energy
Electrical power
Units of energy
Calculating the number of electrons
Resistance in a bulb
Diode
Potential divider
Temperature coefficient
Resistivity
Resistance in a wire
Resistance in parallel
Kirchoff's first law
Kirchoff's second law
Electricity revision
Waves
Progressive wave
Types of wave
Transverse wave
Longitudinal wave
Electromagnetic wave
Wavelength
Wave frequency
Wave period
Wave speed
Wave speed calculations
Oscilloscope
Reflection of light
Refractive index
Refractive index of air
Snell's law
Refraction of light
Total internal reflection
Diffraction of waves
Diffraction grating
Double slit diffraction
Wave superposition
Constructive interference
Destructive interference
Polarised wave
Polarisation
Uses of polarisation
Wave phase difference
Speed of electromagnetic wave
Fibre optic cable
Fibre optic modal dispersion
Fibre optic material dispersion
Chemistry
Atomic structure
Atoms
Nucleus
Protons
Computing
Hardware and software
Hardware
Software
Application software
Operating systems
Operating system role
OS resource management
Types of programming language
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Systems software
Operating systems
Utility programs
Dynamic libraries
Code translation
Source code
Object code
Code translators
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Bytecode
Number systems
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Units of data
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Converting bytes to bits
Decimal prefixes
Binary prefixes
Binary
Unsigned binary
Logic gates
Logic gates
Truth table
NOT gate
AND gate
OR gate
NAND gate
NOR gate
XOR gate
Boolean algebra
Boolean AND
Boolean OR
Boolean XOR
Boolean NOT
Boolean AND one
Boolean AND zero
Boolean OR one
Boolean OR zero
RISC-V assembly
Smallest program
Immediate and register instructions
Setting registers
Copying registers
Adding immediates
Adding registers
Subtraction
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Labels
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C programming
Hello world
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Hello World
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Comments
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Data types
Data types
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Short
C# programming
Hello world
Comments
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Else statements
Iteration
Loops
While loops
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Arrays
Creating arrays
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Iterating arrays
Foreach loops
Methods
Method declaration
Method calling
Named method arguments
Default arguments
Method overloading
User input
Console.ReadLine
Classes
Classes
Class declaration
Object instantiation
Fields
Class methods
Minecraft server
dylancode's Minecraft server optimisation guide
server.properties
view-distance
simulation-distance
sync-chunk-writes
network-compression-threshold
entity-broadcast-range-percentage
bukkit.yml
spawn-limits
ticks-per
spigot.yml
nerf-spawner-mobs
merge-radius
zombie-aggressive-towards-villager
mob-spawn-range
entity-activation-range
wake-up-inactive
entity-tracking-range
hopper
max-tnt-per-tick
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