Combined Mathematics Library

Quadratic functions

Start here: Khan Academy Algebra — Quadratic Equations, Discriminant and Nature of Roots

Polynomial functions

Start here: Khan Academy Algebra — Polynomial Remainder Theorem and Factor Theorem

Partial fractions

Start here: Khan Academy Algebra — Partial Fraction Decomposition Techniques

Indices and logarithms

Start here: Khan Academy Algebra — Laws of Indices and Change of Base Rule for Logarithms

Inequalities

Start here: Khan Academy Algebra — Rational and Modulus Inequalities with Real Numbers

Circular (trigonometric) functions

Start here: Khan Academy Trigonometry — Graphs of Circular Functions and Periodicity

Sine rule and cosine rule

Start here: Khan Academy Trigonometry — Sine Rule and Cosine Rule Applications

Sine rule and cosine rule (Pure Maths)

Start here: Khan Academy Trigonometry — Solving Oblique Triangles and Half-Angle Formulae

Limits of a function

Start here: Khan Academy Calculus — Limits, Continuity and L’Hopital’s Rule

Differentiation techniques

Start here: Khan Academy Calculus — Product Rule, Quotient Rule and Chain Rule for Derivatives

The definite integral and the Fundamental Theorem

Start here: Khan Academy Calculus — Fundamental Theorem of Calculus and Definite Integrals

Area bounded by curves

Start here: Khan Academy Calculus — Area Between Curves and Applications of Integration

Equation of a straight line

Start here: Khan Academy Algebra — Forms of Linear Equations and Slope

Line through the intersection of two lines

Start here: GeoGebra Geometry — Lines Passing Through Intersection of Two Lines (L1 + lambda L2 = 0)

Position of two points relative to a line

Start here: GeoGebra Geometry — Relative Position of Points With Respect to a Line

Cartesian coordinates and the straight line

Start here: Khan Academy Geometry — Coordinate Plane and Section Formulae

Perpendicular distance from a point to a line

Start here: GeoGebra Geometry — Perpendicular Distance from Point to Line

Cartesian equation of a circle

Start here: Khan Academy Geometry — Circles on the Coordinate Plane: Centre and Radius Form

Position of a straight line relative to a circle

Start here: GeoGebra Geometry — Secants, Tangents and Non-Intersecting Lines of Circles

Tangents to a circle from an external point

Start here: Khan Academy Geometry — Length of Tangents and Angle Between Tangents

Circle through the intersection of two circles

Start here: GeoGebra Geometry — Coaxial Systems and Circles Passing Through Intersection (S1 + lambda S2 = 0)

Position of two circles

Start here: GeoGebra Geometry — Relative Positions of Two Circles (Touching Externally & Internally)

Condition for two circles to intersect orthogonally

Start here: GeoGebra Geometry — Orthogonal Intersection of Two Circles (2g1g2 + 2f1f2 = c1 + c2)

Mathematical induction

Start here: Khan Academy Algebra — Principle of Mathematical Induction (Base Case & Inductive Step)

Finite series

Start here: Khan Academy Algebra — Arithmetic and Geometric Series Notation (Sigma Notation)

Sums of elementary series

Start here: Khan Academy Algebra — Sum of First n Natural Numbers, Squares and Cubes

Summation of series

Start here: Khan Academy Algebra — Method of Differences and Telescoping Series

Convergence and divergence of series

Start here: Khan Academy Calculus — Infinite Series Convergence, Partial Sums & Ratio Test

The complex number system

Start here: Khan Academy Algebra — Introduction to Imaginary Numbers, i² = -1 & Real/Imaginary Parts

Algebra of complex numbers

Start here: Khan Academy Algebra — Addition, Subtraction, Multiplication & Division of Complex Numbers

Complex conjugate

Start here: Khan Academy Algebra — Complex Conjugate Properties and Proofs (z + z_bar, z * z_bar)

Modulus of a complex number

Start here: Khan Academy Algebra — Modulus of a Complex Number and Triangle Inequality (|z1 + z2| <= |z1| + |z2|)

The Argand diagram

Start here: Khan Academy Algebra — Polar Form and Euler’s Representation of Complex Numbers (r ei theta)

De Moivre's theorem

Start here: Khan Academy Algebra — De Moivre’s Theorem and Powers of Complex Numbers

Loci and regions of a complex number

Start here: GeoGebra Geometry — Complex Loci: Circles (|z - z0| = r) and Perpendicular Bisectors

Binomial expansion

Start here: Khan Academy Algebra — Binomial Theorem for Positive Integral Index & Pascal’s Triangle

Binomial theorem

Start here: Khan Academy Algebra — Binomial Series for Any Rational Index (|x| < 1)

Factorials

Start here: Khan Academy Algebra — Factorials, Permutations and Counting Principles

Fundamental principle of counting

Start here: Khan Academy Statistics & Probability — Fundamental Counting Principle (Multiplication Rule)

Permutations

Start here: Khan Academy Algebra — Linear Permutations, Repeated Objects & nPr Formula

Combinations

Start here: Khan Academy Algebra — Combinations, nCr Formula and Committee Selection Problems

Properties of matrices

Start here: Khan Academy Algebra — Introduction to Matrices, Order of Matrices and Matrix Operations

Special square matrices

Start here: Khan Academy Algebra — Identity Matrices, Symmetric, Skew-Symmetric and Diagonal Matrices

Transpose and inverse of a matrix

Start here: Khan Academy Algebra — Transpose of a Matrix, Determinants and 2x2 Matrix Inverse

Simultaneous equations by matrices

Start here: Khan Academy Algebra — Solving Systems of Linear Equations Using Matrix Inverses (AX = B)

Systems of coplanar forces

Start here: PhET Balancing Act Interactive Simulation (Moments and Coplanar Forces)

Systems of coplanar forces (statics)

Start here: PhET Balancing Act Simulation — Resultant of Coplanar Forces and Couples

Stresses in the rods of a framework

Start here: GeoGebra Geometry — Method of Joints and Bow’s Notation for Frameworks

Centre of mass of uniform bodies

Start here: PhET Balancing Act Simulation — Centre of Mass of Symmetrical Uniform Bodies

Centre of mass by integration

Start here: Khan Academy Calculus — Centroid and Centre of Mass Using Definite Integrals

Centre of mass of composite bodies

Start here: PhET Balancing Act Simulation — Composite Bodies and Centre of Gravity Calculations

Centre of gravity

Start here: Khan Academy AP Physics 1 — Centre of Gravity vs Centre of Mass in Uniform Gravitational Fields

Stability of bodies in equilibrium

Start here: PhET Balancing Act Simulation — Stable, Unstable and Neutral Equilibrium Conditions

Angle of inclination of suspended bodies

Start here: GeoGebra Geometry — Angle of Tilt of Freely Suspended Laminas and Rods

Newtonian model of motion

Start here: Khan Academy AP Physics 1 — Newton’s Second Law and Instantaneous Acceleration

Velocity and acceleration in circular motion

Start here: Khan Academy AP Physics 1 — Angular Velocity, Radial Acceleration & Tangential Acceleration

Motion in a horizontal circle

Start here: Khan Academy AP Physics 1 — Motion in a Horizontal Circle, Conical Pendulum & Banking

Motion in a vertical circle

Start here: Khan Academy AP Physics 1 — Conservation of Mechanical Energy in Vertical Circles

Simple harmonic motion

Start here: Khan Academy AP Physics 1 — SHM Differential Equation (d2x/dt2 = -w2 x)

Simple harmonic motion on a horizontal line

Start here: PhET Masses and Springs — Horizontal Elastic Spring Oscillations and Amplitude

Simple harmonic motion on a vertical line

Start here: PhET Masses and Springs — Vertical Oscillations with Gravity & Equilibrium Shift

Events of a random experiment

Start here: Khan Academy Statistics & Probability — Random Experiments, Sample Spaces and Mutually Exclusive Events

Probability models for random events

Start here: Khan Academy Statistics & Probability — Addition Rule and Multiplication Rule of Probability

Conditional probability

Start here: Khan Academy Statistics & Probability — Conditional Probability P(A|B) and Independent Events

Bayes' theorem

Start here: Khan Academy Statistics & Probability — Law of Total Probability and Bayes’ Theorem

The nature of statistics

Start here: Khan Academy Statistics & Probability — Population vs Sample, Discrete and Continuous Variables

Measures of central tendency

Start here: Khan Academy Statistics & Probability — Mean, Median and Mode of Grouped Data

Measures of relative position

Start here: Khan Academy Statistics & Probability — Quartiles, Percentiles, Ogive Curves and Box Plots

Measures of dispersion

Start here: Khan Academy Statistics & Probability — Variance, Standard Deviation and Interquartile Range