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Algebra

Foundations, rules, techniques, graphs, functions, sequences, matrices, and more.

Algebra – Recommended Books

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Basic Algebra

Algebra Basics

Operations Associativity Commutativity Distributivity Identity Number Bases Base 10: Hundreds, Tens, Units Algebra – Terminology Algebra 1 – Video Algebra 2 – Video Algebra – Examples Kindle : Basic Algebra

Factors

Factors HCF Multiples LCM Prime Factors Removing Brackets FOIL Factorising Difference of Two Squares

Distance, Speed & Time

Distance, Speed & Time Distance Travelled Average Speed Time Taken Distance–Time Graphs Unitary Conversions

Sequences

Sequences nth Term of a Sequence Recurrence Relations Divergence / Convergence Linear Recurrence Relations Formula for Linear Recurrence Relations Solving Recurrence Relations Special Sequences

Surds

Surds Surds Test

Indices

Indices

Completing the Square

Overview Coefficient Method General Method Solving Quadratic Equations Usefulness for Quadratics

Quadratics

Quadratics Factorising Quadratics Factorising – Alternative Finding Roots Roots That Don’t Factorise Quadratic Formula Deriving the Quadratic Formula Quadratic Graphs Sketching Quadratic Functions Discriminant Quadratic Equations Quadratic Graphs – Tangency Kindle :Quadratics Kindle :Factorising Quadratics Kindle :Quadratic factorsQuadratic Factoriser

Joint Variation

Direct Proportion Indirect Proportion Proportion – Square
Equations & Functions

Equations & Inequalities

Equations Inequalities

Formulae

Formulae in Words Evaluating Formulae Order of Operations Formulae in Symbols Changing the Subject Deriving the Quadratic Formula Using the Quadratic Formula Kindle :Algebra Word Questions

Functions

Functions Set Notation Domain, Codomain & Range One‑to‑One Correspondence Inverse Function Inverse – Algebraic Method Inverse – Graphical Method Composite Functions Simple Graphs of Functions Reflections, Translations, etc.

Simultaneous Equations

Graphical Method Solving by Elimination Vedic Method Gaussian Elimination

Exponentials

Exponentials Growth Functions Decay Functions Exponential/Log Graphs Kindle: Logs and Exponentials

Logarithms

Logarithms Converting Bases Logarithmic Equations Logarithm Laws Log and ln Logarithmic Scales Interactive – Exponential/Log Graphs Interactive – Log/Log & Log/Linear

Algebraic Manipulation

Solving Trig Equations Algebraic Fractions Partial Fractions Factorials Pascal’s Triangle Binomial Theorem Interactive – Pascal’s Triangle

Polynomials

Coefficients etc. Nested Form Dividing Polynomials Factor Theorem Remainder Theorem Synthetic Division Dividing by ax + b Solving Polynomial Equations Sketching Polynomial Equations Interactive :Synthetic Division
More Advanced Alegbra & Functions

Binomial Theorem

Factorials Permutations Combinations Pascal’s Triangle Binomial Coefficients Coefficient Equations Binomial Expansions Interactive Pascal Binomial Theorem Probability & Binomial Binomial & e

Complex Numbers

Complex Numbers Argand Diagrams Polar Form De Moivre’s Theorem Roots of a Complex Number

Functions (More Advanced)

Modulus Function Inverse Functions Polynomials Extrema Concavity & Inflexion Odd & Even Functions Asymptotes

Gaussian Elimination

Augmented Matrix Elementary Row Operations Gaussian Elimination Interactive Gaussian Elimination

Number Theory

Division Algorithm Euclid’s Algorithm Diophantine Equations Pythagorean Triples Number Bases

Partial Fractions

Rational Fractions Partial Fractions Distinct Linear Repeated Linear Irreducible Quadratic

Proof

Mathematical Proof Direct Proof Proof by Contradiction Contrapositive Induction

Sequences – Advanced

Recurrence Relations Fixed Points Arithmetic Sequences nth Term (Arithmetic) Sum to n Terms (Arithmetic) Geometric Sequences Sum to n Terms (Geometric) Infinite Series Sum to Infinity – Geometric Sum of First n Natural Numbers Sigma Notation – Rules Common Series – Sigma Notation

Power Series

Power Series D'Alembert Ratio Test Absolute Convergence Fibonacci Centre of Convergence Taylor Series Maclaurin Series Maclaurin Expansion

Sequences –Applications

Standard Series Examples Iteration Graphical Iteration First Order Second Order False Position Newton–Raphson
🎯Linear Algebra

Vectors

Scalar & vector quantities Components Magnitude Interactive – Vector Magnitudes Position vectors Unit vector Zero vector Equal vectors Adding vectors Subtracting vectors Collinearity Perpendicular vectors Angle between vectors Scalar product Section formula

Vectors (Advanced)

Vector product Scalar triple product Planes Vector equations Equations of a line Intersections Uses
Matrices

Matrices

Matrices Matrix Equality Matrix Addition & Subtraction Matrix Notation Matrix Elements Scalar Multiplication Transpose of a Matrix Matrix Multiplication

Matrices – Determinants

2 × 2 Matrix 3 × 3 Matrix

Matrices – Inverses

Cofactor of a 3 × 3 Matrix Adjoint of a 3 × 3 Matrix Inverse of a Square Matrix Product of a Matrix and Its Inverse Gaussian Elimination for Inverses

Special Matrices

Special Matrices Null Matrix Unit Matrix Transformation Matrices Reflections Rotations Scalings
� Applications to Mechanics

Motion in Straight Lines

Reading graphs Areas of graphs Deriving Newton's equations Equations of motion

Vectors in Motion

Linear motion with bearings Vectors and bearings Relative motion Vectors and forces Law of Statics Single pulleys Pulleys

Projectiles

Projectile Motion Horizontal Range Parametric equations Uses of parametric equations

Forces & Equilibrium

Newton's Laws Triangle of Forces Deriving Lami's Theorem Pulleys Single pulleys Inclined planes Coefficient of friction

Momentum, Impulse, Work & Energy

Linear Momentum Impulse Conservation of Momentum Hooke's Law Work Done Power Kinetic Energy Potential Energy

Horizontal Circular Motion

Angular velocity derivation Angular velocity formulae Centripetal acceleration Uniform circular motion Conical Pendulums Banked Motion

Simple Harmonic Motion

Simple Harmonic Motion Hooke's Law & SHM

Centres of Mass

Turning moments Static rigid bodies Couples Centre of Mass