A Basic Guide to High School Mathematics

A Basic Guide to High School Mathematics (WIP)

Notes by Unit

Chapter 1 - Proof	Proof	Notes
Chapter 2 - Algebra & Functions	Indices Surds Quadratics Simultaneous Equations Inequalities Polynomials & Rational Expressions Graphs & Proportion Functions Graph Transformations Algebraic Fractions Modelling	Notes (WIP)
Chapter 3 - Coordinate Geometry	Coordinate Geometry Circles Parametric Equations Parametric Equation Modelling	Notes (WIP)
Chapter 4 - Sequences & Series	Binomial Expansion Sequences Sigma Notation Arithmetic Sequences Geometric Sequences Modelling with Sequences	Notes (WIP)
Chapter 5 - Trigonometry	Trigonometry Small Angle Approximation Trig Graphs Further Trigonometry Trigonometric Identities Compound Angles & Equivalent Forms Trig Equations Proving Trigonometric Identities Trigonometry in Context	Notes (WIP)
Chapter 6 - Exponentials & Logarithms	Exponentials Exponential Models Logarithms Laws of Logarithms Exponential & Logarithmic Equations Reduction to Linear Form Exponential Growth & Decay	Notes (WIP)
Chapter 7 - Differentiation	Differentiation from First Principles Differentiation Gradients Further Differentiation Implicit Differentiation & Parametric Differentiation Forming Differential Equations	Notes (WIP)
Chapter 8 - Integration	Fundamental Theorem of Calculus Indefinite Integrals Definite Integrals & Parametric Integration Integration as the Limit of a Sum Further Integration Integration with Partial Fractions Differential Equations Differential Equations in Context	Notes (WIP)
Chapter 9 - Numerical Methods	The Change of Sign Method The x = g(x) Method & The Newton-Raphson Method Numerical Integration Numerical Methods in Context	Notes (WIP)
Chapter 10 - Vectors	Introducing Vectors Magnitude & Direction of a Vector Resultant & Parallel Vectors Position Vectors Vector Problems	Notes (WIP)
Chapter 11 - Statistical Sampling	Statistical Sampling	Notes (WIP)
Chapter 12 - Data Presentation & Interpretation	Box Plots, Cumulative Frequency, Histograms Scatter Graphs Central Tendency & Variation Outliers & Cleaning Data	Notes (WIP)
Chapter 13 - Probability	Venn Diagrams, Tree Diagrams, & Two-Way Tables Conditional Probability Modelling with Probability	Notes (WIP)
Chapter 14 - Statistical Distributions	Discrete Random Variables & The Binomial Distribution The Normal Distribution Appropriate Distributions	Notes (WIP)
Chapter 15 - Hypothesis Testing	Introducing Hypothesis Testing Binomial Hypothesis Testing Sample Means Hypothesis Testing	Notes (WIP)
Chapter 16 - Quantities & Units in Mechanics	Quantites & Units in Mechanics	Notes (WIP)
Chapter 17 - Kinematics	Displacement, Velocity, & Acceleration Graphs of Motion SUVAT Calculus in Kinematics Projectiles	Notes (WIP)
Chapter 18 - Forces & Newton's Laws	Introducing Forces & Newton's First Law Newton's Second Law Weight & Tension Newton's Third Law and Pulleys F = ma & Differential Equations The Coefficient of Friction	Notes (WIP)
Chapter 19 - Moments	Moments	Notes (WIP)
Chapter 20 - Proof	Proof	Notes (WIP)
Chapter 21 - Complex Numbers	Introducing Complex Numbers Working with Complex Numbers Complex Conjugates Introducing the Argand Diagram Introducing Modulus-Argument Form Multiply and Divide in Modulus-Argument Form Loci with Argand Diagrams De Moivre's Theorem z = re^(i*theta) nth Roots of Unity Geometrical Problems	Notes (WIP)
Chapter 22 - Matrices	Introducing Matrices The Zero & Identity Matrices Matrix Transformations Invariance Determinants Inverse Matrices Simultaneous Equations Geometrical Interpretation Factorising Determinants Eigenvalues and Eigenvectors Diagonalisation Cayley-Hamilton Theorem	Notes (WIP)
Chapter 23 - Further Algebra & Functions	Roots of Polynomials Forming New Equations Summations Method of Differences Introducing Maclaurin Series Standard Maclaurin Series Limits and l'Hospital's Rule Polynomial Inequalities Rational Function Inequalities Modulus of Functions Reciprocal Graphs Linear Rational Graphs Quadratic Rational Functions Discriminants Conic Sections Transformations	Notes (WIP)
Chapter 24 - Further Calculus	Improper Integrals Volumes of Revolution Mean Value Partial Fractions Differentiating Inverse Trig Integrals of the Form sqrt(a^2-x^2) and 1/(a^2+x^2) Arc Length and Sector Area Reduction Formulae Limits	Notes (WIP)
Chapter 25 - Further Vectors	Equations of Lines Equations of Planes The Scalar Product Perpendicular Vectors Intersections The Vector Product	Notes (WIP)
Chapter 26 - Polar Coordinates	Polar Coordinates Polar Curves Polar Integration	Notes (WIP)
Chapter 27 - Hyperbolic Functions	Hyperbolic Functions Hyperbolic Calculus Hyperbolic Inverse Hyperbolic Inverse Hyperbolic Integration Hyperbolic Identities Hyperbolic Identities	Notes (WIP)
Chapter 28 - Differential Equations	1st Order Differential Equations - Integrating Factors 1st Order Differential Equations - Particular Solutions Modelling 2nd Order Homogeneous Differential Equations 2nd Order Non-Homogeneous Differential Equations 2nd Order Non-Homogeneous Differential Equations Simple Harmonic Motion Damped Oscillations Systems of Differential Equations Hooke's Law Damping Force	Notes (WIP)
Chapter 29 - Numerical Methods	Mid-Ordinate Rule & Simpson's Rule Euler's Step by Step Method Euler's Improved Step by Step Method	Notes (WIP)
Chapter 30 - Tracing an Algorithm	Tracing an Algorithm Complexity	Notes (WIP)
Chapter 31 - Bin Packing	Bin Packing Complexity	Notes (WIP)
Chapter 32 - Sorting Algorithms	Introduction Quick Sort Bubble Sort	Notes (WIP)
Chapter 33 - Graph Theory	Graph Theory	Notes (WIP)
Chapter 34 - Minimum Spanning Trees	Introduction Kruskal's Algorithm Prim's Algorithm Prim's Algorithm with a Matrix	Notes (WIP)
Chapter 35 - Dijkstra's Algorithm	Dijkstra's Algorithm	Notes (WIP)
Chapter 36 - Critical Path Analysis	Critical Path Analysis (CPA) Precedence Tables Activity Networks Dummy Activities	Notes (WIP)
Chapter 37 - Network Flows	Network Flows Cuts Supersinks & Supersources	Notes (WIP)
Chapter 38 - Linear Programming	Drawing Inequalities & The Objective Function Formulating an LP Problem 3-Variable to 2-Variable	Notes (WIP)
Chapter 39 - Simplex Algorithm	Simplex Algorithm	Notes (WIP)
Chapter 40 - LP Solvers	Indicator Variables Shortest Path (Dijkstra's) Longest Path (CPA) Network Flows Critical Path Analysis (Alternative) Matching Allocation Transportation LINDO	Notes (WIP)
Chapter 41 - PMCC	Bivariate Data Correlation & Association The PMCC	Notes (WIP)
Chapter 42 - Linear Regression	Introduction Calculating Regression Lines Interpreting	Notes (WIP)
Chapter 43 - PMCC Hypothesis Testing	PMCC Hypothesis Testing Effect Sizes	Notes (WIP)
Chapter 44 - Spearman's Rank	Spearman's Rank Correlation Coefficient Hypothesis Testing	Notes (WIP)
Chapter 45 - Chi-Squared Contingency Table Tests	The Chi-Squared Statistic Hypothesis Testing	Notes (WIP)
Chapter 46 - Discrete Random Variables	Discrete Random Variables The Expected Value E(X) The Variance Var(X) E(aX+b)=aE(X)+b Var(aX+b)=a^2 Var(X) E(X+Y)=E(X)+E(Y) and Var(X+Y)=Var(X)+Var(Y)	Notes (WIP)
Chapter 47 - Discrete Uniform Distributions	Discrete Uniofrm Distributions	Notes (WIP)
Chapter 48 - Geometric Distributions	Geometric Distributions	Notes (WIP)
Chapter 49 - Binomial Distributions	Binomial Distributions	Notes (WIP)
Chapter 50 - Poisson Distribution	Poisson Distribution	Notes (WIP)
Chapter 51 - Goodness of Fit Tests	Goodness of Fit Tests The Uniform Distribution The Poisson Distribution The Binomial Distribution The Left Hand Tail	Notes (WIP)
Chapter 52 - Energy	Introduction to Energy Conservation of Mechanical Energy The Work-Energy Principle	Notes (WIP)
Chapter 53 - Power	Introduction to Power Horsepower Maximum Speed Work, Energy, & Power	Notes (WIP)
Chapter 54 - Friction	Introduction to Friction Block Sliding Down a Slope Friction Examples Exam-Style Question	Notes (WIP)
Chapter 55 - Momentum & Impulse	Momentum Impulse	Notes (WIP)
Chapter 56 - Collisions	Conservation of Linear Momentum The Coefficient of Restitution HItting the Ground/Hitting the Wall	Notes (WIP)
Chapter 57 - Moments	Moments - The Basics Couples Ladders Pivots/Hinges Sliding & Toppling	Notes (WIP)
Chapter 58 - Centre of Mass	Introducing CoM Laminas Suspending a Lamina Triangles Other Shapes	Notes (WIP)
Chapter 59 - Dimensional Analysis	Introducing Dimensional Analysis Dimensional Consistency Finding Formulae Triangles Other Shapes	Notes (WIP)

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