# SEBE Maths Resources

Select your SEBE unit below to view links to maths resources relating to that unit. If your unit is not listed, check the General SEBE Maths Support section for maths resources on a variety of topics.

#### General SEBE Maths Resources

Resource Site | Link | Resource Type |
---|---|---|

Maths is Fun | Maths is Fun | Simple to complex maths explanations and activities. |

Mathscasts | Mathscasts | Access to a series of videos on foundation maths activities. |

Revision Maths | Revision Maths | Free maths revision resources to help you with revision of high school maths. This covers a range of topics including: Number, Algebra, Ratio, Proportion and Rates of Change, Geometry and Measure, Trigonometry, Statistics and Probability. |

James Cook University maths support | James Cook University - Maths Support | Easy-to-understand explanatory notes, worked examples and exercises for each topic. |

RMIT maths support | RMIT - maths support | Links to explanations and resources on a variety of maths |

University of Colorado | University of Colorado - Simulations | Simulation activities for a variety of maths, chemistry and physics concepts at varying levels of difficulty. |

#### SEB101

Topic | Link | Resource Type |
---|---|---|

Calculating gradient | Revision Maths - Gradients and Graphs | Detailed description on how to calculate the gradient of a curve and a straight line - Text, video, worked example |

Calculating uncertainties | WikiHow - Calculate Uncertainty | A wikiHow on calculating uncertainties - Text, worked example |

Circuits and Ohm's law | Khan Academy - Circuits Part 1 | Series with videos, worksheets and practice questions to hone your skills covering circuits and Ohm's Law. Video series, practice questions, quizzes |

Coulomb's law | Khan Academy - Electric Charge, Electric Force & Voltage | Sal Khan's physics unit covering Electric charge, field and potential. Video series. |

Moment of inertia | SkyCiv - Moment of Inertia Calculator | Moment of inertia and centroid calculator. Online software |

Motion graphs | YouTube - Jennifer Cash - Interpreting Motion Graphs | Motion graphs: position vs time, velocity vs time and acceleration vs time. Video |

Voltmeters and Ammeters | Khan Academy - Voltmeters and Ammeters | video explanation and worked examples. |

Vectors and trigonometry | Maths is Fun - Vectors | Basics of vectors; addition, subtraction, dot product and cross product. Text, examples, practice questions, vectors widget |

Velocity, acceleration, relative speed and distance | YouTube - Derek Owens - Physical Science 1.3c | Complete chapter of videos covering Velocity, Acceleration, Graphing and Conversions. Video series. |

#### SEM327

Text, worked example

Topic | Link | Resource Type |
---|---|---|

Coriolis effect | National Geographic - Coriolis Effect | National Geographic's encyclopaedic entry on the Coriolis effect. Text, slide show. |

Graphical acceleration analysis | University of Arizona - Graphical Acceleration Analysis | Graphical method for acceleration analysis for planar mechanisms.Text, worked example |

Graphical velocity analysis | University of Arizona - Graphical Velocity | Graphical method: four-bar, sliding collar, crank, instantaneous centres. Text, worked example |

Rigid-body dynamics | Real World Physics Problems - Rigid Body Dynamics | Rigid-body dynamics, equations of motion.Text, worked example |

Velocity and acceleration loop | Real World Physics Problems - Velocity & Acceleration | Velocity and acceleration in terms of angular velocity, angular acceleration, relative velocity and relative acceleration.Text, worked example. |

#### SEP291

Topic | Link | Resource Type |
---|---|---|

Engineering Modelling | YouTube - patrickJMT - Integration using U-Substitution | Integration using U substitution.Videos with worked example |

Homogeneous second order linear differential equations | YouTube - patrickJMT - Homogeneous second order linear differential equations | Short video on solving homogeneous second order linear differential equations. Videos with worked example |

Laplace | YouTube - patrickJMT -The Laplace Transform - The Basic Idea of How We Use It | The first in a series of videos explaining the Laplace transform. Videos with worked example |

Method of Undetermined Coefficients | YouTube - patrickJMT - Method of Undetermined Coefficients/ 2nd Order Linear DE | Solving a 2nd order linear non-homogeneous differential equation using the Method of Undetermined Coefficients. Videos with worked example. |

ODE's - solve using integrating factors | YouTube - patrickJMT - Integrating Factor to Solve a Differential Equation | Integrating factors to solve ODE. Videos with worked example |

Separable first order differential equations | YouTube - patrickJMT - Solving Separable First Order Differential Equations - Ex 1 | Solving separable first order differential equations. Videos with worked example. |

#### SIT106

Text, examples, practice questions

Topic | Link | Resource Type |
---|---|---|

Conversion between decimal, fractions and percentages | Maths is Fun - Decimals, Fractions and Percentages | Covers conversions between decimals, fractions, and percentages. Text, examples, practice questions. |

Geometry | Maths is Fun - Geometry | Geometry springboard with links to Plane Geometry, Solid Geometry, Trigonometry. Texts, images and links. |

Greek number system | MacTutor - Greek Number Systems | Using the Greek number systems; the Greek alphabet and symbols. Text, examples. |

Multiples and factors | AMSI - Multiples, Common Multiples And The LCM | Multiples and factors. Includes Lowest Common Multiple (LCM), powers, tests for divisibility and more. Text, examples, practice questions. |

Roman numerals | Maths is Fun - Roman Numerals | How to read and write Roman Numerals - CI. Text, examples, practice questions, conversions tool. |

Tessellations | Maths is Fun - Tessellations | A great site explaining tessellations and a link to a Tessellation Artist widget. Text, images and tessellation programs. |

#### SIT190

Topic | Link | Resource Type |
---|---|---|

Algebra | Khan Academy - Algebra | An Algebra boot camp for your brain! A series of Algebra modules ranging from foundations, equations and inequalities to quadratics and irrational numbers. Video series, practice questions, quizzes. |

Calculus | HELM Workbooks | Quadratics, Exponents, Differentiation, Integration and so much more! This is an excellent resource presented as a series of workbooks. Workbook, practice questions. |

Indices | Laerd Mathematics - Indices & the Law of Indices | Index laws with a great range of practice questions each with worked solutions. Text, practice questions. |

Linear Equations | Maths is Fun - Systems Linear Equations | Written explanation and examples. |

Logarithms | Maths is Fun - Logarithms | The perfect introduction to logarithms. Steps you through the relationship between logs and exponents and links to more. Text, examples, practice questions. |

Trigonometry | RMIT - Trigonometry | Trigonometry covering Pythagoras' theorem, right angled triangles, sine/cosine and trigonometric equations. Video series and booklet with practice questions. |

#### SIT191

Topic | Link | Resource Type |
---|---|---|

Basic theoretical probability | Khan Academy - Probability Library | video explanation and practice problems. |

Confidence intervals | Loughborough University - Statistics Leaflets | Student guide to Statistics presented as a series of leaflets. Includes confidence intervals, t-tests and chi-squared tests. Text, examples, practice questions. |

Probability | Khan Academy - Probability | A program of videos, fact sheets and quizzes to master probability. Video series, practice questions, quizzes. |

Statistical calculator | Calculator Soup - Descriptive Statistics Calculator | Online calculator that generates descriptive statistics. The link includes formulas and definitions. Online calculator, text. |

Statistics | Southern Cross University - Statistics | Introduction to Statistics covering data, graphs, measures of central tendency. Text, practice questions, solutions and videos. |

Statistics and Probability | YouTube - Swinburne - StatsCasts | StatsCasts - YouTube videos for statistics support. Video series. |

#### SIT192

Topic | Link | Resource Type |
---|---|---|

Integers | Khan Academy - Whole Numbers Integers | Integers - the basics. Khan Academy worksheet and questions. |

Limits, derivatives, integrals and more! | YouTube - patrickJMT - Channel | PatrickJMT Math Channels video series on limits, derivatives and integrals. Video series. |

Matrices | Khan Academy - Introduction to the Matrix | Sal Khan on the Introduction to Matrices - with a hint of Keanu. Video, worksheets, practice questions. |

Loughborough University - Workbook | Written explanations and workbook. | |

Modular Arithmetic | Brilliant - Modular Arithmetic | Modular Arithmetic - remainders, congruence, addition, multiplication etc. Text, examples, practice questions. |

Proof by induction | Khan Academy - Proof by Induction | Proof of finite arithmetic series formula by induction. Khan Academy video. |

Sigma notation | Khan Academy- Sigma Notation Sum | Explaining the Sigma Symbol and summation notation. Khan Academy video and text. |

Truth Tables and Logical Equivalence | Millersville University - Truth Tables, Tautologies, and Logical Equivalences | Truth tables, logical equivalence and tautologies. Text, worked examples and summary. |

#### SIT194

Topic | Link | Resource Type |
---|---|---|

calculus | Loughborough University - Workbook | Written explanations and workbook. |

Derivatives: Quotient and Product Rule | Lamar University - Product Quotient Rule | Paul's Online Notes working through the Product and Quotient Rule. Text and examples. |

Functions | YouTube - Mathantics - Algebra Basics: What Are Functions? | Introductions to functions and the general terms used. Videos with worked examples. |

Geometry and vectors | RMIT - Vectors | Written explanation and examples |

Integration methods | Khan Academy - Integral Calculus | Khan academy "course" on integrals, includes various integration methods. Video series, worksheets and practice questions. |

Limits | Maths is Fun - Limits | Introduction to limits. Text, examples, practice questions. |

Maclaurin and Taylors Series | Khan Academy - Maclaurin and Taylors Series | Explanation of Maclaurin and Taylor series. Video series, worksheets and practice questions. |

Newton-Raphson method | YouTube - ExamSolutions - How to use the Newton Raphson method | How to use the Newton-Raphson method. Worked examples explained through videos. |

Partial fractions | Lamar University - Partial Fractions | Integration by Partial Fractions. Text and examples. |

Simpsons and Trapezoidal Rules | Imperial College London - Numerical Methods: The Trapezium Rule and Simpson's Rule | Numerical methods of integration using Simpson's and the Trapezium rules. Text and examples. |

Trig functions and applications with triangles | Khan Academy - Basic Trigonometry | Trigonometric ratios and triangles. Video series, worksheets and practice questions. |

#### SIT199

Topic | Link | Resource Type |
---|---|---|

Algebra | Loughborough University - HELM Workbooks | Basic Algebra, functions, equations, inequalities and so much more! This is an excellent resource presented as a series of workbooks. Workbook, practice questions. |

Complex numbers | YouTube - Derek Owens - Complex Numbers | Introduction to complex numbers with worked examples. Access to part 2. Videos with worked examples. |

Matrices | Khan Academy - Introduction to the Matrix | Introductions to functions and the general terms used. Videos with worked examples. |

Set theory | YouTube - Worldwide Centre of Mathematics - Intro to Sets | Series of videos covering sets, subsets and functions. Video series. |

Vectors and their applications | YouTube - High School Physics Explained - Understanding Vectors | Vectors and vector addition summarised in a video with worked examples. Videos with worked examples. |

#### SIT281

Topic | Link | Resource Type |
---|---|---|

Affine ciphers | Crypto Corner - Affine Cipher | Website stepping through the concept of Affine ciphers with an example/cipher generator to play with. Text, cipher widget. |

Chinese remainder theorem | YouTube - Randell Heyman - The Chinese Remainder Theorem made Easy | A worked example showing the CRT step by step. Videos with worked examples. |

Euclidean Algorithm | YouTube - GVSUMath - The Euclidean Algorithm | Step by step video finding the gcd of two numbers using the Euclidean Algorithm. Videos with worked example. |

Euler's Theorem | YouTube - Randell Heyman - Euler's Theorem Made Easy | Euler's theorem worked through with three examples. Goes through the notation, examples and provides links to additional videos. Videos with worked examples. |

Extended Euclidean Algorithm - Fast Modular Exponentiation | University of Colorado Denver - The Extended Euclidean Theorem | Step by step on how to find the gcd of two integers using the Extended Euclidean Algorithm. Text, worked example. |

Polynomial Long Division | Maths is Fun - Polynomial Long Division | Polynomial long division Maths is Fun style. Text, video examples, practice questions. |

#### SIT291

Topic | Link | Resource Type |
---|---|---|

ANOVA | Maths and Statistics - One Way ANOVA By Hand | ANOVA testing example by hand or excel. Worked example and "how to" video. |

Differential equations | RMIT - Differential Equations | First order linear, second order homogeneous and non-homogeneous differential equations. Worksheets. |

Double integrals | Khan Academy - Double Integrals | Double integrals over varying regions. Text, video, practice questions. |

Lagrange multipliers and optimisation | Khan Academy - Lagrange Multipliers and Constrained Optimisation | Lagrange multipliers and optimisation theory and practice. Video series, practice questions. |

#### SIT292

Topic | Link | Resource Type |
---|---|---|

Eigenvalues and eigenvectors | HELM Workbook – Eigenvalues and Eigenvectors | Eigenvalues and eigenvectors; concepts, applications and numerical determination. Workbook, practice questions. |

Gaussian and Gauss-Jordan Elimination | YouTube - Bri The Math Guy - Gaussian Elimination and Gauss Jordan Elimination (Gauss Elimination Method) | Quick summary on what you need to know for Gauss and Gauss-Jordan elimination. Video with worked examples. |

Gram-Schmidt and Vector Spaces | MIT - Linear Algebra Lecture Series | A series of videos produced by MIT covering matrices. Lecture 17: orthogonal matrices and Gram-Schmidt. Video series. |

Matrices & Determinants | Maths is Fun - Matrix Determinant | Clear explanation on 2x2 and 3x3 matrix determinant calculation. Text, examples, practice questions |

Matrix solution of equations | Loughborough University - Matrix Solution of Equations | Matrix solution of equations using Cramer's Rule, inverse matrix method and Gaussian elimination. Workbook, practice questions. |

Set Theory Relations - Symmetry, Reflexivity and Transitivity | YouTube - Trefor Bazett - Reflexive, Symmetric, and Transitive Relations on a Set | Reflexive, Symmetric and Transitive Relations on a set. Videos with worked examples. |

Vector Spaces | YouTube - Adam Panagos - Linear Algebra Example Problems - Vector Space Basis Example #1 | Vector spaces and calculation for basic linearly independent vectors. Videos with worked examples. |

#### SLE111

Topic | Link | Resource Type |
---|---|---|

Equivalent ratios | Khan Academy - Equivalent Ratios | Equivalent ratios; introductions, review and practice. Video, text, quizzes, worked examples, practice questions. |

Fractions | RMIT - Fractions | How to add, subtract, divide and multiply fractions as well as how to convert between decimals and fractions. Video series, worked examples |

Genetics probability | YouTube - Shomu's Biology - How to solve genetics probability problems | Shomu's Biology presents a probability video for genetics. Video. |

Introduction to ratios | Khan Academy - Ratio Example Problems | Introduction to the basics of ratios with practice questions. Video, examples, practice questions. |

Mendelian Genetics and probability | Khan Academy - Probabilities in Genetics | Khan Academy's series on Introduction to heredity. Includes Mendelian genetics and probability, Punnett squares and probability basics. Video, text, quizzes, worked examples, practice questions. |

#### SLE123

Topic | Link | Resource Type |
---|---|---|

Energy transfer | Khan Academy - Electric Charge, Electric Force and Voltage | Electrical concepts explained through a series of videos. Video series. |

Physics | The Physics Classroom - Topics | Home page for access to Kinematics, Newton's Laws, Vectors and more. Text, examples, practice questions. |

Maths is Fun - Physics | Physics springboard with links to Units, Motion, Force and more. Text, examples, practice questions. | |

Rearranging and solving physics equations | YouTube - QMCPhysics - Physics Skills - Rearranging Equations | Rearranging force, wave speed, energy, speed and power equations. Video. |

Rearranging velocity equations | YouTube - Brian Corbett - Science 10 physics: rearrange basic formulas | Rearranging speed, velocity and acceleration equations. Video. |

#### SLE132

Topic | Link | Resource Type |
---|---|---|

Lab report writing skills | Deakin University - Reading and Writing For Science | Lab report writing explained with interactive interface. Text, interactive interface, questions. |

Pressure | Khan Academy - Pressure | Pressure due to gravity, fluid pressure and pressure at atmospheric level. Text, formulas, examples. |

Scaling in microscopy | Rice University - Measurement with the Light Microscope | Measuring and scaling objects seen under the microscope. Text, example questions. |

Surface to volume ratio | Study.com - Surface Area to Volume Ratio | Surface to volume ratio online crash course. Video, example questions. |

#### SLE133

Topic | Link | Resource Type |
---|---|---|

Balancing Chemical Equations | Chemistry LibreTexts - How to Write Balanced Chemical Equations | Written explanation and examples. |

WikiHow - Balance Chemical Equations | Written explanation and worked examples. | |

Formula mass and mole calculations | BBC ByteSize - Revision | Written explanation and worked examples. |

Logarithms | YouTube - Khan Academy - Logarithms | Mario claims that this is everything you need to know about logs! Video |

Live Science - Logarithms | Written explanation and worked examples. | |

Mole calculations | YouTube - Ketzbook - Mole Conversions Made Easy: How to Convert Between Grams and Moles | Mole conversions: convert between grams and moles. Video. |

Scientific notation | University of Adelaide - Scientific Notation Rounding Revision | University of Adelaide's Maths Learning Centre: Scientific notation and rounding. Text, practice questions. |

Significant figures | Khan Academy - Significant Figures | Sal Khan will step you through the how to of significant figures in a series of videos with a practice worksheet. Text, practice questions. |

#### SLE155

Topic | Link | Resource Type |
---|---|---|

Approximation rounding | BBC ByteSize - Revision | Written explanation and sample questions. |

Chemistry fundamentals | University of North Carolina - Chemistry Fundamentals | Chemistry fundamentals including nomenclature, stoichiometry, gas laws and thermodynamics. Text, practice questions. |

Henderson-Hasselbach equation | Chem Team - Introduction to the Henderson-Hasselbalch Equation | Henderson-Hasselbach equation (equilibrium and buffers) alternate explanation with link to practice questions. Text, practice questions with answers and explanations. |

Introduction to using a Scientific calculator | University of Wollongong - Using a Scientific Calculator | A handy resource on how to use your Scientific calculator. Text and practice. |

Logarithms | Math Centre - Logarithms | Logarithms: the why, what and how. Text, practice questions. |

Oxidation number and redox reactions | Khan Academy - Oxidation Number | Khan Academy's videos and worksheets on oxidation number and redox reactions. Videos, text. |

Specific heat | BrightStorm - Specific Heat | Video explanation. |

Thermodynamics | Khan Academy - Thermodynamics | Has great sections on entropy, enthalpy, Gibbs free energy, specific heat capacity equations and more. Video series, practice questions. |

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