Maths Bridging Course - Algebra, Trigonometry And Calculus.

Comprehensive Maths Bridging course covering Number, Algebra, Trigonometry, Precalculus and Calculus.

What you'll learn
Essential life changing content starting from basic number through to Calculus
Must know techniques of factorisation, simplifying and working with a variety of number types
Core foundational topics such as number, logarithmic laws, algebra and linear equations.
Advanced foundational topics such as advanced algebra, trigonometry, functions, transformations, differentiation and integration.
Requirements
Some experience with high school mathematics needed. You will learn everything else you need to arrive at University ‘maths ready’.
Description
This course is designed to have you ready and prepared to study mathematics, science or engineering at university. It follows a carefully crafted sequence of lessons that build upon each other. It starts at working with integers and finishes with integral calculus and covers all the major topics that you will need. You will be able to work through the course form start to finish or jump in with the topics that you need to brush up on.The majority of the tutorial videos are no more then 10 minutes saving you time. All modules have a single A4 concept map which summarise all the key information for you saving you time.Taking this course will ensure you are ready for university and will put you in a great position to achieve your goals. You will have access to all learning videos topic summary’s and checks of understanding.This course will ensure you have the foundational mathematics knowledge to thrive at University. You will cover must know techniques of factorisation, simplifying and working with a variety of number types and foundational topics such as number, logarithmic laws, algebra and linear equations. You will then progress onto more advanced topics such as advanced algebra, trigonometry, functions, transformations, differentiation and integration.

Overview

Section 1: Introduction

Lecture 1 Welcome

Section 2: Module 1 Working with numbers

Lecture 2 Positive and negative numbers

Lecture 3 Order of operations

Lecture 4 Introduction to fractions and adding and subtracting

Lecture 5 Decimals and percentages

Lecture 6 Rounding Decimals

Lecture 7 Rational and irrational numbers

Lecture 8 Introduction to surds and simplifying surds

Lecture 9 Simplifying Surds

Section 3: Module 2 - Index and logarithmic laws

Lecture 10 Index or Power

Lecture 11 Index laws

Lecture 12 More index law examples

Lecture 13 Scientific notation

Lecture 14 Logarithms

Lecture 15 Logarithm laws

Lecture 16 Further examples of log laws

Lecture 17 Change of base theorem

Section 4: Module 3 - Trigonometry Part 1

Lecture 18 Triangles

Lecture 19 Pythagoras theorem

Lecture 20 Trigonometry

Lecture 21 The sine rule

Lecture 22 Solving triangles with the sine rule

Lecture 23 The cosine rule - Calculating side length

Lecture 24 The cosine rule - Calculating angle

Lecture 25 Measuring angles

Lecture 26 Measuring angles in radians

Lecture 27 Converting radians to degrees

Lecture 28 Two special triangles

Section 5: Module 4 - Algebra Part 1

Lecture 29 Introduction to algebra

Lecture 30 Introduction to Algebra - Language

Lecture 31 Introduction to algebra - Operations with like Terms

Lecture 32 Commutive, associative and distributive law

Lecture 33 Expanding brackets or 'parentheses'

Lecture 34 Expanding brackets special cases

Lecture 35 Factorizing

Lecture 36 Factorizing expressions

Lecture 37 Factorizing quadratics

Lecture 38 Factorizing quadratics example

Lecture 39 Multiplying and dividing algebraic fractions

Lecture 40 Adding and subtracting algebraic fractions

Section 6: Module 5 - Algebra Part 2

Lecture 41 Introduction to linear equations

Lecture 42 Solving linear equations

Lecture 43 Cross multiply technique

Lecture 44 Rearranging Formula

Lecture 45 Solving quadratics by factorizing

Lecture 46 Solving by quadratic formula

Lecture 47 Solving log equations

Lecture 48 Solving Indicial equations (Part 1)

Lecture 49 Solving Indicial equations (Part 2)

Lecture 50 Exponential growth and decay

Lecture 51 Solving trigonometric equations

Lecture 52 More trigonometric equations

Lecture 53 Other trigonometric equations

Section 7: Module 6 - Functions Part 1

Lecture 54 Introduction to functions

Lecture 55 Linear equations

Lecture 56 Sketching linear functions

Lecture 57 Special linear equations

Lecture 58 Find the equation of a given line

Lecture 59 Parallel and perpendicular lines

Lecture 60 Simultaneous equations

Section 8: Module 7 - Functions Part 2

Lecture 61 Quadratics

Lecture 62 The discriminant

Lecture 63 linear transformations

Lecture 64 Transformation of quadratics

Lecture 65 The Absolute function

Lecture 66 Hybrid (Piecewise) functions

Lecture 67 Inverse functions

Lecture 68 Graphs of exponential and logarithmic functions

Lecture 69 Composite functions

Section 9: Module 8 - Trigonometry Part 2

Lecture 70 The unit circle

Lecture 71 Sine, cosine and tangent of angles in any quadrant

Lecture 72 Examples of sin cos tan

Lecture 73 Graphs of sine and cosine trig functions

Lecture 74 Phase shift

Lecture 75 Changing amplitude and period of sine and cosine functions

Lecture 76 Vertical shift and putting it all the transformations together

Lecture 77 Transformations of sine and cosine functions worked examples

Section 10: Module 9 - Calculus Part 1

Lecture 78 Limits

Lecture 79 Continuous functions

Lecture 80 Rate and instantaneous rate

Lecture 81 Derivative from 'first principles' or 'by the definition'

Lecture 82 Table of Derivatives Part 1

Lecture 83 Examples of derivatives

Lecture 84 Graph of function vs its derivative

Lecture 85 Nature of turning points

Lecture 86 Equations of tangents to curves

Lecture 87 Greatest and least value of a function

Section 11: Module 10 - Calculus Part 2

Lecture 88 The chain rule

Lecture 89 A short cut for chain rule

Lecture 90 Product Rule

Lecture 91 The Quotient rule

Lecture 92 Introduction to Integration

Lecture 93 Integration constant

Lecture 94 Integral as area

Lecture 95 Table of Integrals

Lecture 96 Integral examples

Lecture 97 Integral example- determining a quantity

Anyone who will be studying maths, science and/or engineering at university.,Students who want to truly master the essential topics before arriving at university.,Anyone who need to brush up on key topics that they didn’t master in high school.,High School students studying advanced mathematics who could benefit from some expert teaching.,Those with an interest in mathematics who love learning for the fun of it.