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Master Number, Logarithms, Algebra, Functions, Trigonometry, Calculus and arrive at University ‘maths ready!’

What you will 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.

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.


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NOTE:  In accordance with UDEMY policy those under 18 may use the services only if a parent or guardian opens their account, handles any enrollments, and manages their account usage.

 

English
language

Content

Introduction

Introduction

Module 1 Working with numbers

Positive and negative numbers
Order of operations
Introduction to fractions and adding and subtracting
Decimals and percentages
Rounding Decimals
Rational and irrational numbers
Introduction to surds and simplifying surds
Simplifying Surds

Module 2 – Index and logarithmic laws

Index or Power
Index laws
More index law examples
Scientific notation
Logarithms
Logarithm laws
Further examples of log laws
Change of base theorem

Module 3 – Trigonometry Part 1

Triangles
Pythagoras theorem
Trigonometry
The sine rule
Solving triangles with the sine rule
The cosine rule – Calculating side length
The cosine rule – Calculating angle
Measuring angles
Measuring angles in radians
Converting radians to degrees
Two special triangles

Module 4 – Algebra Part 1

Introduction to algebra
Introduction to Algebra – Language
Introduction to algebra – Operations with like Terms
Commutive, associative and distributive law
Expanding brackets or ‘parentheses’
Expanding brackets special cases
Factorizing
Factorizing expressions
Factorizing quadratics
Factorizing quadratics example
Multiplying and dividing algebraic fractions
Adding and subtracting algebraic fractions

Module 5 – Algebra Part 2

Introduction to linear equations
Solving linear equations
Cross multiply technique
Rearranging Formula
Solving quadratics by factorizing
Solving by quadratic formula
Solving log equations
Solving Indicial equations (Part 1)
Solving Indicial equations (Part 2)
Exponential growth and decay
Solving trigonometric equations
More trigonometric equations
Other trigonometric equations

Module 6 – Functions Part 1

Introduction to functions
Linear equations
Sketching linear functions
Special linear equations
Find the equation of a given line
Parallel and perpendicular lines
Simultaneous equations

Module 7 – Functions Part 2

Quadratics
The discriminant
linear transformations
Transformation of quadratics
The Absolute function
Hybrid (Piecewise) functions
Inverse functions
Graphs of exponential and logarithmic functions
Composite functions

Module 8 – Trigonometry Part 2

The unit circle
Sine, cosine and tangent of angles in any quadrant
Examples of sin cos tan
Graphs of sine and cosine trig functions
Phase shift
Changing amplitude and period of sine and cosine functions
Vertical shift and putting it all the transformations together
Transformations of sine and cosine functions worked examples

Module 9 – Calculus Part 1

Limits
Continuous functions
Rate and instantaneous rate
Derivative from ‘first principles’ or ‘by the definition’
Table of Derivatives Part 1
Examples of derivatives
Graph of function vs its derivative
Nature of turning points
Equations of tangents to curves
Greatest and least value of a function

Module 10 – Calculus Part 2

The chain rule
A short cut for chain rule
Product Rule
The Quotient rule
Introduction to Integration
Integration constant
Integral as area
Table of Integrals
Integral examples
Integral example- determining a quantity