# The Ultimate Resource for Core Maths for Advanced Level: PDF 20 Book Review and Tips

## Core Maths for Advanced Level PDF 20

If you are looking for a comprehensive and accessible book that covers all the core topics of mathematics for advanced level, you might want to check out Core Maths for Advanced Level PDF 20. This book is written by L.Bostock and S.Chandler, who are experienced authors and teachers of mathematics. The book is designed to prepare students for A-level examinations, as well as other equivalent qualifications. It covers the syllabus of various boards, such as Edexcel, OCR, AQA, CIE, etc.

## Core Maths For Advanced Level Pdf 20

In this article, we will give you an overview of what this book contains, why you should study core maths for advanced level, what topics are covered in the book, how to use it effectively, and where to get it. By the end of this article, you will have a clear idea of whether this book is suitable for you and how it can help you achieve your academic goals.

## Why you should study core maths for advanced level

Core maths is the foundation of all higher-level mathematics. It covers the essential skills and concepts that you need to master before moving on to more advanced topics. By studying core maths for advanced level, you will be able to:

Develop your logical thinking and problem-solving abilities

Enhance your numerical fluency and accuracy

Apply mathematical techniques to real-world situations

Prepare yourself for further studies in mathematics or related subjects

Improve your chances of getting into your preferred university or college

Increase your employability and career prospects in various fields

Core maths is not only useful for students who want to pursue mathematics or science-related courses, but also for those who want to study humanities, social sciences, arts, or business. Mathematics is a universal language that can help you communicate, analyze, and understand different aspects of the world. By studying core maths for advanced level, you will be able to broaden your horizons and explore new possibilities.

## What topics are covered in core maths for advanced level

Core Maths for Advanced Level PDF 20 covers all the major topics that you need to know for your A-level examinations. The book is divided into 10 chapters, each focusing on a specific topic. The chapters are:

Algebra and functions

Coordinate geometry and graphs

Sequences and series

Exponentials and logarithms

Trigonometry

Differentiation

Integration

Numerical methods

Vectors

Revision exercises

Each chapter contains clear explanations, worked examples, exercises, and answers. The book also provides revision exercises at the end, which cover all the topics in the book. The book is suitable for both self-study and classroom use. Let's take a closer look at each chapter and what it covers.

### Algebra and functions

This chapter covers the basics of algebra and functions, such as:

Manipulating algebraic expressions and equations

Using indices and surds

Factorizing and simplifying expressions

Solving linear, quadratic, cubic, and simultaneous equations

Understanding and using functions and their notation

Finding inverse and composite functions

Sketching graphs of functions and finding their domains and ranges

Using the modulus function and its graph

Solving inequalities and representing them on graphs

### Coordinate geometry and graphs

This chapter covers the basics of coordinate geometry and graphs, such as:

Using coordinates to locate points on a plane

Finding the distance and midpoint between two points

Finding the gradient of a line and its equation

Finding the equation of a parallel or perpendicular line

Finding the intersection of two lines

Sketching graphs of linear, quadratic, cubic, reciprocal, and rational functions

Finding the roots, intercepts, turning points, and asymptotes of graphs

Using transformations to map graphs onto other graphs

Using calculus to find the gradient and tangent of a curve at a point

### Sequences and series

This chapter covers the basics of sequences and series, such as:

Understanding and using the terms sequence, term, series, sum, etc.

Finding the nth term and the sum of an arithmetic sequence or series

Finding the nth term and the sum of a geometric sequence or series

Using sigma notation to represent series

Finding the sum to infinity of a convergent geometric series

Using the binomial theorem to expand expressions of the form (a+b)^n

Finding the coefficient of a particular term in a binomial expansion

Using Pascal's triangle to generate binomial coefficients

### Exponentials and logarithms

This chapter covers the basics of exponentials and logarithms, such as:

Understanding and using exponential functions and their graphs

Solving exponential equations using logarithms or change of base formula

Understanding and using logarithmic functions and their graphs

Solving logarithmic equations using exponentials or laws of logarithms

Using laws of logarithms to simplify or expand expressions involving logarithms

Finding the value of logarithms using a calculator or tables

Using natural logarithms (ln) and exponential functions (e^x)

### Trigonometry

This chapter covers the basics of trigonometry, such as:

Understanding and using trigonometric ratios (sine, cosine, tangent) in right-angled triangles

Finding angles or sides in right-angled triangles using trigonometry

Using Pythagoras' theorem to find missing sides in right-angled triangles

Understanding and using trigonometric ratios (secant, cosecant, cotangent) in any triangles

Finding angles or sides in any triangles using sine rule or cosine rule

Finding the area of any triangle using half-angle formula

Understanding and using trigonometric identities (such as sin^2 x + cos^2 x = 1)

Simplifying or proving trigonometric expressions using identities

Solving trigonometric equations using identities or inverse functions

Understanding and using radians as a measure of angles

Converting between degrees and radians

Finding arc length, sector area, or segment area using radians

### Differentiation Differentiation

This chapter covers the basics of differentiation, such as:

Understanding and using the concept of derivative as the rate of change of a function

Finding the derivative of a function using the limit definition or the rules of differentiation

Finding the derivative of various types of functions, such as polynomial, trigonometric, exponential, logarithmic, etc.

Using the chain rule, product rule, and quotient rule to differentiate composite or complex functions

Using differentiation to find the gradient, tangent, normal, or stationary point of a curve

Using differentiation to find the maximum or minimum value of a function or a real-world problem

Using differentiation to find the rate of change or the rate of approximation of a function or a real-world problem

### Integration

This chapter covers the basics of integration, such as:

Understanding and using the concept of integral as the reverse process of differentiation

Finding the indefinite integral of a function using the rules of integration

Finding the indefinite integral of various types of functions, such as polynomial, trigonometric, exponential, logarithmic, etc.

Using the substitution method or the integration by parts method to integrate complex functions

Finding the definite integral of a function using the fundamental theorem of calculus

Using integration to find the area under a curve or between two curves

Using integration to find the volume of revolution of a curve around an axis

### Numerical methods

This chapter covers the basics of numerical methods, such as:

Understanding and using numerical methods to find approximate solutions to equations or problems that cannot be solved analytically

Using the bisection method or the linear interpolation method to find roots of equations

Using the Newton-Raphson method or the secant method to find roots of equations more efficiently

Using numerical methods to solve simultaneous equations or differential equations

Using numerical methods to find approximate values of integrals or derivatives

Evaluating the accuracy and reliability of numerical methods and their results

### Vectors

This chapter covers the basics of vectors, such as:

Understanding and using vectors to represent magnitude and direction

Writing vectors in column form or component form

Adding, subtracting, multiplying, and dividing vectors

Finding the modulus or length of a vector

Finding the unit vector or direction vector of a vector

Finding the angle between two vectors

Finding the scalar product or dot product of two vectors

Finding the vector product or cross product of two vectors

Using vectors to model and solve geometric problems involving lines, planes, triangles, etc.

#### How to use core maths for advanced level PDF 20 effectively This book is designed to help you learn and practice core maths for advanced level in a systematic and efficient way. Here are some tips and strategies for using this book effectively: - Read each chapter carefully and try to understand the concepts and methods explained in it. - Work through each example and check your understanding by comparing your solution with the given solution. - Attempt each exercise and check your answers with the given answers. If you get stuck or make a mistake, try to identify where you went wrong and how you can improve. - Review each chapter periodically and revise the key points and formulas. - Use the revision exercises at the end of the book to test your knowledge and skills on all topics covered in the book. - Seek help from your teacher or tutor if you have any doubts or difficulties. Where to get core maths for advanced level PDF 20 If you are interested in getting this book, you have several options: - You can download it for free from this link: https://www.pdfdrive.com/core-maths-for-advanced-level-e158019.html - You can buy it online from Amazon or other e-commerce platforms: https://www.amazon.com/Core-Maths-Advanced-Level-Bostock/dp/0748755098 - You can borrow it from your school or local library: https://www.worldcat.org/title/core-maths-for-advanced-level/oclc/59414464 Conclusion Core maths for advanced level is a vital subject that can help you achieve your academic and career goals. Core Maths for Advanced Level PDF 20 is a great book that can help you learn and master core maths in a comprehensive and accessible way. It covers all the essential topics and concepts that you need to know for your A-level examinations. It also provides clear explanations, worked examples, exercises, answers, and revision exercises to help you practice and improve your skills. Whether you are studying core maths for advanced level for the first time or revising it for your exams, this book can be a valuable resource for you. FAQs

Q: What is the difference between core maths and further maths for advanced level? A: Core maths is the compulsory part of the A-level mathematics course that covers the basic topics and skills that are required for all students. Further maths is the optional part of the A-level mathematics course that covers more advanced and specialized topics and skills that are suitable for students who want to pursue mathematics or related subjects at a higher level. Q: How many hours should I spend on studying core maths for advanced level per week? A: There is no definitive answer to this question, as it depends on your individual goals, abilities, and preferences. However, a general guideline is to spend at least 4 to 6 hours per week on studying core maths for advanced level, in addition to your regular classes. You should also allocate some time for revision and practice before your exams. Q: What are some other books or resources that can help me with core maths for advanced level? A: There are many other books or resources that can help you with core maths for advanced level, such as: - Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Textbook + e-book by Greg Attwood et al. - Cambridge International AS & A Level Mathematics: Pure Mathematics 1 Coursebook by Sophie Goldie et al. - Oxford A Level Mathematics for Edexcel: AS Pure Mathematics A by David Bowles et al. - Khan Academy: https://www.khanacademy.org/math/algebra2 - Mathplanet: https://www.mathplanet.com/education/algebra-2 - Mathsisfun: https://www.mathsisfun.com/algebra/index.html 71b2f0854b