About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Master the Difference Quotient: Key to Calculus Success

GCSE Maths: Master Essential Skills for Exam Success

Numbers and Relations

Place value

Comparing and ordering numbers

Comparing Integers

Comparing Numbers

Comparing Fractions

Rounding numbers

Rounding Decimals

Rounding Integers — Up to 9999

Adding and Subtracting Integers

Introduction to integer addition

Adding 1-digit integers

Opposite Integers — Up to 10

Adding integers

Adding 2-digit integers

Introduction to integer subtraction

Integer Subtraction — Missing Value

Subtracting 1-digit integers

Subtracting integers

Subtracting 2-digit integers

Application of integer operations

Application of Integer Operations – Word Problem

Application of Integer Operations  – Word Problem

Multiplying and Dividing Integers

auto-gen

Understanding integer multiplication

Multiplying 1-digit Integers

Multiplying 1-digit integers Mixed Sign

Multiplying integers

Multiplying 2-Digit Integers

Multiplying 1 and 2 Digit Integers

Understanding integer division

Dividing by 1-Digit Integers

Dividing by 1-Digit Integers Mixed Sign

Dividing integers

Dividing by 2-Digit Integers

Dividing by 2-Digit Integers Mixed Sign

Applications of integer operations

Multiple Integer Operations

Three Step Integer Operations Combined Multiply Divid

Three Step Integer Operations Divide Add Or Minus Multiply

Three Step Integer Operations Divide Add Or Minus

Three Step Integer Operations Multiply Add Minus Divide

Three Step Integer Operations Multiply Add Or Minus

Operations with decimals

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (BIDMAS)

Mixed Operations with Decimals

Mixed Operations

Identify the Order of Operations

Order of Operations — Word Problem

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Adding and Subtracting Fractions

Using models to add and subtract fractions

Add Fractions With Models

Subtract Fractions With Models

Adding fractions with like denominators

Adding Fractions — with like denominators — 3-digit without simplifying

Adding Fractions — with like denominators — 3-digit

Adding Fractions — Word problem: baking

Add fractions with like denominator

Adding Fractions — with like denominators — 1-digit

Adding Fractions — with like denominators — 2-digit

Adding Fractions — Word problem: beads

Subtracting fractions with like denominators 

Subtract fractions with like denominator

Subtracting Fractions — with like denominators — 2-digit

Subtracting Fractions — with like denominators — Larger 2-digit

Subtracting Fractions — with like denominators — 3 digit

Subtracting fractions — Word problem: competition

Subtracting fractions — Word problem: snack

Adding and subtracting fractions with unlike denominators

Adding and Subtracting Fractions — Find the lowest common denominator (LCD)

Adding and Subtracting Fractions — Find the LCD and evaluate

Add fractions with unlike denominator

Subtract fractions with unlike denominator

Adding and Subtracting Fractions — Word problem: cargo ship

Adding Fractions — with unlike denominators

Subtracting Fractions — with unlike denominators

Adding and subtracting mixed numbers

Adding Mixed Numbers — Word Problem

Subtracting Mixed Numbers — Word Problem

Add mixed fractions with like denominator

Add mixed fractions with unlike denominator

Multiplying and Dividing Fractions

Multiplying fractions and whole numbers

Multiply a fraction with a whole number

Multiplying Fractions — with whole numbers — 1 digit

Multiplying Fractions — with whole numbers — 2 digits

Application of Multiplying Fractions and Whole Numbers – Word Problems

Dividing fractions with whole numbers

Divide a fraction by a whole number

Divide a Fraction by a Whole Number

Divide a Fraction by a Whole Number Number RHS

Multiplying proper fractions

Multiply Proper Fractions — 1 Digit Fractions

Multiplying improper fractions and mixed numbers

Multiply Mixed Numbers

Dividing fractions and mixed numbers

Divide Fractions and Mixed Numbers – Word Problem

Dividing Mixed numbers

Dividing Mixed Numbers

Applications of fraction operations

Fraction Operations

Percents

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Representing percents

Representing Percents

Representing Percents — Word Problem

Representing Percents Two Graphs – Word Problem

Percents, fractions, and decimals

Conversion — Decimal to Fraction

Conversion — Decimal to Percent

Conversion — Fraction to Decimal

Conversion — Fraction to Percent

Conversion — Percent to Decimal

Conversion — Percent to Fraction

Percents – Word Problem

Convert a Decimal to a Fraction

Convert a Decimal to a Percent

Convert a Fraction to a Decimal

Convert a Fraction to a Percent

Convert a Percent  to a Decimal

Convert a Percent to a Fraction

Percents Fractions And Decimals – Word Problem

Percent of a number

Percent of a Number

percent of a number – Word Problem

Percent of a Number  Fraction Percent

Percent of a Number Integer Percent 

Percent of a number number With Decimal Percent 

Percent of a Number  Three Digits Number Percent

Adding and multiplying percents

Add and Multiply Percents — Word Problem

Add and Multiply Percents – Word Problem

Ratios, Rates, and Proportions

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Get better marks with our complete help for GCSE Maths! Our maths tutors have you all covered - whether it&apos;s for <a href="http://qualifications.pearson.com/en/qualifications/edexcel-gcses/mathematics-2015.html">Edexcel</a> (Pearson), <a href="http://www.aqa.org.uk/subjects/mathematics/gcse">AQA</a>, <a href="https://www.ocr.org.uk/qualifications/by-subject/mathematics/">OCR</a> or <a href="http://www.wjec.co.uk/qualifications/mathematics/mathematics-gcse/">WJEC</a>.

Aligning with the new GCSE maths 9 - 1 specifications of all exam boards, our comprehensive lessons cover content in all six topic areas including Number; Algebra; Ratio, proportion and rates of change; Geometry and measures; Probability; and Statistics. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest gcse maths questions. Then, strengthen your understanding with tons of GCSE maths practice questions.

All our lessons are taught by experienced maths teachers. Let&apos;s finish your maths revision in no time, and get a 9 in that GCSE maths exam.

GCSE Maths

math

<h2>Is GCSE Maths Hard?</h2>
If you&apos;re concerned about studying GCSE maths, you&apos;re not alone. Thousands of students just like you see maths as a difficult thing to learn and can struggle to grasp some of the more complex areas of the subject. Though it does seem like a daunting challenge, maths isn&apos;t that hard to get your head around once you have a firm understanding of the basics. Remember, you&apos;re not expected to know everything from day one. Learning mathematics will take time and in doing so, will greatly improve your chances of getting into college/university.
If you want GCSE maths help or would like additional GCSE revision materials for your GCSE maths quiz, our online video tutorials will walk you through all the relevant topics that are bound to come up in your end of year exams. We offer step-by-step guides for the following popular topics:
<ul type="disc">
<li>Circle Theorem</li>
<li>Standard Form</li>
<li>Law of Indices</li>
<li>Bearings</li>
<li>Statistics</li>
<li>Algebraic Expressions</li>
<li>Vectors</li>
</ul>
Our GCSE maths tutorial videos will show you easy to understand solutions to even the hardest GCSE maths test questions. Furthermore, you can test your knowledge using our GCSE maths practice materials. The content we deliver to you has been designed by experienced GCSE maths teachers and we have worked to ensure that we cover all the topics you&apos;d find in current CGP maths books.
We understand that different schools and colleges will follow different awarding bodies. With that in mind, we have constructed our content to cover the following:
<ul type="disc">
<li>Edexcel GCSE Maths</li>
<li>AQA Maths GCSE</li>
<li>OCR GCSE Maths</li>
<li>WJEC GCSE Maths</li>
</ul>
We also understand and appreciate that every learner learns differently. To that end, we have decided to take a "from the ground up" approach that starts from the basics, assumes no prior knowledge, and covers all areas of GCSE maths. Each area of our content has been designed to seamlessly flow from one topic to the next, allowing you to build off what you&apos;ve just learned, introducing more complex elements when you&apos;re ready.
As a subscriber to our online tutorial service, you&apos;ll have direct access to all the GCSE maths videos on our site. Regardless of whether you&apos;re looking for topics relating to GCSE maths foundation or higher, we&apos;ve got you covered.
If you&apos;re currently in school and studying GCSE maths, or you&apos;re a returning student about to sit a retake exam, <a href="https://www.studypug.com/uk/">StudyPug</a> can help. We have resources that can help you with your GCSE maths exam prep and your GCSE maths homework. No prior knowledge is needed and you only study the content that&apos;s relevant to you. There&apos;s no need to go over what you already know unless you want to.
If you&apos;re a parent with a child studying GCSE maths, our platform can greatly reduce the anxiety associated with revising for their exams. Check out our blog for more <a href="https://www.studypug.com/blog/5-simple-tricks-parents-use-to-ease-their-kids-maths-anxiety/">information on anxiety and how you can help them combat it</a>.

<h2>How to Revise for GCSE Maths?</h2>
When it comes to performing well in your GCSE maths test, you should revise, revise, revise! The best way to learn is with repetition. Take what you&apos;ve been taught in the classroom and go over it at home. Give yourself some study time outside of school hours and utilize a platform like StudyPug to help you along the way. We have GCSE maths revision materials and practice tests to help you highlight key areas to improve on. Taking the time to use these tools will help you to digest the information and more importantly, to retain it. It can also make a dramatic difference to your performance in class and in your exams.
Understandably, getting yourself in the mood to study can be difficult. If it&apos;s hard for you to stay focused in class or if you find it difficult or boring to work from a textbook, StudyPug may just be what you&apos;re looking for. We offer an extensive collection of fun and easy online revision aides that cover the same GCSE maths questions that can be found in those boring maths books.
Our easy practice GCSE maths courses offer you 24/7 help and as they&apos;re delivered via a video format, you can pause, rewind, or fast-forward the info, allowing you to skip content that&apos;s not relevant and learn at your own pace. We find that a lot of our students prefer the video format as the content is delivered in a conversational way that&apos;s easier to follow.
We want to make the learning experience more enjoyable for you. To do that, we&apos;ve made an effort to ensure that the content being delivered speaks to you. Our step-by-step examples have been crafted by maths teachers who know how to breakdown the complex language of maths into more manageable pieces of information.
Regardless of the subject area you need help with, we have the exam solutions for you and we&apos;re confident our platform will help you prepare for your upcoming GCSE maths paper. Outside of exam revision, we also have content that can help you perform better in class. Think of our platform as "GCSE maths made easy", your one stop shop for all your GCSE maths needs.
To get you started, we&apos;re offering a collection of free GCSE maths lessons across the following subject areas:
<ul type="disc">
<li>Pythagorean Theorem & Estimating Square Roots</li>
<li>Multiplying Fractions and Whole Numbers</li>
<li>Enlargements and Reductions with Scale Factors</li>
<li>Solving Linear Equations Using Multiplication and Division</li>
<li>Adding and Subtracting Radicals</li>
<li>And much more!</li>
</ul>
Visit <a href='[[region_textbook.html|{"textbook_key":"uk-gcse-maths"}]]'>StudyPug</a> today and see how we can make a difference to your performance.

<h2>How to Get a 9 in GCSE Maths?</h2>
As mentioned above, revision can dramatically improve your performance in exams and it&apos;s essential if you&apos;re looking to achieve the highest grade possible. Get yourself into the habit of completing maths worksheets and using GCSE maths past papers to sit mock exams. Work within the time limits for each paper and have family members or friends mark them for you. Review your performance and isolate areas of weakness. You can then use that information to build more effective GCSE revision strategies, leaving you with a much more rounded understanding of all areas of GCSE maths. Sit several mock exams and chart your progress to see improvements. Doing this can help raise your confidence and will show that the revision is working!
If you get a few questions wrong in a specific topic, revisit the whole topic, make sure you cover your bases and truly understand the area and where you went wrong. There&apos;s no guarantee that the question will appear on your actual test but a similar one might, so its key that you understand how to answer all questions in the subject area not just the one or two that you got wrong.
Regardless of whether you&apos;re studying foundation or higher maths, it&apos;s important that you can answer questions across all topics in your syllabus. Furthermore, you&apos;ll have to demonstrate that you cannot only answer the question but can show how you arrived at your conclusion. When marking papers, examiners need to see that you can interpret and accurately display a clear understanding of complex mathematical problems. Put simply, you must be able to show your thought process. Don&apos;t just give the answer, show how you arrived at the solution. You could potentially receive additional marks for showing you understanding of the problem and how you attempted to work it out.
Use revision tools like <a href="https://www.studypug.com/uk/">StudyPug</a> to help you. As your virtual GCSE maths tutor, we have 1000s of lessons online to help you study maths. Our videos cover every aspect of GCSE maths so if you&apos;re struggling with the Pythagorean theorem, need help with quadratics, or anything else, we&apos;ve got the content to help!

https://dmn92m25mtw4z.cloudfront.net/img/textbook/uk/textbook-GCSE-maths.png

Mastering the Difference Quotient: Your Gateway to Calculus

What You'll Learn

Recognize the difference quotient as a form of the slope formula

Apply the formula f(x+h) - f(x) over h to find rates of change

Evaluate difference quotients for linear, polynomial, rational, and radical functions

Simplify complex expressions by factoring and canceling common terms

Use algebraic techniques like LCD and conjugate multiplication to handle fractions and roots

What You'll Practice

Finding difference quotients for linear and quadratic functions

Simplifying difference quotients of cubic polynomials

Working with rational functions and eliminating nested fractions

Applying conjugate multiplication to simplify radical expressions

Why This Matters

This Unit Includes

8 Video lessons

Practice exercises

Learning resources

Skills

Difference Quotient

Slope Formula

Function Notation

Polynomial Functions

Rational Functions

Radical Functions

Algebraic Simplification

Factoring