Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

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Jenni

06/04/2023

Maths

GCSE AQA Further Maths Differentiation

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Maths

Algebra

Using and interpreting graphs

Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

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AQA Further Maths GCSE Differentiation is a crucial topic for students preparing for their exams. This summary covers key concepts, formulas, and examples to help with AQA Further Maths GCSE revision.

Differentiation is the process of finding the gradient function of a curve. It's essential for solving various problems in Further Maths GCSE topics and appears frequently in AQA Further Maths GCSE past papers.

Key points:

The gradient function is written as f'(x) or dy/dx
Differentiation of a constant is always zero
Special cases where standard differentiation rules don't apply
Practical applications in finding gradients at specific points

...

06/04/2023

426

Differentiation
y=x² dy = nx²
da
dy
You CANT do dx when...
→xis in brackets
→x is in denominator
→x is in root form
The gradient function of

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Advanced Differentiation Techniques and Applications

This section delves deeper into Differentiation Further Maths GCSE concepts, providing more complex examples and applications.

Highlight: Differentiation of a constant is always zero. d/dx $constant$ = 0

Let's explore a comprehensive example that demonstrates various aspects of differentiation:

a) For f $x$ = 4x^2 - 8x + 3, find the gradient when x = 3

First, we find the gradient function: f' $x$ = 8x - 8

Then, we substitute x = 3: f' $3$ = 8 $3$ - 8 = 24 - 8 = 16

Example: The gradient at x = 3 is 16

b) Find the coordinates of the point on the graph of y = f $x$ where the gradient is 8

We set the gradient function equal to 8: 8x - 8 = 8 Solving this, we get x = 2

To find y, we substitute x = 2 into the original function: f $2$ = 4 $2$ ^2 - 8 $2$ + 3 = 16 - 16 + 3 = 3

Example: The coordinates are $2, 3$

c) Find the gradient of y = f $x$ at the points where the curve meets the line y = 4x - 5

We set the original function equal to the line equation: 4x^2 - 8x + 3 = 4x - 5

Solving this quadratic equation, we get x = 1 or x = 2

Now, we can find the gradients at these points using the gradient function: At x = 1: f' $1$ = 8 $1$ - 8 = 0 At x = 2: f' $2$ = 8 $2$ - 8 = 8

These examples demonstrate how to apply differentiation in various scenarios, which is crucial for AQA Further Maths GCSE past papers and Further Maths GCSE practice papers.

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Subjects

Maths

Algebra

Using and interpreting graphs

Maths

•

426

•

6 Apr 2023

•

2 pages

Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

Jenni

@jennii007

Differentiation is the process of finding the gradient... Show more

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Advanced Differentiation Techniques and Applications

This section delves deeper into Differentiation Further Maths GCSE concepts, providing more complex examples and applications.

Highlight: Differentiation of a constant is always zero. d/dx $constant$ = 0

Let's explore a comprehensive example that demonstrates various aspects of differentiation:

a) For f $x$ = 4x^2 - 8x + 3, find the gradient when x = 3

First, we find the gradient function: f' $x$ = 8x - 8

Then, we substitute x = 3: f' $3$ = 8 $3$ - 8 = 24 - 8 = 16

Example: The gradient at x = 3 is 16

b) Find the coordinates of the point on the graph of y = f $x$ where the gradient is 8

We set the gradient function equal to 8: 8x - 8 = 8 Solving this, we get x = 2

To find y, we substitute x = 2 into the original function: f $2$ = 4 $2$ ^2 - 8 $2$ + 3 = 16 - 16 + 3 = 3

Example: The coordinates are $2, 3$

c) Find the gradient of y = f $x$ at the points where the curve meets the line y = 4x - 5

We set the original function equal to the line equation: 4x^2 - 8x + 3 = 4x - 5

Solving this quadratic equation, we get x = 1 or x = 2

Now, we can find the gradients at these points using the gradient function: At x = 1: f' $1$ = 8 $1$ - 8 = 0 At x = 2: f' $2$ = 8 $2$ - 8 = 8

These examples demonstrate how to apply differentiation in various scenarios, which is crucial for AQA Further Maths GCSE past papers and Further Maths GCSE practice papers.

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Differentiation Basics and Rules

Differentiation is a fundamental concept in AQA GCSE Further Maths. It involves finding the gradient function of a curve, which is crucial for various mathematical applications.

The gradient function of a curve y=f $x$ is written as f' $x$ or dy/dx. This function allows us to find the gradient of the curve for any value of x.

Highlight: You cannot directly differentiate when x is in brackets, in the denominator, or in root form.

For the basic form y=x^n, the differentiation rule is:

dy/dx = nx^ $n-1$

Example: For f $x$ = x^3, the gradient function f' $x$ = 3x^2

An alternative method for finding the gradient function involves using the limit definition:

f' $x$ = lim $h→0$ $f(x+h$ - f $x$ ) / h

Example: For f $x$ = 3x^2, we can find f' $x$ by calculating: f' $x$ = lim $h→0$ $3(x+h$ ^2 - 3x^2) / h After simplification, we get f' $x$ = 6x

This page provides essential information for AQA Further Maths GCSE Differentiation questions and is crucial for AQA Further Maths GCSE revision.

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Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

Advanced Differentiation Techniques and Applications

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Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

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I love this app ❤️ I actually use it every time I study.

Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

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Advanced Differentiation Techniques and Applications

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Differentiation Basics and Rules

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