Last updated on Oct 23, 2026

First Principles Differentiation (AQA A-Level Mathematics): Quizzes

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First Principles Differentiation

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In first principles, what happens to the chord as $h \to 0$ ?

It becomes a tangent

What is the gradient of $y = x^2$ ?

$2x$

What is the first principles formula for the gradient of $F(x)$ ?

$\lim_{h \to 0} \frac{F(x+h) - F(x)}{h}$

Using first principles, what is the gradient of $y = x^4$ ?

$4x^3$

For $F(x) = x^n$ where $n \in \mathbb{R}$ , what is the gradient?

$nx^{n-1}$

Which is NOT a name for the gradient formula?

The integral

How is $\frac{dy}{dx}$ pronounced?

dy by dx

In $f'(x)$ , what does the number of dashes indicate?

Times differentiated

Using first principles, $\frac{dy}{dx}$ for $y = x^2 + 2x$ is:

$2x + 2$

For $y = 3x^2 + 2x$ , what is $\frac{dy}{dx}$ when $x = 1$ ?

$8$

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

Explore AQA A-Level Mathematics Exam Questions by Topics

Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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