Last updated on Sep 20, 2026

Gradient of a Curve (HSC SSCE Mathematics Advanced): Quizzes

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Gradient of a Curve

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What formula calculates the gradient of a line through points $A(x_1, y_1)$ and $B(x_2, y_2)$ ?

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Why can't a single gradient value describe an entire curve?

The steepness changes at different points

What is a tangent to a curve?

A line touching the curve at exactly one point

How is the gradient of a curve at a point defined?

As the gradient of the tangent at that point

What is the gradient of a curve when its tangent is horizontal?

Zero

What is a secant line?

A line through two points on the curve

What is the formula for the gradient of a secant through $P(c, f(c))$ and $Q(c + h, f(c + h))$ ?

$\frac{f(c + h) - f(c)}{h}$

What happens to the secant gradient as $h$ approaches zero?

It approaches the tangent gradient

Which notation represents the derivative of $f(x)$ ?

$f'(x)$

If $f'(x) = 3x + 2$ , what is the gradient of the tangent to $y = f(x)$ at $x = 4$ ?

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Gradient of a Curve (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What formula calculates the gradient of a line through points A(x1,y1)A(x_1, y_1)A(x1​,y1​) and B(x2,y2)B(x_2, y_2)B(x2​,y2​)?

Why can't a single gradient value describe an entire curve?

What is a tangent to a curve?

How is the gradient of a curve at a point defined?

What is the gradient of a curve when its tangent is horizontal?

What is a secant line?

What is the formula for the gradient of a secant through P(c,f(c))P(c, f(c))P(c,f(c)) and Q(c+h,f(c+h))Q(c + h, f(c + h))Q(c+h,f(c+h))?

What happens to the secant gradient as hhh approaches zero?

Which notation represents the derivative of f(x)f(x)f(x)?

If f′(x)=3x+2f'(x) = 3x + 2f′(x)=3x+2, what is the gradient of the tangent to y=f(x)y = f(x)y=f(x) at x=4x = 4x=4?

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Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

What formula calculates the gradient of a line through points $A(x_1, y_1)$ and $B(x_2, y_2)$ ?

What is the formula for the gradient of a secant through $P(c, f(c))$ and $Q(c + h, f(c + h))$ ?

What happens to the secant gradient as $h$ approaches zero?

Which notation represents the derivative of $f(x)$ ?

If $f'(x) = 3x + 2$ , what is the gradient of the tangent to $y = f(x)$ at $x = 4$ ?