Last updated on Sep 21, 2026

Circles and Semicircles (HSC SSCE Mathematics Advanced): Quizzes

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Circles and Semicircles

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What is the equation of a circle with centre at $(0, 0)$ and radius $r = 8$ ?

$x^2 + y^2 = 64$

What is the radius of the circle $x^2 + y^2 = 81$ ?

$r = 9$

Does the point $(5, 12)$ lie on the circle $x^2 + y^2 = 169$ ?

Yes, gives $169 = 169$

What are the y-intercepts of the circle $x^2 + y^2 = 36$ ?

$(0, 6)$ and $(0, -6)$

A circle centred at the origin passes through $(0, 9)$ . What is its equation?

$x^2 + y^2 = 81$

Which semicircle does $y = sqrt{49 - x^2}$ represent?

Upper semicircle

Which semicircle does $x = -sqrt{25 - y^2}$ represent?

Left semicircle

What is the domain of $y = sqrt{16 - x^2}$ ?

$[-4, 4]$

What is the range of $x = sqrt{9 - y^2}$ ?

$[-3, 3]$

What does a positive square root indicate for a semicircle equation?

Upper or right semicircle

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Circles and Semicircles (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What is the equation of a circle with centre at (0,0)(0, 0)(0,0) and radius r=8r = 8r=8?

What is the radius of the circle x2+y2=81x^2 + y^2 = 81x2+y2=81?

Does the point (5,12)(5, 12)(5,12) lie on the circle x2+y2=169x^2 + y^2 = 169x2+y2=169?

What are the y-intercepts of the circle x2+y2=36x^2 + y^2 = 36x2+y2=36?

A circle centred at the origin passes through (0,9)(0, 9)(0,9). What is its equation?

Which semicircle does y=sqrt49−x2y = sqrt{49 - x^2}y=sqrt49−x2 represent?

Which semicircle does x=−sqrt25−y2x = -sqrt{25 - y^2}x=−sqrt25−y2 represent?

What is the domain of y=sqrt16−x2y = sqrt{16 - x^2}y=sqrt16−x2?

What is the range of x=sqrt9−y2x = sqrt{9 - y^2}x=sqrt9−y2?

What does a positive square root indicate for a semicircle equation?

Explore HSC SSCE Mathematics Advanced Revision Notes 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 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 is the equation of a circle with centre at $(0, 0)$ and radius $r = 8$ ?

What is the radius of the circle $x^2 + y^2 = 81$ ?

Does the point $(5, 12)$ lie on the circle $x^2 + y^2 = 169$ ?

What are the y-intercepts of the circle $x^2 + y^2 = 36$ ?

A circle centred at the origin passes through $(0, 9)$ . What is its equation?

Which semicircle does $y = sqrt{49 - x^2}$ represent?

Which semicircle does $x = -sqrt{25 - y^2}$ represent?

What is the domain of $y = sqrt{16 - x^2}$ ?

What is the range of $x = sqrt{9 - y^2}$ ?