The Circle

 

New Topic: The Circle

By the end of this topic you will:

• know that the equation of the circle centre (a,b) and radius r is (x – a)² + (y – b)² = r²

• know that x² + y² + 2gx + 2fy + c = 0 represents a circle centre (–g, –f) and
radius r = √(g² + f² – c), provided g² + f² – c > 0

• be able to determine the equation of a circle

• be able to solve problems with the intersection of a line and a circle,
and a tangent to a circle

• be able to determine whether two circles touch each other

 

Homework: Circles Set2

Due: Monday 7th December

ALL pupils should be able to complete Q1 – 4

MOST pupils should be able to complete Q7

SOME pupils should be able to complete Q6

DO NOT DO Q5

 

Circles Set2 Solutions

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The Circle

New Topic: The Circle, MiA Unit 2 Ch4

By the end of this topic you will:

• know that the equation of the circle centre (a,b) and radius r is (x – a)² + (y – b)² = r²

• know that x² + y² + 2gx + 2fy + c = 0 represents a circle centre (–g, –f) and
radius r = √(g² + f² – c), provided g² + f² – c > 0

• be able to determine the equation of a circle

• be able to solve problems with the intersection of a line and a circle,
and a tangent to a circle

• be able to determine whether two circles touch each other

Homework: Circles Set1

Due: Tuesday 13th January

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The Circle

New Topic: The Circle, MiA Unit 2 Ch4

By the end of this topic you will:

• know that the equation of the circle centre (a,b) and radius r is (x – a)² + (y – b)² = r²

• know that x² + y² + 2gx + 2fy + c = 0 represents a circle centre (–g, –f) and
radius r = √(g² + f² – c), provided g² + f² – c > 0

• be able to determine the equation of a circle

• be able to solve problems with the intersection of a line and a circle,
and a tangent to a circle

• be able to determine whether two circles touch each other

Homework: Circles Set1

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Circles 2 – Arcs & Sectors

Having investigated the relationships between the radius, diameter, circumference and area of a circle, I can apply my knowledge to solve related problems.  MTH 4-16b

In this topic we will extend our knowledge of the circle by learning how to calculate the length of an arc of a circle and calculate the area of any sector of a circle given the angle at the centre.  We will use our knowledge to solve problems including finding the angle at the centre given an arc length or sector area.

Homework: Arcs & Sectors

Task 1: Find the minor arc length for (c), (d) and (e), the sector area OAB for (f), (g) and (h).

Task 2: In your group solve the allocated problem, Q3, Q4 or Q5, and be prepared to present your solution to the class on the whiteboard.

Due: Thursday 12th September

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Circles

In this topic you will learn how to:

• find the length of an arc of a circle
• find the area of a sector of a circle
• calculate lengths/angles using the relationship between tangent and radius
• use the interdependence of the centre, bisector of a chord and a perpendicular to a chord to solve problems

Class exercises: Textbook p59-77

Additional support:  Int2 Unit 1 – Circles

Homework: Outcome 1.5 – Circles – Due date TBA

If you have missed any of the topic or would like extra explanation and practice please look at these revision notes from the Maths4Scotland Int2 website:

Arcs & Sectors

 

Please comment below if you have any questions about the homework exercise or the topic.

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The Circle

New Topic: Compound Angle Formulae, MiA Unit 2 Ch3

By the end of this topic you will:

• know that the equation of the circle centre (a,b) and radius r is (x – a)² + (y – b)² = r²

• know that x² + y² + 2gx + 2fy + c = 0 represents a circle centre (–g, –f) and
radius r = √(g² + f² – c), provided g² + f² – c > 0

• be able to determine the equation of a circle

• be able to solve problems with the intersection of a line and a circle,
and a tangent to a circle

• be able to determine whether two circles touch each other