Responsive WordPress Themes are very popular lately. But what is a responsive wordpress theme really? Let’s take a closer look at responsive wordpress themes.

The way we use computers and the web has changed. But mobile devices are much smaller devices when compared to regular desktops. But they still provide a lot of features for us to us. One of them is to be able to use internet. As of mobile internet usage grows it brought a new confusion. What happens when a website reviewed on a mobile device?

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The first answer was navigating the entire web page. But because of mobile devices are so small it was hard to navigate a website. You’d be have to keep scrolling left to right and top to bottom. And ofcourse that wasn’t user friendly at all. And web designers were not really liking it either. Then the new well known trend has begun. If the web page is too big to be seen on mobile, let’s make it smaller for mobile.

 



A function is called rational function if it can be expressed as (f(x)=frac { p(x) }{ q(x) } ) where P and Q are functions of the variable x.

This section is focussing on how to sketch the graphs of rational functions.

1.Vertical Asymptote

Consider a function of the form (f(x)=frac { 1 }{ x-c } )

The graph of the function f(x) has a vertical asymptote  when the denominator function takes the value 0.

The vertical asymptote of (f(x)=frac { 1 }{ x-c } ) is at some values of x where the denominator (x-c)=0.

Therefore This function f(x) has vertical asymptote at x = c.

Example:

Consider the function(f(x)=frac { 1 }{ x-3 } )

This function has vertical asymptote where the denominator x – 3 = 0.

Therefore the function f(x) has vertical asymptote at x = 3 and the equation of vertical asymptote is x = 3.

From the interactive diagram given below, use the slider to change the values of ‘c’  in the function (f(x)=frac { 1 }{ x-c } )

2. Horizontal Asymptote

Consider a rational function of the form (f(x)=a+frac { b }{ x-c } )

The graph of f(x) has horizontal asymptote at y = a and the equation of horizontal asymptote is y = a.

Also as seen the the prevision section the graph f(x) has a vertical asymptote at x =c;

Example:

Consider a rational function (f(x)=3+frac { b }{ x-2 } )

This function has vertical asymptote x = 2 and the horizontal asymptote y = 3

From the interactive diagram given below, use the slider to change the values of ‘ a and c’  in the function(f(x)=a+frac { b }{ x-c } )

From the interactive diagram given below, use the slider to change the values of ‘ a ,b and c’  in the function(f(x)=a+frac { b }{ x-c } )



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision



Property 1 :  Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.
Property2 :  Angles subtended by an arc in the same segment of a circle
Property 3 :  The opposite angles in a cyclic quadrilateral add up to 180 degrees- the angles are supplementary.
Property4 :  The angle in a semi-circle is a right angle.
Property 5:   The angle between a tangent and the radius drawn to the point of contact is 90 degrees.
Property6 :  From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Theorem 1 :
Angle subtended at the Centre of a circle is twice the angle subtended at the circumference.

Theorem 4 :
The angle in a semi-circle is a right angle.

Theorem 5:
The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

 

Theorem 6 :
From any point outside a circle just two tangents to the circle may be drawn and they are of equal length.

Problem Solving

Problem: 1

ABCD is a cyclic quadrilateral. Sides AB and DC are produced or extended to meet at E. Sides DA and CB are produced to F.
If angle AFB is 30 degrees and angle BEC is 20 degrees, find all angles of quadrilateral ABCD.

Solution :

The diagram for the questions is give below.

Use the interactive graph given below to see the angles.

Skill builder questions

Practice worksheet – 1 Circle Theorem worksheet 1 of 4
Practice worksheet – 2 Circle Theorem worksheet 2 of 4
Practice worksheet – 3 Circle Theorem worksheet 3 of 4
Circle theorems – Revision


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