Probabilty

Probability means how likely it is that something will happen. For example getting two sixes when you roll a pair of dice (dice is the plural of 'die').

Relative frequency

How often something happens divided by all outcomes.

Circles and Prisms

Circumference of a Circle:

Circumference means the perimeter of a circle

Circumference = 2 × π × Radius

Area = π r²

Prisms

A prism is an object that has the same area all along its length.
 

We can find the volume of a prism by multiplying the area of the base by the length.

Bearings and loci

Objectives 

• Bearings

• Locus from a fixed point

• Constructing a perpendicular bisector

• (to find the locus that is equidistant from two points)

• Locus from a line

• Constructing the bisector of an angle

• (to find the locus that is equidistant from two lines)

Bearings

Locus from a fixed point

A locus means a path. 'Loci' is the plural of locus. It shows us the path or region that a point can travel according to certain rules. 

The locus of all points at a fixed distance from a line.Watch the video here.

The locus of points that are equidistant from two points: Constructing a Perpendicular Bisector

You can find the method by clicking on the image below:

Watch the video.

The locus of all points that are equidistant from two lines: Bisecting an angle

We use this method to find the locus of all points that are equidistant from two lines.

Some real world examples of loci

Watch a video of how loci apply in the real world.

Graphing and Solving Linear Equations

• The equation of a line
• Solving two simultaneous equations using a graph
• Trial and Improvement method to solve an equation

Linear Equations

Solving two simultaneous equations using a graph

Trial and Improvement method to solve an equation

Using this method we 'guess' the first value x and then try other values until we find one that works. Click the image below for an example:

Reflection, Translation, Rotation and Enlargements

Reflection:

Translations

Rotation

Enlargement

Click the image above for more information, watch a video here.

Enlargements

Constructions

- Constructing the perpendicular bisector of a line
- Finding the perpendicular from a point to a line
- Bisecting an angle

Constructing a Perpendicular Bisector

You can find the method by clicking on the image below:

Watch the video.

Bisecting an angle

Angles of Polygons

Interior and Exterior Angles

Exterior Angles of a Polygon
Remember, a polygon is any shape that has 3 or more straight sides (no curves).

Click on the hexagon above to see that:

The exterior angles of any polygon add up to 360°

Interior Angles

90° + 60° + 30° = 180°	80° + 70° + 30° = 180°
It works for this triangle!	Let's tilt a line by 10° ... It still works, because one angle went up by 10°, but the other went down by 10°

The Interior Angles of a Triangle add up to 180° 

Because there are Two Triangles in a Square

The interior angles in this triangle add up to 180° (90°+45°+45°=180°)

... and for this square they add up to 360° ... because the square can be made from two triangles!

Because a pentagon has three triangles, the sum of the interior angles add up to 3x180° = 540°






 In general:

The sum of the interior angles of a polygon that has n sides, is:

(n-2) x 180°

Triangles in a circle:

The triangle drawn on the diameter of a circle is always 

a right angled triangle