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

Areas and volumes

Objectives:

• Area of rectangles and triangles

• Area of parallelograms and trapeziums

• Volume of cuboids

• Parts of a circle, circumference and area.

 

Area of a rectangle:

 

Area of a triangle:

More: Area of a triangle inside a rectangle

Area of a parallelogram:

Area of a trapezium:

(Note: this shape is also known as a trapezoid, but for your exam just use trapezium!)

Cuboids

A cuboid is a box-shaped object. Click the image below for more information.

V = l × w × h

Nets

A 'net' is the shape you get when you cut along the edges of a three dimensional object and lay it out flat.

 

Parts of a circle:

Copy the picture below, label the green and blue sections:

Answer is here.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Circle: Area and circumference

Homework:

P162  Ex 18.1     Q 3

P165  Ex 18.2A  Q3

P165  Ex 18.2B  Q 1b, Q2b

P170  Ex 18.3B  Q 1, 2

P172  Ex 18.4     Q 3

P174  Ex 18.5A   Q 1 - 9

P176  Ex 18.5B  Q 1c, 1d, 2c, 2d.

P177  Ex 18.5C  d, e

Similar Triangles and Sine, Cosine, Tangent.

• Identify similar shapes

• Use Sin, Cos and Tan for acute angles

Similarity

Two shapes are Similar if the only difference is size (and possibly the need to turn or flip one around). Information on similar triangles.

See if you can figure out how tall a tree is without having to measure its height:

Right angled triangle ratios

Sine, Cosine and Tangent ratios

Remember:

Sohcahtoa

Soh...	Sine = Opposite / Hypotenuse
...cah...	Cosine = Adjacent / Hypotenuse
...toa	Tangent = Opposite / Adjacent

Click the image below for some extra exercises and further information:

Homework:

P289 Ex1 Q. 6, 11, 13, 16, 17

P293 Ex 2 Q. 17-20

P293 Ex 3 Q. 4, 6, 7, 10, 11, 12

Angle Properties

• Identify: Supplementary, vertically opposite, corresponding and alternate angles.

• Know that angles of a triangle add up to 180°

• Know that the exterior angle of triangle is equal to the sum of the two interior opposite angles.

• Know that angles of a quadrilateral add up to 360°

Supplementary Angles (add to 180°)

 

Vertically Opposite Angles..... are equal

 

Corresponding Angles (look for an 'F' shape)...... are equal

 

Alternate Angles (look for a 'Z' shape)....are equal

Angles of a triangle add up to 180°

A + B + C = 180°

Exterior angle of triangle is equal to the sum of the two interior opposite angles.

C = A + B

Angles of a quadrilateral add up to 360°

80° + 100° + 90° + 90° = 360°

Homework:

P153  Ex 16.4C  Q3-6 

P156  Ex 17.1B  Q4-8

P158  Ex 17.2     Q3, 5, 6

P160  Ex 17.3A  Q3, 4

P160  Ex 17.3B   Q1, 4