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

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

Form 8 Christmas Revision

Please download the Christmas revision document available at the following link:

http://sdrv.ms/1c8Sc7r




 
Please review the work we have done this year and on here.
Have a great Christmas and New Year!
Best wishes,
Mr. Healy

Fractions, Decimal and Percentages

Objectives:

• Convert fractions to decimals

• Change decimals to fractions

• Putting fractions in order -converting to decimals -common denominators

• Calculating a fraction of a quantity

• Mixed numbers

• Multiplying and dividing by fractions

• Percentages

Fractions Review

Decimals

Percentages

Homework

Exercise 15.1A	Fractions to Decimals
	Q3
	Q6
Exercise 15.1B	Decimals to fractions
	Q3, 4
Exercise 15.1 C	Ordering
Q 1, 2	Q 3, 4
Exercise 15.2A	Mixed Numbers
	Q 4, 5, 6
Exercise 15.2B	+ & -
	Q 4, 6
Exercise 15.2C	x & ÷
	Q 3, 4 Q 9, 10

Exercise 15.3A	Percentages
	Q 3, 4
Exercise 15.3 B
	Q 3, 4
	Q 9, 10

Statistical Calculations

Objectives:

• Calculating the mean, median, mode and range for statistical data.

• Know which is the best to use.

Review of mean, median and mode:

Large and small values

You need to know that very large or very small figures in a list of data can affect the mean and the range.
The median and the mode are less affected.

Homework:

Page 112  Ex. 12.1   Q:1

Page 115  Ex  12,2   Q:2

 

Letters as numbers and solving equations

Objectives:

• Link numbers to letters. 

• Solve equations: know that what we do on one side of the equation we must do on the other.

• Write mathematical sentences.

Linking numbers to letters.

Try the quiz:

Order of operations, Indices

Order of Operations:

 

Order of operations with numbers and letters:

What is the meaning of "Like and unlike terms"?

Solving Equations: