BestMaths Online

Coordinates on Maps

Maps often use a grid or system of coordinates to fix the position of a place on a map.

On this map the approximate locations of the three places can be given as: Northtown B10 Landville A11 Hare's Rocks B11

Coordinates in Mathematics

In mathematics, the position of points can be given much more accurately.

Two number lines are drawn at right angles. This grid is called a number plane or a Cartesian graph.

The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The x-axis and the y-axis cross at the origin, O A point is given by a pair of coordinates (x, y). Coordinates are sometimes called ordered pairs. The first number is the position along the x-axis. The second number is the position along the y-axis. e.g. Point A is given by (3, 5) Point B is given by (-3, -2)

Sequences 

In mathematics, numbers are often arranged in a sequence.
Often a sequence follows a rule or pattern. Each number in a sequence is called a term.

Sequence − Example One
Some sequences are obvious: 2, 4, 6, 8, 10... This is the sequence of EVEN numbers.
To continue writing the sequence simply keep adding 2.

Comparing this sequence to the set of counting numbers N = {1, 2, 3, 4..}

The sequence can be shown as a graph:

The formula for this pattern is 2n. The next term, the sixth, would be 2 × 6 = 12

Sequence − Example Two
The sequence 1, 4, 7, 10, 13... is the sequence starting at 1 with three added each time.
To continue writing the sequence simply keep adding 3.

Comparing this sequence to the set of counting numbers {1, 2, 3, 4..}

The sequence can be shown as a graph:

The formula for this pattern is 3n − 2 . The next term, the sixth, would be 3 × 6 − 2 =16

Sequence − Example Three
Another kind of sequence is1, 4, 9, 16, 25... This is the sequence of square numbers.
To continue writing the sequence keep squaring the whole numbers, 6² = 36 etc.

Comparing this sequence to the set of counting numbers {1, 2, 3, 4..}

The sequence can be shown as a graph:

The formula for this pattern is n² . The next term, the sixth, would be n²= 36

 

Patterns

Sequences can also be of diagrams or geometric patterns.
For example:

Graphs

As well as graphs for sequences, there are many other types of graphs.
All graphs must have certain features:

• A title
• Labelled axis indicating units used
• Even scales

Line Graphs

Line graphs show how quantities are changing. Below are four examples:

Statistical Graphs