Maths Revision: A2: Sequences and linear graphs

What is an example of a general term?

Tn = n2  + 3

What is the nth term?

if it the term is the first in the sequence its nth term is 1, second term is 2 etc. etc. etc.

What tells you which term it is?

Tn- whatever the small n is, is the number that the term is in the sequance

What is a diverging sequance?

if every term is bigger than the last (it is increasing)

What is an oscillating sequance?

if the terms alternate between positive and negative

How can you tell if an oscillating sequance is diverging or not?

if the difference between the terms is increasing

Give an example of this

2, -4, 6, -8, 10, -12

What is a converging sequance?

when each term is smaller than the one before, but will never be will never be equal to 0. get closer and closer to 0.

Give an example of this

1,  1/2, 1/3, 1/4, 1/5

What to look for in a sequance

• does it add by the same number?
• does it add by more each time?
• does it minus by the same number?
• does it minus by more each time?
• does it multiply by the same number?
• does it devide by the same number?
• does it add the two previous terms?
• is it a pattern sequance?
• is it the previous number squared?

How can you put this into a table if they havn't already made a table

put pattern number in the first column and number of ---------

How to figure out the nth term rules:

• Figure out the difference between every term... this is the number before n
• Figure out the first term minus the difference (if its - number it would be for example 2n -3)
• How to find a terms position (n) in a sequance:

1.) write for example if the  term was 23 that you had to figure out the position of  and the rule was 3n- 2  you would write 3n-2=23

2.) cancel down so that you have only n on one side and a number on the other

3.) the number is the position of n

4.) if n is not a whole number and is a decimal it is not in the sequance

What is an arithmetic and linear sequence?

when the difference between each term is the same every time

first row: term number (n)

second row: _n

the _ is the common difference

third row: term

What is the equation for straight line graphs:

y = mx + c

What does m stand for?

the gradient

What does c stand for?

the y-intercept

What tells you where a line would slop upwards or downwards?

m

How?

if m is a positive number then the gradient and line slopes upwards. if m is a negative number then the gradient and line slopes downwards.

vertical line:

you write x = _ (the _ being whatever x always equals)

horisantal line:

you write y = _ (the _ being whatever y always equals)

what does y = x look like?

a diagonal line where the y intercept is 1 and the gradient is also 1. it has a positive gradient therefore the line slopes upwards.

what does y = -x look like?

a diagonal line where the y intercept is 1 and the gradient is also 1. it has a positive gradient therefore the line slopes downwards.

what do sloping lines that cross at the y intercept have the equation of?

y=mx

what do you write if m = 1/-1

y = x + c

y = -x + c

Cancelling down

• when multiplying fractions by a significant figure, write write sf. as sf./1
• EXAMPLE
• to get rid of a divide, multiply both sides by whatever is devided (or on the bottom line)
• you can't cancel down things on opposite sides of the equals sign
• when x or / you must x or / everything on the opposite side

finding where two lines cross/meet

• get at least on of the two equations to y=mx+c
• wherever you see y in the harder equation, replace it with write whatever y = in the easy one
• simplify to find what x equals, so y is before the equals sign and x is after the equals sign
• subtitute what x is into the easy equation to find y

IT DOESN'T ACTUALLY HAVE TO START WITH FINDING Y.

How to find out the gradient of a line:

change in the vertical direction / change in the horisontal direction

finding what to equation of a line is when give two points in it (that would join to give the line)

• figure out the change in the two y figures in the (x,y)'s (lets call this Z)
• figure out the change in the two x figures in the (x,y)'s (lets call this Y)
• figure out Z/Y
• substitute the x and y from the first (x,y) and m into the equation y= mx+C (LETS CALL THIS A)
• look at A, and rearange so you get c= _____

what changes in perpendicular lines?

the y intercept (c)

• Change M by making it a negative number and make it the RECIPRICAL 
• The rest of the equation you keep the same

EXAMPLE:

If M equals 4/3 turn it into -3/4