Maths Revision: A1: Expressions

• an INDEX is a power 34
• the BASE  is the number which is raised to the power eg. 34
• standard form is: A x 10n
• A is a number more than or the same as 1 and less then 10
• this would be shown in the exam as 1  A < 10
• A must have ONLY ONE significant figure before the decimal point. (e.g 2.3 x 107 = 23,000,000)
• n is the number of places the decimal point moves
• if n is positive then the original number is positive
• if n is negative then the original number is negative
• N is not the the number of 0's its how many times to move the decimal point
• Why are the following NOT standard form?

-10.6 x 105

-0.2 x 10-3

Positive Numbers:

1.) find 'A' (the number but with only the first significant figure before the decimal point and the rest after)

2.) count how many places the decimal point has to move to the left to make the A. (if there is no decimal point) imagine there is a decimal point at the end of the figure. THIS IS N. as this is for a positive figure N will be positive.

Negative Numbers:

1.) find 'A' (the number but with only the first significant figure before the decimal point and the rest after)

2.) count how many places the decimal point has to move to the right to make A. THIS IS N. as this is for a negative figure N will be negative.

• (if there is no decimal point) imagine there is a decimal point at the end of the figure
• the N will tell you how many places to move the decimal point to the left

Positive numbers:

1.) move the decimal point in A to the right however many times N says. REMEMBER TO FILL THE GAPS WITH 0's. (e.g. 9.8 x 10 5 = 980,000)

Negative numbers:

1.) move the decimal point in A to the left however many times N says. REMEMBER TO FILL THE GAPS WITH 0's and one before the decimal point.. (e.g. 9.8 x 10 5 = 980,000)

IF N IS THE SAME (107 x 107)

1.) add together the bases and leave n the same

IF N IS NOT THE SAME (eg. 107 x 106)

1.) Write the numbers in full not in standard form

2.) add or subtract

3.) Convert back to standard index form

Multiplying Index Form

• multiply the base terms (A) 
• ADD the indecies
• EXAMPLE:

(3 x 104 ) x (5 x 106 )

Deviding Index Form

• devide the base terms (A)
• MINUS the indecies
• EXAMPLE:

(6 x 108 ) % (4 x 103 )

Things to remember

• imagine all letters that dont have a indecies have 1 (Y x Y = Y1 x Y1 =Y2)
• if a bracket looks like this (X x Y)2, write it out as (X x Y) (X x Y)

Single bracket:

KNOW WELL

Double brackets:

KNOW WELL

STUCK ON QUESTIONS ...

• 1G
• 2G
• 2H
• 6
• 7B

What is a quadratic equation?

an equation in which the highest power of an unknown quantity (eg x ) is a square (2)

WITH A NON QUADRATIC EQUATION:

1.) Look for the HCF (highest common factor) of the coefficient - the highest number they devide by.

THE COEFFICIENT IS ANY NUMBER THAT MAY BE INFRONT OF A LETTER

EXAMPLE: of 9 and 6, its 3 and of 6 and 3 its 3

2.) Then look for the HCF of the algebraic terms (eg indecies or letters)

3.) put the HCF of both of these before the bracket,

4.) figure out what is needed to go inside the bracket so that it can times out to give the origininal equation

WITH A QUADRATIC EQUATION:

please see A4

this is the simple equation for quadratics :ax2+ bx + c

WITH DOUBLE BRACKETS IN GENERAL- when x2 has no Coefficient:

1.) rearrange into Standard format (ax2+ bx + c)

2.)draw double brackets

3.) Put x at the start of both of them (x        ) (x       )

4.) for the other numbers in each bracket find - What two numbers add to give B -What two numbers multiply to give C. They will be the numbers.

5.) switch round the + and the - and the numbers and then check by multiplying out untill you get the original quadratic equation.

When might a quadratic be a single bracket?

if there aren't any 2 numbers that multiply to give C and add to give B

ax2+ bx + c

C is the constant

Factorising quadratics when 'A' isn't 1

1.) rearrange into standard format

2.) multiply A by C (lets call the product of this M)  

3.) find two numbers that multiply to give M and add to give B

4.) write the quadritic equation out but with the two numbers from part 3 included

EXAPMLE:  ax2+ Mx +Mx + c

5.) split the terms into two....

EXAPMLE:  ax2+ Mx         Mx + c  

6.) Factorise each terms seperately the brackets should be the same eg 2x ( 2x + 3) + 5 (2x +3)

7.) take the brackets and make this the first bracket eg (2x+3)

8.) take the outside figures of both sections and make this into the second bracket eg. (2x + 5)

:(

NOT RULES.

JUST LOOK AT EXAMPLES