Algebra Test Cheat Sheet
21/04/2017 |
Mordialloc College |
Discovery 8F |
Vocabulary
Expression: A number sentence without an equal sign. Has at least two terms and one operation. |
Coefficient: A number that does not stand by itself. It is attached to the variable. |
Constant: A number that stands by itself. |
Term: Each part of an expression separated by an operation. |
Variable: A letter that stands for a particular numerical value. |
Reminders
The number comes before the letter. |
You do not need to write the multiplication sign. |
FOIL
First Outside Inside Last |
eg. (a + 4)(a + 7) |
= a2 + 7a + 4a + 28 |
= a2 + 11a + 28 |
Substitution
To replace a pronumeral with a given value. |
eg. 2y + 3 |
If y was1, then the expression would be |
2 x 1 + 3 |
Expanding and Factorising Expressions
To expand an expression, multiply each term in the bracket by the number on the outside. |
eg. 2(y + 2x) = 2y + 4x |
To factorise an expression, find a common factor to place outside of the brackets. |
eg. 3(2x + 7) = 6x + 21 |
|
|
Number Laws
Commutative Law |
The Commutative Law refers to the order in which two numbers may be added, subtracted, multiplied or divided. |
It holds true for addition and multiplication but not subtraction and division. |
Associative Law |
The Associative Law refers to the order in which three numbers may be added, subtracted, multiplied or divided, taking two at a time. |
Like the Commutative Law, it holds true for addition and multiplication but not subtraction and division. |
Identity Law |
The Identity Law states that when a zero is added to a number/any number is multiplied by one, the original number remains unchanged. |
Inverse Law |
The Inverse states that when a number is added to its additive inverse/multiplied by its reciprocal, the result is one. |
Inverse Operations and Backtracking
Inverse operations are reverse operations that undo each other. |
Addition (+) and subtracting (-) are inverse operations. Multiplication (x) and division (÷) are also inverse operations. |
When backtracking, you have to work backwards with reverse BODMAS and inverse operations. |
eg. 2x - 3 = 19 |
19 + 3 ÷ 2 = x |
∴ x = 10.5 |
|
|
Indices and Index Notation
Indices is the plural form of index. An index is a shorthand way of writing a repeated multiplication. |
It is written as a small number to the right and above the base number. |
The base is the number that is being multiplied and the index (plural indices) is the number of times it is multiplied. |
In this example: 82 = 8 × 8 = 64 |
Other names for index are exponent or power. |
Index notation is similar to expanded notation, but going one step further and writing multiples of 10 as indices. |
eg. 3,657,428 in index notation would be (3 x 106) + (6 x 105) + (5 x 104) + (7 x 103) + (4 x 102) + (2 x 101) + (8 x 100). |
Usually, indexes of 1 and 0 are not included in index notation. This is because 101 is equal to 10 and 100 is equal to 1. |
Like and Unlike Terms
Terms containing exactly the same pronumerals, regardless of order, are called like terms. |
Unlike terms are terms that have different variables. |
Examples of like terms: |
12 x and 7 x |
12 and 7 |
12mno and 12mon |
Examples of unlike terms: |
12x and 7m |
12x and 7 |
12x and 7x² |
When simplifying expressions, we can add or subtract like terms only. Expressions which do not have like terms cannot be added or subtracted. |
eg. 5x + 3x - 7 + 8x = 16x - 7 |
|
Created By
Metadata
Favourited By
Comments
No comments yet. Add yours below!
Add a Comment
Related Cheat Sheets
More Cheat Sheets by Phoebe12