Algebra Test Cheat Sheet
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.
The number comes before the letter.
You do not need to write the multiplication sign.
First Outside Inside Last
eg. (a + 4)(a + 7)
= a2 + 7a + 4a + 28
= a2 + 11a + 28
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
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.
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.
The Identity Law states that when a zero is added to a number/any number is multiplied by one, the original number remains unchanged.
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