Algebra Test Cheat Sheet21/04/2017 | Mordialloc College | Discovery 8F |
VocabularyExpression: 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. |
RemindersThe number comes before the letter. | You do not need to write the multiplication sign. |
FOILFirst Outside Inside Last | eg. (a + 4)(a + 7) | = a2 + 7a + 4a + 28 | = a2 + 11a + 28 |
SubstitutionTo 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 ExpressionsTo 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 LawsCommutative 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 BacktrackingInverse 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 NotationIndices 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 TermsTerms 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 |
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