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21/04/2017
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Mordialloc College
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Discovery 8F
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Expression: A number sentence without an equal sign. Has at least two terms and one operation.
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Coefficient: A number that does not stand by itself. It is attached to the variable.
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Constant: A number that stands by itself.
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Term: Each part of an expression separated by an operation.
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Variable: A letter that stands for a particular numerical value.
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The number comes before the letter.
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You do not need to write the multiplication sign.
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First Outside Inside Last
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eg. (a + 4)(a + 7)
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= a2 + 7a + 4a + 28
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= a2 + 11a + 28
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To replace a pronumeral with a given value.
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eg. 2y + 3
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If y was1, then the expression would be
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2 x 1 + 3
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To expand an expression, multiply each term in the bracket by the number on the outside.
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eg. 2(y + 2x) = 2y + 4x
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To factorise an expression, find a common factor to place outside of the brackets.
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eg. 3(2x + 7) = 6x + 21
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Commutative Law
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The Commutative Law refers to the order in which two numbers may be added, subtracted, multiplied or divided.
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It holds true for addition and multiplication but not subtraction and division.
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Associative Law
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The Associative Law refers to the order in which three numbers may be added, subtracted, multiplied or divided, taking two at a time.
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Like the Commutative Law, it holds true for addition and multiplication but not subtraction and division.
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Identity Law
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The Identity Law states that when a zero is added to a number/any number is multiplied by one, the original number remains unchanged.
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Inverse Law
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The Inverse states that when a number is added to its additive inverse/multiplied by its reciprocal, the result is one.
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Inverse operations are reverse operations that undo each other.
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Addition (+) and subtracting (-) are inverse operations. Multiplication (x) and division (÷) are also inverse operations.
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When backtracking, you have to work backwards with reverse BODMAS and inverse operations.
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eg. 2x - 3 = 19
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19 + 3 ÷ 2 = x
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∴ x = 10.5
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Indices is the plural form of index. An index is a shorthand way of writing a repeated multiplication.
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It is written as a small number to the right and above the base number.
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The base is the number that is being multiplied and the index (plural indices) is the number of times it is multiplied.
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In this example: 82 = 8 × 8 = 64
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Other names for index are exponent or power.
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Index notation is similar to expanded notation, but going one step further and writing multiples of 10 as indices.
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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).
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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.
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Terms containing exactly the same pronumerals, regardless of order, are called like terms.
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Unlike terms are terms that have different variables.
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Examples of like terms:
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12 x and 7 x
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12 and 7
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12mno and 12mon
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Examples of unlike terms:
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12x and 7m
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12x and 7
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12x and 7x²
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When simplifying expressions, we can add or subtract like terms only. Expressions which do not have like terms cannot be added or subtracted.
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eg. 5x + 3x - 7 + 8x = 16x - 7
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