S5_Unit_1_Outcome_2

# S5_Unit_1_Outcome_2 - Higher Higher Unit 1 Outcome 2...

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Outcome 2 www.mathsrevision.com Higher Outcome 2 Higher Unit 1 Higher Unit 1 www.mathsrevision.com www.mathsrevision.com What is a set Recognising a Function in various formats Composite Functions Exponential and  Log Graphs Connection between Radians and degrees & Exact values Solving Trig Equations Basic Trig Identities Graph Transformations Trig Graphs

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Outcome 2 www.mathsrevision.com Higher Outcome 2 Sets & Functions Sets & Functions Notation & Terminology SETS :  A set is a collection of items which have     some  common property. These items are called the members  or elements  of the  set. Sets can be described  or listed  using “curly bracket”  notation.
Outcome 2 www.mathsrevision.com Higher Outcome 2    eg {colours in traffic lights}    eg   {square nos. less than 30} DESCRIPTION LIST NB: Each of the above sets is finite  because we can list every member =  {red, amber, green} = { 0, 1, 4, 9, 16, 25} Sets & Functions Sets & Functions

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Outcome 2 www.mathsrevision.com Higher Outcome 2 Sets & Functions Sets & Functions N = {natural numbers} = {1, 2, 3, 4, ……….} W = {whole numbers}  = {0, 1, 2, 3, ………. .} Z = {integers}  = {….-2, -1, 0, 1, 2, …. .} Q = {rational numbers} This is the set of all numbers which can be written as fractions  or ratios . eg    5 =  5 / 1      -7 =  -7 / 1      0.6 =  6 / 10  =  3 / 5                             55% =  55 / 100  =  11 / 20    etc We can describe numbers by the following sets:
Outcome 2 www.mathsrevision.com Higher Outcome 2 R = {real numbers} This is all   possible numbers.  If  we  plotted values on a number line then  each of the previous sets would leave gaps but the set of real numbers  would give us a solid line. We should also note that N   “fits inside”   W   W  “fits inside”    Z     Z   “fits inside”    Q    Q   “fits inside”    R Sets & Functions Sets & Functions

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Outcome 2 www.mathsrevision.com Higher Outcome 2 Sets & Functions Sets & Functions Q Z W N When one set can fit inside another we say  that it is a subset  of the other. The members of R which are not inside Q are called irrational   numbers.   These cannot be expressed as fractions and include   π   ,   2,    3 5   etc R
Outcome 2 www.mathsrevision.com Higher Outcome 2 To show that a particular element/number belongs to a particular set  we use the symbol  .    eg    3   W   but     0.9   Z  Examples { x   W: x < 5 } =   { 0, 1, 2, 3, 4 } { x   Z: x   -6 } =   { -6, -5, -4, -3, -2, ……. . } { x   R: x 2  = -4 } =    { }  or   Φ This set has no elements and is called the empty set .

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S5_Unit_1_Outcome_2 - Higher Higher Unit 1 Outcome 2...

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