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Math
Discrete Math
Specialist Maths
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Terms in this set (23)
Intergers
...-3, -2, -1, 0, 1, 2, 3...
Whole Numbers
0, 1, 2, 3...
Counting/Natural Numbers
1, 2, 3
Irrational Numbers
Numbers that do not terminate
Where do numbers like √3 or √7 fit in the classification of numbers
Irrational Numbers
Surds - Fractions
- Simplify if possible
- Leave in √ format if not possible (e.g if irrational)
-Add or Subtract using common denominators
Surds & Indices
https://emac.hotmaths.com.au/lessonSection/lesson.action#/exercise/
Construct a length of 10¹ using a right angled triangle.
3² + 1² = 10²
C Level Question - Surds
√ 1183
=√(169x7)
=13√ 7
C Level Question - Surds
5√7 + 2√3 - 3√7
=2√7 + 2√3
=2(√7 + √3)
A Level Question - Surds
1, 2, 5, 8, 9
https://emac.hotmaths.com.au/lessonSection/lesson.action#/exercise/
Multiplication Princple
The multiplication principle states that if one operation can be performed in n ways, followed by another operation in m ways, then the combined operation can be performed in n × m ways.
Mutually exclusive operations
Operations that have no common elements are mutually exclusive operations.
Addition principle
The addition principle states that if two mutually exclusive operations can be performed in n and m ways, then the number of ways of performing one or the other is n + m ways
Factorials
For integers n 0, n factorial (or factorial n) is symbolised n! and deﬁned as
n! = n × (n − 1)! = n × (n − 1) × (n − 2) × (n − 3) × ... × 3 × 2 × 1
By deﬁnition, 0! = 1.
Permutations
The number of permutations of n things ( P n , n P n , P(n, n) or P n ) is given by P n = n!.
The number of permutations of n things taken r at a time ( n P r , n P r , P(n, r) or P r n ) is given by n! n P r = n × (n − 1) × (n − 2) × (n − 3) × ... × (n − r + 1) = ------------------( n - r )!
Permutations cont...
The number of permutations of n things, of which a are alike, is given by ----- .
a!
n! If there are another b, c, ... alike, the number of permutations is given by ----------------------- . a!b!c! ...
Permutations cont...
The number of circular permutations of n different things is given by (n − 1)!.
The probability of an event that can occur in n(event) ways is given by n ( event ) P(event) = ---------------------------------------n ( sample space )
where n(sample space) is the number of occurrences in the sample space
Combinations
A combination of a group of objects is a selection of some or all of the objects.
The number of combinations of n things taken r at a time ( n C r , ( r n ), n C r , C(n, r) or C r n ) is given by n P r n! n ( n - 1 ) ... ( n - r + 1 ) n C = ------- = ------------------------ = -------------------------------------------------------r r! r! ( n - r )! r!
Combinations cont...
Important results for combinations include:
- n C n = n C 0 = 1
- n C 1 = n
- n C r = n C n − r
Some students arrive at the basketball court and decide to make up two teams to play a practice game. How many different pairs of teams of equal numbers can be made if there are:
a) Seven students?
Ways of choosing umpire = ⁷C₁ = 7
Ways of choosing a team of three from six players = ⁶C₃
Ways of choosing two teams of three from six players = ⁶C₃/2
Ways of choosing two teams of three from seven players = ⁶C₃/2 x 7
Logarithims
https://emac.hotmaths.com.au/lessonSection/lesson.action#/exercise/
A Level Questions
1½, 2, 3, 4
https://emac.hotmaths.com.au/lessonSection/lesson.action#/exercise/
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Devise an algorithm for listing the vertices of an ordered rooted tree in level order.
discrete math
Paul has two coolers. The first contains eight cans of cola and three cans of lemonade. The second cooler contains five cans of cola and seven cans of lemonade. Paul randomly selects one can from the first cooler and puts it into the second cooler. Five minutes later Betty randomly selects two cans from the second cooler. If both of Betty’s selections are cans of cola, what is the probability Paul initially selected a can of lemonade?
discrete math
Encrypt the message WATCH YOUR STEP by translating the letters into numbers, applying the given encryption function, and then translating the numbers back into letters. a) f(p) = (p + 14) mod 26 b) f(p) = (14p + 21) mod 26 c) f(p) = (−7p + 1) mod 26
question
Determine the correct check digit for the UPC. 6-53569-39973-? (Scrabble)
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