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GOOD MORNINGGOOD MORNING Shania QQ:1246640685

MSN: [email protected]

Shania QQ:1246640685MSN: [email protected]

www.themegallery.com

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Contents

Math words quiz

Factors-prime factors

Multiples-LCM

Patterns and sequences

SETS!!!


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Math words quiz

10 minutes!!!


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Factors

Factors of a number are the whole numbers that multiply together to give the original number

E.g. The factors of 12 are? 12 is the the original number So which numbers can multiply

together to give 12? 1×12, 2×6, 3×4 That is, 1,2,3,4,6,12 are factors of

12. We use F(12) as a short way of

writing factors of 12. F(12)={1,2,3,4,6,12} Factor pairs of 12 are (1,12), (2,6),

(3,4)

Among these 6 factors 2 and 3 are prime factors.

[Prime factors of a number are factors of the number that are also prime number.]


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Writing numbers as the product of prime factors

Prime factors2,3,5,7,11,13…12=4×3,but 4 is not prime number,

we break 4 down further 12=2×2×3 that we have written 12 as the product of prime factors


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•Step 1

• Step 2

•Step 3

Try to divide the given number by the first prime number -- 2

Continue until 2 will no longer divide into it

Try the next prime number, 3, then 5, 7 and so on, until final answer is 1

Steps


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Examples

Write 60 as a product of prime factors.

Write 3465 as a product of prime factors.

So 3465=3×3×5×7×11


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Several rules

The number is ended by 0,2,4,6,8 can be divided

by 2.

The sum of all digits of the number can be divided

by 3, that is, the number can be divided by 3.

3465 3+4+6+5=18 18/3=6

so 3465 can be divided by 3

So does 5, 7, 11 and 13


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Multiples

Definition: the multiples of number are the products of that numbers and 1,2,3,4,5…(Natural number)

E.g. The multiples of 3 are??? 3, 6, 9, 12, 15… The first five multiples of 3:

M(3)={3,6,9,12,15}


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LCM-Lowest common multiple

最小公倍数The smallest number that is a

multiple of two or more numbers12, 24, 36 are multiples of 3 and 4.

BUT, 12 is the smallest one, that is, 12 is the LCM of 3 and 4.


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Two ways to find LCM

ONE: ①List the multiples of each numbers of each numbers ②and then pick out the lowest number that appears in every one of the lists. (applicable for small numbers)

ANOTHER: Expressing each number as a product of prime factors


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Sets

Any collection of objects – have sth in common, some connection with each other.

{ } braces , comma

The object in a set we called element of the set ∈

5 ways to express sets


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5 ways

1. Listed set {1,2,3,4.5}2. Described set {first five natural

numbers}3. Set builder notation to describe

sets mathematically {x:x≦10 and x is an even number}

4. Represented by a name or a letter {red, blue, yellow} {Thomas, Joise}

5. Venn diagram


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Special sets

Finite sets and infinite sets

Universal set rectangular Venn diagram

It can change from problem to problem

{ } empty set


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Relationships between sets

Equal sets: same cardinality and same elements “=“

Equivalent sets: same number of elements

Subsets: A is the subset of set B if all of the elements of A are elements of B

A⊂ B （子集） B⊃ A (superset 扩散集） In our book ， different from Chinese book

How many subsets? Include {} and equal set Use permutation and combination to prove.


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Continue

Complement set A’ contains all of the elements of the universal set not in A. set A and its complement A’ are disjoint- A∩A’=empty set

Power set: All subsets of a given set A

If a set has n elements it will have 2^n subsets


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Intersection and union of sets

A∪B : the union of sets A and B.

A∩B : the intersection of sets A and B. The elements common to set A and B.


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Laws

1. A ∩ A = A2. A ∩ B = B ∩ A (commutative law) 3. A ∩ B ∩ C = A ∩ (B ∩ C) (associative la

w) 4. A ∩ φ = φ ∩ A = φ 5. A ∪ (A ∩ B) = A 6. A ∩ (A ∪ B) = A 7. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (distri

butive law) 8. A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (distri

butive law)

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