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Math Block Test 1

Sally Stroobant Math NCEA Level 1 English

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Math Block Test 1

Factors
- What is a factor?
  - A factor is a number which divides exactly into another number is called a factor of that number.
    - Step 1: Can 20 be divided in 1 exactly?
      - 20÷1=20
        Yes
        1 and 20 are factors of 20
        Step 2: Can 20 be divided in 2 exactly?
        20÷2=10
        Yes
        2 and 10 are factors of 20
        Step 3: Can 20 be divided in 3 exactly?
        20÷3=6.666
        No
        3 is not a factor of 20
        Step 4: Can 20 be divided in 4 exactly?
        20÷4=5
        Yes
        4 and 5 are factors of 20
        Step 5: Can 20 be divided into 5 exactly?
        20÷5=4
        Yes
        But we already have 4 and 5 down as factors so that means we have listed all the factors.
        The factors of 20 are 1, 2, 4, 5, 10, 20
        The factors of 16 are 1, 2, 4, 8, 20
        The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
        The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
Highest and Lowest Common Factors
- The highest or the lowest number that both supplied numbers have as factors.
  - HCF of 18 and 30
    - Step 1: List factors of 18
      - 1, 2, 3, 6, 9, 18
        Step 2: List factor of 30
        1, 2, 3, 5, 6, 10, 15, 30
        Step 3: Identify the common factors
        1, 2, 3, 6
        Step 4: Identify the highest or the lowest of them
        6
        The HCF of 18 and 30 is 6
        The LCF of 18 and 30 is 1
        The LCF will always be 1
Prime Numbers
- Numbers that can only divide into themselves and 1
  - To find if it is prime fast
    - Step 1: Is it a multiple of 2, 3, 5, 7?
      - If not it is prime.
Factor Trees
- hellopeople
  - The numbers at the end are prime numbers
    - Collect like terms
BEDMAS
- Brackets, Exponents, Division, Multiplication, Addition, Subtraction
  - If just Multiplication and Division then work left to right
    - If just Addition and Subtraction then work left to right
      - If combination then work in BEDMAS
        Step 1: Work out the brackets
        (2²x5+20)x2²
        Step 2: Work out the exponents within the brackets
        (4x5+20)x2²
        Step 3: Work out the multiplication within the brackets
        (20+20)x2²
        Step 4: Work out the addition within the brackets
        (40)x2²
        Step 5: Remove unnessasary brackets
        40x2²
        Step 6: Work out exponents
        40x4
        Step 7: Work out multiplication
        160
Multiples
- Multiples of a number are the numbers divisible by that number
  - Eg. multiples of 3 is 6, 9, 12, 15 etc because 6 is divisible by 3 and so are all the rest of the numbers
Lowest Common Multiple
- The smallest number that both the supplied numbers have as multiples
  - LCM of 8 and 12
    - Step 1: List the first 5 multiples of 8
      - 8, 16, 24, 32, 40, 48
        Step 2: List the first 5 multiples of 12
        12, 24, 36, 48, 60, 72
        Step 3: Identify the common numbers
        24, 48
        Step 4: If there are none list the next 5 multiples
        Step 5: Take the lowest common number
        That is your LCM
Rounding Decimal Places
- Step 1: Look at where you want to round the number to
  - ₂.₇5₆
    - Step 2: Look at the number to the right to decide wheather to round up or down.
      - In this case it is a 6 so we round up
        5 AND ABOVE: ROUND UP
        4 AND BELOW: ROUND DOWN (DON'T DO ANYHING)
        Step 3: Round up or down to the specified amount of d.p.
        Step 4: Make sure you have specified how many places you have rounded it to
Rounding significant figures
- Step 1: Decide on the most significant figure (1s.f.)
  - - Step 2: Decide if the number is closest to 6,000,000 or 7,000,000 for 1s.f. (in this case)
      - $7,000,000 (1s.f.)
        or
        Step 1: Decide on the second most signifigant figure (2 s.f.)
        Step 2: Decide if the number is closest to 6,700,000 or 6,800,000 for 2s.f (in this case)
        $6,700,000 (2s.f.)
        or
        Step 1: Decide of the third most significant figure (3 s.f.)
        Step 2: Decide if the number is closest to 6,720,000 or 6,730,000 (3s.f.)
        $6,730,000
        Same with decimals
        but
Algebra Attached
- Algebra
Indices
- - Simplifing indices
    - To multiply numbers, which have the same base, add the powers
      - 2⁵x2⁶=2¹¹ not 2048
        To divide which have the same base, subtract the powers
        Brackets with powers
        Special things you need to watch out for
        eg
Squares and Cubes
- Squares are essentially the number times itself
  - 3²=3x3=9
    - Square roots
      - The opposite of squaring
        Step 1: Work out what you would have orgionally squared to get this number you see before your eyes
        ?x?=81
        9x9=81
        Step 2: Congratulate yourself, you have found the square root of the number
        Cubes
        Cubes of a number is pretty much the number times itself, times the orgional number
        5³=5x5x5=125
        Cube Roots
        The same as square roots, cube roots are pretty much the opposite of a cube
        Step 1: Work out what would you time 3 time to get that number
        ?x?x?=216
        6x66=216
        Cube root is 16
Simplifying
- Adding and Subracting
  - a+a=2a
    - - c+c+d+d+b+c+a+d=a+b+3c+3d
        2a+7b-5+a-2b=3a+5b-5
        Simplifying Pyramid
        Multiplication and Division
        Multiplication
        Step 1: Write it out in separately with numbers and then letters
        7b x 3a=7 x 3 x a x b
        Step 2: Do the multiplication of the numbers
        21 x a x b
        Step 3: Remove all "x" signs
        21ab
        Division
        Step 1: Divide the numbers.
        12÷3=4
        Step 2: Cancel out the letters
        And yo got the answer
        more examples
      - Same for subraction
Standard Form
- 1.65x10⁵=1650000
  - The first number must always be a value between 0 and 9 inclusive
    - The power number (the 5 in the example) is the number of spaces the decimal point moves
      - Positive and the decimal point moves to the right, adding more zeros in if there are no more digits there
        Negitve and it moves to the left, again adding more zeros into the number if there are no more digits there