Math Block Test 1

1. What is a factor?
   1. A factor is a number which divides exactly into another number is called a factor of that number.
      1. Step 1: Can 20 be divided in 1 exactly?
         1. 20÷1=20
            1. Yes
               1. 1 and 20 are factors of 20
                  1. Step 2: Can 20 be divided in 2 exactly?
                     1. 20÷2=10
                        1. Yes
                           1. 2 and 10 are factors of 20
                              1. Step 3: Can 20 be divided in 3 exactly?
                                 1. 20÷3=6.666
                                    1. No
                                       1. 3 is not a factor of 20
                                          1. Step 4: Can 20 be divided in 4 exactly?
                                             1. 20÷4=5
                                                1. Yes
                                                   1. 4 and 5 are factors of 20
                                                      1. Step 5: Can 20 be divided into 5 exactly?
                                                         1. 20÷5=4
                                                            1. Yes
                                                               1. But we already have 4 and 5 down as factors so that means we have listed all the factors.
                                                                  1. The factors of 20 are 1, 2, 4, 5, 10, 20
                                                                     1. The factors of 16 are 1, 2, 4, 8, 20
                                                                        1. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
                                                                           1. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100

1. The highest or the lowest number that both supplied numbers have as factors.
   1. HCF of 18 and 30
      1. Step 1: List factors of 18
         1. 1, 2, 3, 6, 9, 18
            1. Step 2: List factor of 30
               1. 1, 2, 3, 5, 6, 10, 15, 30
                  1. Step 3: Identify the common factors
                     1. 1, 2, 3, 6
                        1. Step 4: Identify the highest or the lowest of them
                           1. 6
                              1. The HCF of 18 and 30 is 6
                                 1. The LCF of 18 and 30 is 1
                                    1. The LCF will always be 1

1. Numbers that can only divide into themselves and 1
   1. To find if it is prime fast
      1. Step 1: Is it a multiple of 2, 3, 5, 7?
         1. If not it is prime.

1. hellopeople
   1. The numbers at the end are prime numbers
      1. Collect like terms

1. Brackets, Exponents, Division, Multiplication, Addition, Subtraction
   1. If just Multiplication and Division then work left to right
      1. If just Addition and Subtraction then work left to right
         1. If combination then work in BEDMAS
            1. Step 1: Work out the brackets
               1. (2²x5+20)x2²
                  1. Step 2: Work out the exponents within the brackets
                     1. (4x5+20)x2²
                        1. Step 3: Work out the multiplication within the brackets
                           1. (20+20)x2²
                              1. Step 4: Work out the addition within the brackets
                                 1. (40)x2²
                                    1. Step 5: Remove unnessasary brackets
                                       1. 40x2²
                                          1. Step 6: Work out exponents
                                             1. 40x4
                                                1. Step 7: Work out multiplication
                                                   1. 160

1. Multiples of a number are the numbers divisible by that number
   1. 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

1. The smallest number that both the supplied numbers have as multiples
   1. LCM of 8 and 12
      1. Step 1: List the first 5 multiples of 8
         1. 8, 16, 24, 32, 40, 48
            1. Step 2: List the first 5 multiples of 12
               1. 12, 24, 36, 48, 60, 72
                  1. Step 3: Identify the common numbers
                     1. 24, 48
                        1. Step 4: If there are none list the next 5 multiples
                           1. Step 5: Take the lowest common number
                              1. That is your LCM

1. Step 1: Look at where you want to round the number to
   1. ₂.₇5₆
      1. Step 2: Look at the number to the right to decide wheather to round up or down.
         1. 1. In this case it is a 6 so we round up
               1. 5 AND ABOVE: ROUND UP
                  1. 4 AND BELOW: ROUND DOWN (DON'T DO ANYHING)
                     1. Step 3: Round up or down to the specified amount of d.p.
                        1. 1. Step 4: Make sure you have specified how many places you have rounded it to

1. Step 1: Decide on the most significant figure (1s.f.)
   1. 1. Step 2: Decide if the number is closest to 6,000,000 or 7,000,000 for 1s.f. (in this case)
         1. $7,000,000 (1s.f.)
            1. or
               1. Step 1: Decide on the second most signifigant figure (2 s.f.)
                  1. 1. Step 2: Decide if the number is closest to 6,700,000 or 6,800,000 for 2s.f (in this case)
                        1. $6,700,000 (2s.f.)
                           1. or
                              1. Step 1: Decide of the third most significant figure (3 s.f.)
                                 1. 1. Step 2: Decide if the number is closest to 6,720,000 or 6,730,000 (3s.f.)
                                       1. $6,730,000
                                          1. 1. Same with decimals
                                                1. 1. but

Attachments:

• Algebra

1. 1. Simplifing indices
      1. To multiply numbers, which have the same base, add the powers
         1. 2⁵x2⁶=2¹¹ not 2048
            1. 1. To divide which have the same base, subtract the powers
                  1. 1. 1. Brackets with powers
                           1. 1. 1. Special things you need to watch out for
                                    1. 1. 1. eg

1. Squares are essentially the number times itself
   1. 3²=3x3=9
      1. Square roots
         1. The opposite of squaring
            1. Step 1: Work out what you would have orgionally squared to get this number you see before your eyes
               1. ?x?=81
                  1. 9x9=81
                     1. Step 2: Congratulate yourself, you have found the square root of the number
                        1. Cubes
                           1. Cubes of a number is pretty much the number times itself, times the orgional number
                              1. 5³=5x5x5=125
                                 1. Cube Roots
                                    1. The same as square roots, cube roots are pretty much the opposite of a cube
                                       1. Step 1: Work out what would you time 3 time to get that number
                                          1. ?x?x?=216
                                             1. 6x66=216
                                                1. Cube root is 16

1. Adding and Subracting
   1. a+a=2a
      1. 1. c+c+d+d+b+c+a+d=a+b+3c+3d
            1. 1. 2a+7b-5+a-2b=3a+5b-5
                  1. Simplifying Pyramid
                     1. 1. Multiplication and Division
                           1. Multiplication
                              1. 1. 1. Step 1: Write it out in separately with numbers and then letters
                                       1. 7b x 3a=7 x 3 x a x b
                                          1. Step 2: Do the multiplication of the numbers
                                             1. 21 x a x b
                                                1. Step 3: Remove all "x" signs
                                                   1. 21ab
                           2. Division
                              1. 1. Step 1: Divide the numbers.
                                    1. 12÷3=4
                                       1. 1. Step 2: Cancel out the letters
                                             1. 1. And yo got the answer
                                                   1. 1. more examples
         2. Same for subraction

1. 1.65x10⁵=1650000
   1. The first number must always be a value between 0 and 9 inclusive
      1. The power number (the 5 in the example) is the number of spaces the decimal point moves
         1. Positive and the decimal point moves to the right, adding more zeros in if there are no more digits there
            1. Negitve and it moves to the left, again adding more zeros into the number if there are no more digits there