aqa maths higher section 1- numbers

aqa maths higher section 1- numbers

1. BIDMAS- THE ORDER IN WHICH WE COMPLETE PARTS OF A SUM

   • B- BRACKETS
     • I- INDICES (SQUARES)
       • D- DIVISION
         • M- MULTIPLICATION
           • A- ADDITION
             • S- SUBTRACTION

2. TYPES OF NUMBER

   • INTEGERS (aka. whole numbers)
   • RATIONAL NUMBERS (aka. numbers that can be written as whole numbers, fractions or recurring decimals)
     • IRRATIONAL NUMBERS (aka. numbers that cant be written as fractions or recurring decimals, eg. pi)
   • SQUARES-
     • 1 , 4 , 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
   • CUBES
     • 1, 8, 27, 64, 125
   • PRIMES (aka. a number that only divides by itself and 1)
     • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43
     • FACTOR TREES-aka how to find a bunch of prime numbers that fit in your original number
       • START POINT- 420
         • DIVIDES INTO : 42
           • divides into: 6
             • divides into: 2- a prime!
             • divides into: 3- a prime!
           • divides into: 7- a prime!
         • AND: 10
           • divides into: 5- a prime!
           • divides into: 2- a prime!
     • ALL PRIMES END IN 1,3, 7 OR 9
   • FACTORS OF A NUMBER = all the numbers that will divide into the original number
     • LOWEST COMMON MULTIPLE- the smallest number that's divisble by all the numbers in the question
       • FIRST: LIST THE MULTIPLES OF ALL THE NUMBERS, SECOND: FIND THE SMALLEST ONE IN ALL THE LISTS- THIS IS THE LCM
         • multiples of 12- 12, 24, 36, 48,
           • multiples of 15- 15, 30, 45,
             • , 60
           • , 60
     • HIGHEST COMMON FACTOR- the biggest number that will divide IN TO ALL the numbers in the question.
       • FIRST: LIST THE FACTORS OF ALL THE NUMBERS, SECOND: FIND THE BIGGEST ONE IN ALL THE LISTS- THIS IS THE HCF
         • factors of 36- 1, 2, 3, 4, 6, 9, 12,
           • , 18
             • , 18
           • factors of 54- 1, 2, 3, 6, 9,

3. FRACTIONS

   • SIMPLIFYING FRACTIONS- divide the top and bottom by the same number until the fraction can be divided no futher