Math sec1 SA2 review

• Examples of whole numbers are 0,1,2,3
• Even numbers are numbers that are divisible by 2.
• Odd numbers are whole numbers that cannot be divided evenly by 2.
• A factor is a number that divides another number evenly.

  
• A multiple is the number you get when you multiply a certain number with an integer.

  
• Prime numbers are only divisible by 1 and themselves.
• Composite numbers have more than 2 different factors.
• 0 and 1 are neither prime nor composite.
• A square root is is a value that can be multiplied by itself to give the original number.

  
• Integers are numbers that is not a fraction but a whole number.
• A number is considered to be a perfect square if it can be written as a square of an integer. For example, 9 is a perfect square because 3 × 3 = 32 =9. 
• The formula to find the perfect square.

  A) 225

  B) 225

  
• To find out whether a number is prime or composite, we check if its divisible by all prime numbers less than or equal to its square root.
• Twin primes are prime numbers that differ by 2.
• Cousin primes are prime numbers that differ by 4.
• Sexy primes are prime numbers that differ by 6.
• 5⁴ is the index notation of 5x5x5x5.
• The process of expressing 18 as a product of its prime factors is called prime factorization.
• When we do prime factorization, we must answer in index notation.

  
• HCF stands for Highest Common Factor.

  How to find HCF:

  1. write each number as a product of its prime factors.
  2. List the common factors of all the numbers.
  3. The product of all common prime factors is the HCF (use the lower power of each common factor)

  
• LCM stands for Lowest Common Multiple.

  How to find LCM:

  1. write each number as a product of its prime factors
  2. multiple ALL of its prime factors together. (choose each of the common prime factors with the higher index and the remaining factor)

  
• For a number to be a perfect square, the index of each prime factor must be even.
• For a number to be a perfect cube, the index of each number must be a multiple of three.
• Numbers greater than 0 are called positive numbers.
• Numbers that are less than 0 are called negative numbers.
• An integer is any WHOLE number.
• A rational number is a fraction or decimal whose denominator is not zero.
• Prime number


  A number that can only be divided by one and itself
• To find a prime number between a small range

  1. Eliminate the even numbers

  2. Eliminate the multiples of 5

  3. Check the rest of the numbers
• Composite number


  A number that can be divided by multiple numbers
• How to do index notation

  1. Use a factor tree

  2. Divide the number using the smallest prime number it can be divided by until its undividable

  3. Take the numbers it was divided by and the last ones to list the index notation
• HCF


  Lowest, common
• LCM


  Highest, all
• Given that k is a whole number and 126k is a perfect square number, find the smallest possible value of k
• Perfect square number


  It has to be in the from of n² or the multiples of it (n⁴, n⁶, n⁸)
• Index notation for 126

  126 = 2 x 3² x 7
• To get the squared number, we only need to multiply 2 by 2 and 7 by 7 because 3 is already squared
• The numbers used to multiply (2 and 7) have a product of 14, which is the smallest possible value of k
• Approximation


  When you know the number (rounding)
• Estimation


  When you don't know the number, basically guessing (unknown value)