Mathematics

• Natural Numbers

  Used to count objects - start at 1 and continue forever

  N={1; 2; 3; 4; 5;...}
• Whole Numbers

  When the number 0 is included.

  
• BODMAS

  Brackets

  Operations

  Division and Multiplication [Left to Right]

  Addition and Subtraction [Left to Right]
• The Commutative Property

  'Move Around'

  • ONLY WORKS WITH ADDITION AND MULTIPLICATION
• The Associative Property

  'Group'

  • ONLY WORKS FOR ADDITION AND MULTIPLICATION
• The Identity Property of Zero

  Add/subtract 0 to from any number and it will be that number.
• The Identity Property of One


  Any number multiplied/divided by one, the result will be that number.
• The Multiplication Property of Zero

  Any number multiplied by zero will equal to zero.
• The Division Properties of Zero

  Property 1:

  • Dividing zero by any non-zero number is equal to zero.

  Property 2:

  • Dividing any number by zero is undefined
• Factor

  Divides a number exactly without leaving any remainder
• Prime Numbers

  Have exactly 2 factors; 1 and the number itself
• Composite Numbers

  Have more than 2 factors.
• Note:

  1 is neither a prime number nor a composite number = it is a universal factor.
• Power Notation

  Writing the product of repeated numbers in a compacted form.

  • BASE: The number that is multiplied various times.
  • EXPONENT: The number of times the base occurs in the product.
  • POWER: Consists of the base with its exponent.

  
• Prime Factorization of Numbers

  Express numbers with 2/more digits as products of prime factors.

  
• Finding the Highest Common Factor (HCF)

  
• Finding the Lowest Common Multiple (LCM)

  
• Ratio

  Compare two/more quantities; tells us how much of one thing there is compared to another thing.

  
• Ratios:

  1:6 and 4:24 are equivalent ratios
• Writing ratios in simplest form: find the HCF then divide each number in the ratio by the HCF.
• Part-to-Part ratios

  Relationship between two or more distinct groups of things.
• Part-to-Whole Ratios

  Provide the relationship between different ratio parts and the whole population of parts.
• Increasing or Decreasing Quantities in a given ratio

  
• Decreasing Quantities

  
• Rates

  Is a ratio of 2 quantities that have different units of measurement.

  e.g. 120 km : 2 hours

  
• Percentage:

  • Fraction with a denominator of 100
  • Decimal form
  • Ratio = compares a number to 100

  'of' = multiply

  
• Profit

  Difference between the income received from sales and the amount spent in buying, operating, or producing something.
• Loss

  Income received is less than the costs.
• Discount

  Amount/percentage deducted from the normal selling price
• VAT (Value-added Tax)

  Money that a business must pay to SARS for income received from the sales. SA = VAT rate is 15%

  
• Simple Interest and Hire Purchase Loans

  Money borrowed = pay back with interest.
• Simple Interest and Hire Purchase Loans

  Invest money = interest can be earned.
• Simple Interest and Hire Purchase Loans

  Simple Interest = calculated as a fixed percentage of amount borrowed/invested -> per year/annum.
• Simple Interest and Hire Purchase Loans

  Original amount is known as the principle amount/capital.
• Simple Interest and Hire Purchase Loans (Formulas)


  Simple Interest = r x P x t

  Total Amount = P + simple interest

  • P = Principal
  • r = interest rate
  • t = number of time periods
• Hire Purchase Loan (Agreement)

  Purchase expensive items without having to pay the full amount at the time of purchase. Make an initial down payment (deposit) and pay balance plus simple interest in monthly instalments over a specified time.

  
• Exchange Rates

  Currency = system of money used in a country/economic region.

  Exchange rate = value of one country's currency in relation to another currency.

  Bitcoin = international digital currency (cryptocurrency)