Year 11 Exam  >  Year 11 Notes  >  Mathematics for GCSE/IGCSE  >  Mathematical Operations

Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Mathematical Symbols

What mathematical symbols do I need to know?

  • Starting with the basic four operations
    +  Addition, plus, sum, total
    -  Subtraction, minus, difference, take away
    x Multiplication, product, times
    ÷ Division, quotient, divide, share
  • Equals signs
    = Equal to e.g. 3 x + 7 = 19
    ≠ Not equal to e.g.  Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11 
    ≈ Approximately equal to e.g. π ≈ 3.14
    ≡ Identical to e.g. 12 x + 6 ≡ 3 (4 x + 2)
  • Inequality signs
    > Greater than e.g. 5 > - 2
    < Less than  Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11
    ≥ Greater than or equal to
    ≤ Less than or equal to
  • Other helpful symbols
    ()  Brackets: used to group symbols e.g. Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11
    3 x   Powers (also called indices, order or exponents): repeated multiplication of the base number
    e.g. 34 = 3 x 3 x 3 x 3 = 81
    √ Square root: opposite of squaring e.g.Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11
    ±  Plus Minus: Used to allow for two distinct answers, often in quadratics
    a ±  b is shorthand for a + b and a - b
    e.g. x = 3 ±  2.5 leading to x = 5.5 and x = 0.5
    π Pi: the ratio of the circumference of a circle to its diameter

Order of Operations (BIDMAS/BODMAS)

What is the order of operations (BIDMAS/BODMAS)?

  • If there are multiple operations then they must be done in the following order:
    • Brackets: ( )
      • Perform the calculation(s) inside any brackets first
    • Indices or Order: ˄, 2, 3, √, etc
      • These include powers, roots, reciprocals
    • Divisions or Multiplications: × or ÷
      • If there are more than one of these then work them out left to right
    • Additions or Subtractions: + or -
      • If there are more than one of these then work them out left to right
  • The acronyms BIDMAS and BODMAS can help you remember

What do I do if the calculation involves fractions, powers or roots?

For fractions there are invisible brackets around the numerator and around the denominator

  • Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11
  • Instead of using brackets we extend the fraction line to show exactly what is on the top and what is on the bottom

For powers there are invisible brackets around the power

  • Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11
  • Instead of using brackets we write the whole to the right of the number and raised

For roots there are invisible brackets under the root

  • Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11
  • Instead of using brackets we extend the line on the root symbol to show exactly what is being rooted
The document Mathematical Operations | Mathematics for GCSE/IGCSE - Year 11 is a part of the Year 11 Course Mathematics for GCSE/IGCSE.
All you need of Year 11 at this link: Year 11
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FAQs on Mathematical Operations - Mathematics for GCSE/IGCSE - Year 11

1. What does BIDMAS/BODMAS stand for?
Ans. BIDMAS/BODMAS stands for Brackets, Indices (or Orders), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right). It is an acronym used to remember the order of operations in mathematics.
2. Why is it important to follow the order of operations in mathematical calculations?
Ans. Following the order of operations ensures that mathematical expressions are evaluated correctly and consistently. If the order is not followed, the result of a calculation may be incorrect.
3. How do you apply the order of operations when solving a mathematical expression?
Ans. To apply the order of operations, you must perform operations inside parentheses or brackets first, then evaluate any exponents or roots, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.
4. Can you provide an example of how the order of operations works in a mathematical expression?
Ans. For example, in the expression 3 + 2 x 4, you would first multiply 2 by 4 to get 8, then add 3 to get a final result of 11. If you were to add 3 and 2 first, the result would be 10, which is incorrect.
5. Why is it important to use parentheses or brackets in mathematical expressions?
Ans. Parentheses or brackets are used to indicate which operations should be performed first, overriding the normal order of operations. They help clarify the intended meaning of an expression and ensure that calculations are carried out correctly.
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