maths, proportion, formulae, sequences and inequalities

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  • maths
    • Number patterns
      • Sequences
        • each number is a term
        • eg. Square no.s, Cube no.s, powers of 2, trisngular no.s etc.
      • finding the nth term
        • nth  term of a linear sequence is an+b
          • a = common difference
          • So, if the nth term is the first term, add in value of first term.
          • e.g. 3 = 2 x 1 + b
            • b = 1
            • nth term is 2n + 1
          • use it to find b
    • Inequalities
      • solved in a similar way to equations
      • Dividing by a negative reverses direction of inequality
      • On a number line
        • solid circle means included
        • hollow circle means excluded
      • Graphs of inequalities
        • A graph is used to find a region containing the values that satisfy an equation
        • the line of the inequality is the boundary
          • An excluding boundary is a dotted line
          • Including boundary is solid.
        • Used in linear programming
          • Usd to solve allocation problems
    • Formulae
      • Need to be able to write a formula for given information
      • Using formulae
        • Describes relationship between 2 or more variables
        • Must have an = in it
      • Substituting into formula
        • Similar to substituting into expressions
        • replace letters with the values given
        • work out value on calculator
      • rearranging formulae
        • subject of a formula is the letter on its own on one side of =
        • What you do to one side, do to the other
        • Collect all of subject terms that appear together
      • Quadratic formulae
        • Used when completing the square and factorisation don't work.
        • x= -b+ sqrt b2 - 4ac/2a
    • Proportion
      • Direct Proportion
        • As one increases, so does the oher
        • Graph goes through the origin
        • Graph is a straight line
      • Inverse proportion
        • When y is multiplied by a number, x is divided by that number
        • graphs of y against x go to infinity when one of them Is 0.
        • A curve
      • Variation
        • include statements such as 'd varies as the square of x'
        • E.g, the value of a diamond varies directly with the square of its weight
          • So, is a diamond weighing 5g is 2500, ow heavy is one worth 5000
        • 1. change sentence into proportionality statement
          • So, is a diamond weighing 5g is 2500, ow heavy is one worth 5000
        • 2. replace proportionality symbol wit = k to make an equation. V=kw2
        • 3. substitute in values in question
        • rearrange to find value of k
        • 5. put k value back into equation, now answer
  • Proportion
    • Direct Proportion
      • As one increases, so does the oher
      • Graph goes through the origin
      • Graph is a straight line
    • Inverse proportion
      • When y is multiplied by a number, x is divided by that number
      • graphs of y against x go to infinity when one of them Is 0.
      • A curve
    • Variation
      • include statements such as 'd varies as the square of x'
      • E.g, the value of a diamond varies directly with the square of its weight
        • 1. change sentence into proportionality statement
          • 2. replace proportionality symbol wit = k to make an equation. V=kw2
          • 3. substitute in values in question
          • rearrange to find value of k
          • 5. put k value back into equation, now answer

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