Last Minute Maths

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Recurring Decimals

  • Write the recurring decimal equal to n, and write out some of its digits
  • Multiply both sides by 10 for one recurring digit, 100 for two recurring digits etc.
  • Subtract n to remove the recurring part
  • Divide both sides by 99 to write as a fraction
  • Simplify the fraction
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Inequalities

On a number line:

  • An open circle shows that that number is NOT included
  • A closed circle shows it IS included
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Completing the Square

x^2 + 2bx + c = (x + b)^2 - b^2 + c

  • Remove the square from x
  • Half the number before b
  • Put the above together in a bracket and square them
  • Take b^2 away from the expression
  • Add/subtract what is necessary to get to the original c
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Tranformations of Graphs

  • y = f(x) + a = move UP a units
  • y = f(x) - a = move DOWN a units
  • y = f(x + a) = move LEFT a units
  • y = f(x - a) = move RIGHT a units
  • y = af(x) = stretch in VERTICAL direction, SF a
  • y = f(ax) = stretch in HORIZONTAL direction, SF 1/a
  • y = -f(x) = reflection in X-axis
  • y = f(-x) = reflection in Y-axis
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Density

Density = mass/volume

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Enlargements

  • SF = enlarged length/original length
  • Draw lines from each vertex through the centre of enlargement
  • The corresponding point is SF times the distance from the centre of enlargement
  • If the SF is negative the enlargement will be on the opposite side of the centre of enlargement and upside down
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