Maths

• Exterior angle of a regular polygon


  Equals 360 degrees divided by the number of sides
• Sum of interior angles of a polygon


  Equals (n - 2) * 180 degrees, where n is the number of sides
• Angles on a straight line


  Add up to 180 degrees
• Finding missing angle in a quadrilateral


  Calculate one missing angle using angles on a straight line

  2. Use the formula for sum of interior angles to calculate the other missing angle
• Rearranging formulas to get a particular letter by itself


  1. Get the letter by itself

  2. Get rid of other terms

  3. Divide/multiply both sides

  4. Swap sides to get letter on left
• Pythagoras


  1. a^2 + b^2 = c^2

  2. Where c is the hypotenuse
• 5^2 + 4^2


  = x^2
• 8^2 + y^2


  = 12^2
• Finding distance between two coordinates

  1. Use Pythagoras

  2. a = x2 - x1

  3. b = y2 - y1

  4. c = √(a^2 + b^2)
• Linear sequence


  A sequence where the difference between each term is constant
• Linear sequence


  • 5, 8, 11, 14, ...
• Finding the nth term of a linear sequence


  1. Identify the common difference

  2. Write the multiples of the common difference (e.g. 3n)

  3. Add the starting value (e.g. +2)
• The nth term formula for the sequence 5, 8, 11, 14, ... is 3n + 2
• Nth term


  A formula that can be used to find any term in a sequence
• The nth term is useful for finding terms in the sequence without having to continue the sequence
• Finding the first 5 terms using the nth term


  Substitute n = 1, 2, 3, 4, 5 into the formula
• Decreasing sequence


  A sequence where the difference between each term is negative
• Decreasing sequence


  • 20, 15, 10, 5
• Finding the nth term of a decreasing sequence


  1. Identify the common difference (e.g. -5)

  2. Write the multiples of the common difference (e.g. -5n)

  3. Add the starting value (e.g. +25)
• The nth term formula for the sequence 20, 15, 10, 5 is -5n + 25
• Solving questions involving patterns

  1. Identify the pattern

  2. Extend the pattern to the required term

  3. Apply the pattern to solve the question
• Patterns made from grey tiles

  • Pattern 1: 3 grey tiles, 1 white tile in the middle
  • Pattern 2: 7 grey tiles, 2 white tiles
  • Pattern 3: 10 grey tiles, 3 white tiles
• Drawing pattern number 4

  1. Add 1 more grey tile to the top row

  2. Add 1 more grey tile to the middle row

  3. Add 1 more grey tile to the bottom row
• As the pattern number increases


  The number of grey tiles increases by 3
• The quickest way to find the number of grey tiles in pattern 10 is to continue the sequence
• The number of grey tiles in pattern 10 is 31
• Jenny needs 46 grey tiles for pattern 18, but this is incorrect
• Explaining how Jenny is right

  1. Continue the sequence for 18 terms

  2. Be very careful when adding the numbers in the sequence
• nth term


  An expression that gives the number of grey tiles in the mth term of the sequence
• The nth term for this sequence is 3n + 1
• Patterns made from sticks


  • Pattern 1: 5 sticks
  • Pattern 2: 9 sticks
  • Pattern 3: 13 sticks
• Drawing pattern number 4


  Add another rectangle and diagonal line to the previous pattern
• The number of sticks in pattern 8 is 33
• Josh cannot make a pattern using all 106 sticks, as the sequence only contains odd numbers
• Scenario with two parallel lines and a transversal


  • Two groups of angles
  • Each group contains two different angles
  • The two different angles always add up to 180 degrees
  • Vertically opposite angles are always the same
• Using rules to find unknown angles

  1. Alternate angles are the same

  2. Corresponding angles are the same

  3. Allied angles add up to 180 degrees
• Alternate angles are the two angles found in the corners of a Z shape
• Corresponding angles are the two angles found in an F shape
• Allied angles are the interior angles of a C shape
• Allied angles, co-interior angles, and interior angles all mean the same thing