year9maths

• Cube a number


  It isn't always bigger
• Power of 1


  a = 1
• If same base


  Add powers
• Area


  base x height/2
• Parallelogram


  A=base x height
• Expanding double brackets


  £9 (+3) (x-3) XX3 - x²-2x-15
• Sequences


  A pattern of number, shapes etc.
• Types of sequences


  • Linear/arithmetic
  • Quadratic
  • Geometric
  • Other
• Linear/arithmetic


  Increases/decreases by the SAME amount each time
• Quadratic


  The number it increases/decreases by changes in line with a linear sequence
• Geometric


  Multiply or divide by same amount each time
• Parallelogram


  • -2 pairs of parallel sides
  • -diagonal bisect
  • -opposite angles are equal
  • -adjacent angles add up to 180° (coenteria)
  • -opposite sides same length
• Rhombus


  • -all sides same length
  • -diagonals bisect at 90°
  • -2 pairs of parallel sides
  • -opposite angles equal
  • -adjacent angles add up to 180°
• Rectangle


  • -diagonals cross at 90° (NO bisect)
  • no pairs of parallel lines
  • -2 pairs of equal length sides (opposite)
  • -angles between different length sides
• Trapezium


  • -1 pair of parallel sides
  • NOT-angles between parallel sides: 180
  • -diagonals do Net bisect
• Fractions


  1. +for+ and fractions, use Common denominator

  2. if no co, use lowest common multiple

  3. (mixed numbers, make improper fractions)

  4. for x, just do it

  5. for ÷, use reciprocal
• Solving equations + inequalities

  1. If there are inequality symbols: <, >, ≤, ≥

  2. EG -4 is less than 4

  3. £76 is greater than 6

  4. 5 ≤ 8 is less than or equal to 5

  5. K ≥ 7 is greater than or equal to 7

  6. 3 < g ≤ 5 is greater than 3 and less than or equal to 5
• Square numbers


  Up to 15: 1=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36, 7²=49, 8²=64, 9²=81, 10²=100, 11²=121, 12²=144, 13²=169, 14²=196, 15²=225
• Cube numbers


  1. 5 + 10: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 10³=1000
• Standard Form


  a x 10^n, where a is between 1 and 10
• Percentage calculations


  Initial amount x multiplier
• Solving linear equations


  1. EG 5x+6=21

  2. 5x=15

  3. x=3
• Solving equations with unknowns on both sides

  1. EG 2x+3=6x-5

  2. -4x=-8

  3. x=2
• Solving equations with fractions

  1. EG x+2=5

  2. x=3

  3. EG 2x-c+6=6

  4. 2x-c=0

  5. 2x=c-6

  6. x=(c-6)/2
• The nth term


  EG 5, 10, 15, 20, 25 = 5n
• Angle types


  • Right angle = 90°
  • Reflex angle = between 180° and 360°
  • Acute angle = less than 90°
  • Obtuse angle = between 90° and 180°
• Angles around a straight line


  Add up to 180°
• Angles around a point


  Add up to 360°
• Vertically opposite angles


  Are equal
• Angles in a triangle

  Add up to 180°
• Angles in a quadrilateral

  Add up to 360°
• Parallel lines


  Never meet, same gradient, different y-intercept
• Perpendicular lines


  Meet at 90° (right angle), product of gradients is -1
• Quadratic graphs


  Highest power = 2, make a table of values, draw axis, plot coordinates, join with smooth curve, turning point, x-intercepts (roots)
• Manipulating algebraic expressions


  1. Simplify - collect like terms

  2. Expanding brackets - multiply each term inside by the term outside

  3. Factorising - put back into brackets using the Highest Common Factor
• Prisms


  3D shapes with a constant cross-section, surface area = total area of all faces, volume = area of cross-section x depth
• Parts of a circle

  • Diameter
  • Chord
  • Circumference
  • Radius
  • Major segment
  • Minor segment
  • Major arc
  • Minor arc
  • Tangent
• Straight line graphs


  Gradient = change in y / change in x, y-intercept, midpoint
• Converting units of time

  Adding/subtracting times, converting between hours/minutes
• Speed, distance, time


  1. Distance = speed x time

  2. Speed = distance / time

  3. Time = distance / speed

  4. Average speed = total distance / total time