Maths yr9 end of year

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Transformation re-cap

  • Draw reflections, translations, rotations & enlargements.                                                             
  • draw each corner of the shape then join together                                                                      
  •  if a there is a diagonal reflection count the squares diagonally away from the mirror line          
  • Describe each transformation:
  • reflection-equation of the line of symmetry e.g. x=1
  • rotation-centre of roation e.g. (4,5) -- anti/clockwise -- angle e.g. 90o.
  • translation-(move the shape) (top number left or right, bottom number up or down) minus=down/left   +=up/right. Vector e.g. (4/2).
  • enlargement- scale factor e.g. 2 -- C.O.E e.g. (2,3)
  • If S.F. is smaller that 1 the shape will become smaller.If the S.F. is negative it will go to the left side/other side of the C.O.E.
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Similarity and Congruence

Congruence- same size, same shape.

  • SSS- side, side, side.
  • SAS- side, angle, side.(the angle MUST be between the two side)
  • AAS- angle, angle, side. (Side MUST be corrosponding on both)
  • RHS- right angle, hypotenuese, side.

Similarity- same shape, different size ,enlargement.

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Probability

  • Mutually exlusive- outcomes are mutually exclusive if they cannot happen at the same time e.g. the probability of rolling a 2 and a odd number at the same time on a dice is mutually exclusive.
  • If the question says whats is the probability of getting a jack AND a queen you 'x' the fractions together.
  • If the question say what is the probability of getting a jack OR a queen you '+' the fractions together.
  • For tree diagrams id the question says john repalced the ball then the fractions will stay the same on all branches.
  • If its says he didnt replace them then you will minus it away from the demoniator (and the top if needed) e.g 9/10 red balls, john picks a red ball out and doesnt put it back he then picks another one- meaning the next branch would be 8/9.
  • TREE DIAGRAMS.
  • When adding make sure the denominator stays the same.
  • PACK OF CARDS:52
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Trigonometry

# = theta

  • SOH---sin # =opp/hyp
  • CAH---cos # =adj/hyp
  • TOA--- tan # =opp/adj
  • Make sure your caculator is in the D mode.( SHIFT--MODE--3)
  • Steps to solve trig problems=
  • 1. sketch triangle
  • 2. label- hyp(opposite right angle), opp(opposite theta) , adj(the one left).
  • 3.choose formulae (MUST WRITE THE FORMULAE RULE)
  • 4. subsitute in numbers
  • 5.solve
  • If you are finding the theta you must use: sin-1, cos-1, tan-1. 

DO NOT ROUND ANYTHING UNTIL FINAL ANSWER.

 

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Pythagoras

  • Pythagoras theorem-C2=A2+B2.
  • Steps to Pythagoras theorem:
  • 1. sketch and label.
  • 2. write-C2=A2+B2
  • 3. Find the hypotenuse.
  • 4. sun in numbers.
  • 5. solve
  • Pythagorean triples-- main ones-- 3,4,5--5,12,13--8,15,17--2,24,25.
  • Multiple of the pythagoras triples--3,4,5= 6,8,10 + 9,12,15 + 30,40,50.  5,12,13= 10,24,26 + 50,120,130.
  • Pythagoras questions on graphs-
  • 1. plot points
  • 2. join point together
  • 3.count the the spaces between the co-ordinates to get the length(do not count hypotenuse)
  • 4. USE PYTHAGOREAS TO WORK OUT THE HYP.
  • If the hyp already has a marked  length use - C2-B2=A2
  • 3D pythagoras-bbc bitesize
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