# 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
• 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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