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YR 9 LAYER TEST 1


PROBABLILITY
P(A) means the probability that a happens

Eg- ½ a chance of getting heads when you toss a coin

P(A') means the probability that A doesn't happen

Eg- ½ a chance of NOT getting heads when you toss a coin.


(P')=1-P(A)
If two events…

Page 2

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TREE DIAGRAMS.
A box contains 2 black counters and 4 white counters. One counter is picked at
random. The tree diagram below shows this.




Suppose the counter is not put back. The contents of the box will be different.
If it was black the box would now contain 1 black…

Page 3

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Algebra
Multiplying out Brackets



(x+2)(x+7)
X²+2x+7x+14


Middle terms cancel
out

Page 4

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Factorising Quadratic Equations




If necessary re-arrange FIRST.
Eg:
x(x-5)=2(x+9)
x²-5x=2x+18
x²-7x=18
x²-7x-18=0
then solve the equation.
Factorise the answer to make...

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(x+2)(x-9)=0
So x can be equal to +2 or ­9


Changing the subject of a formula.
What is the subject?

V=u+at
V would be the subject.

To make u the subject.
V=u+at
Take at from both sides

v-at=u


Similar shapes
Two shapes are mathematically similar if one is an
enlargement…

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If these shapes are similar find x and y?




Similar Triangles
Two triangles are similar if they...
Have the same angles as each other
All pairs of corresponding sides are in the same ratio
Two pairs are in the same ratio and the angle between then is
the same on…

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TRIGONOMETRY.

Page 8

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SOH-CAH-TOA
Sine= opp
hyp
cosine= adj
hyp
tangent= opp
adj

Page 9

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Tan
Finding a Side




tan20= x/7
x=7 X tan20
=2.547

Finding an angle




tanx=3/7

Page 10

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x=tan¹(3/7)

x=23.2


sin




sin20=a/7

a=7 X sin20

=2.39 (3 s.f)


Cos




cos B=5/11

B=cos¹ (5/11)

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