Block Five Flashcards

1
Q

How to solve an simultaneous equation

A
  • times each sun to have at least one term the same number
  • if it is the same sign you subtract
  • if it is a different sign you add
    you then factorise your find one term such as x
  • substitute the answer in to find the other term
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2
Q

What must you do to get full marks when solving simultaneous equations

A

you just write a sentence to clarify your answer
you must ensure you write just p and not £0.9p

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3
Q

Pythagoras theroem in right angles triangles

A

a2 + b2 = c*2
c= the hypotenuse - longest side

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4
Q

how to find the unknown side using pythagoras theroem

A

a2 + b2 = c2
change the subject
18
2 = y2 - 92
y2 = 324 - 81
y
2 = 243
y= 15.6m

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5
Q

What can pythagoras theroem by used to prove

A

whether a triangle is right angled or not

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6
Q

How to solve an equation using pythagoras’ theroem

A

C2 = X
A
2 + B* 2 = X
1.32 = 1.69
0.5
2 + 1.2 *2 = 1.69
so by the converse of pythagoras this is a right angles triangle

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7
Q

What must you write in order to get full marks

A

you must write
so by the converse of pythagoras this is / is not a right angled triangle

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8
Q

What is an amplitude of the graph

A

half the distance between the maximum and minimum values of the graph

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9
Q

what is the period of a graph

A

the distance along the x axis over which the graph completes one full wave
ther period of y = sinx and y = cosx is 360

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10
Q

in the equation y = a Cosx + b
what does a mean

A

amplitude

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11
Q

in the equation y = a Cosx + b
what does b mean

A

if the graph has moved up of down

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12
Q

how to identify a cos graph

A

a cos graph starts at the max amplitude and goes down

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13
Q

how to identify a sin graph

A

a sin graph starts at zero and goes up to the max value

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14
Q

in the equation y = a Sin ( bx ) + c
what does bx mean

A

if the period has changed
e.g Y = Sin 2 x
period = 180

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15
Q

what does sin ( x + a ) mean

A

sin ( x - a ) and cos ( x - a )
is if graph has moved to the right

sin ( x + a ) and cos ( x + a )
is if graph has moved to the left

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16
Q

how to identify a tan graph

A

the amplitude is infinite

17
Q

What is the period of a tan graph

A

y = tanx is 180

18
Q

Describe what is positive in a cast diagram

A

x all is positive
180 - x sin is positive
180 + x cos is positive
360 - x tan is positive

19
Q

solve Sinx = 1/2

A

x = Sin-1 ( 1/2 )
- using the cast diagram we know that because the fraction is positive we have to look at the two sectors which have a positive value for sin

x = 30 , 180 - 30
x = 30 , 150

20
Q

solve 5tanx + 2 = 0

A
  • rearrange tanx = - 2/5
    this time the fraction is negitive so we have to pick the two sections when tan is negitive

x = 180-60 , 180+60
x = 120 , 240

21
Q

what does tanx equal

A

tanx = sinx / cosx

22
Q

what does 1 equal

A

sin2x + cos2x = 1

23
Q

when solving trig indenties

A

you just make sure the left side matches the right hand side

24
Q

what are exact values

A

they can be used to solve trig equations without a calculator

25
what does SohCahToa stand for
Sin = opp/ hypot Cos = adj / hypot Tan = opp / adj
26
describe the yellow triangle in exact values
hypot = 2 adj = 1 opp = root 3 bottom left angle = 60 top angle = 30 right angle = 90
27
describe the blue triangle in exact values
opp = 1 adj = 1 hypot= root 2 inside angles = 45 right angle = 90
28
what do we use SohCahToa for
to find any missing angle or side in a right angled triangle only
29
how to solve 3D pythagoras
first you must find d by using pythagoras AD2 = length x bridth AD = root L x B then find the other triangle AB * 2 = root ( LxB) + H AB = root 90 eg AB = 3 root 10 cm
30
What is a chord
a line joins from one side to the other side of a circle is called a chord
31
What is the biggest chord in a circle
diameter
32
when is pythagoras theroem used in a circle
Where a right angles triangle can be formed
33
How do the radius and chord interact
a radius and chord intersect at the right angle radius divides chord in equal parts
34
How to calculate the height of a circle
Take away the radius from overall height use pythagoras theron to find height of triangle and then add or subtract that onto your value