Block Five

Question 1

How to solve an simultaneous equation

Answer 1

• 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

Question 2

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

Answer 2

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

Question 3

Pythagoras theroem in right angles triangles

Answer 3

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

Question 4

how to find the unknown side using pythagoras theroem

Answer 4

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

Question 5

What can pythagoras theroem by used to prove

Answer 5

whether a triangle is right angled or not

Question 6

How to solve an equation using pythagoras’ theroem

Answer 6

C2 = X
A2 + B* 2 = X
1.32 = 1.69
0.52 + 1.2 *2 = 1.69
so by the converse of pythagoras this is a right angles triangle

Question 7

What must you write in order to get full marks

Answer 7

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

Question 8

What is an amplitude of the graph

Answer 8

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

Question 9

what is the period of a graph

Answer 9

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

Question 10

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

Answer 10

amplitude

Question 11

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

Answer 11

if the graph has moved up of down

Question 12

how to identify a cos graph

Answer 12

a cos graph starts at the max amplitude and goes down

Question 13

how to identify a sin graph

Answer 13

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

Question 14

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

Answer 14

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

Question 15

what does sin ( x + a ) mean

Answer 15

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

Question 16

how to identify a tan graph

Answer 16

the amplitude is infinite

Question 17

What is the period of a tan graph

Answer 17

y = tanx is 180

Question 18

Describe what is positive in a cast diagram

Answer 18

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

Question 19

solve Sinx = 1/2

Answer 19

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

Question 20

solve 5tanx + 2 = 0

Answer 20

• 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

Question 21

what does tanx equal

Answer 21

tanx = sinx / cosx

Question 22

what does 1 equal

Answer 22

sin2x + cos2x = 1

Question 23

when solving trig indenties

Answer 23

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

Question 24

what are exact values

Answer 24

they can be used to solve trig equations without a calculator

Question 25

what does SohCahToa stand for

Answer 25

Sin = opp/ hypot
Cos = adj / hypot
Tan = opp / adj

Question 26

describe the yellow triangle in exact values

Answer 26

hypot = 2
adj = 1
opp = root 3
bottom left angle = 60
top angle = 30
right angle = 90

Question 27

describe the blue triangle in exact values

Answer 27

opp = 1
adj = 1
hypot= root 2
inside angles = 45
right angle = 90

Question 28

what do we use SohCahToa for

Answer 28

to find any missing angle or side in a right angled triangle only

Question 29

how to solve 3D pythagoras

Answer 29

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

Question 30

What is a chord

Answer 30

a line joins from one side to the other side of a circle is called a chord

Question 31

What is the biggest chord in a circle

Answer 31

diameter

Question 32

when is pythagoras theroem used in a circle

Answer 32

Where a right angles triangle can be formed

Question 33

How do the radius and chord interact

Answer 33

a radius and chord intersect at the right angle
radius divides chord in equal parts

Question 34

How to calculate the height of a circle

Answer 34

Take away the radius from overall height
use pythagoras theron to find height of triangle and then add or subtract that onto your value