Maths

Question 1

Inverse functions

Answer 1

Example:
F(x) = 3x+2 find f-¹(x)

Let Y = f(x). Y=3x+2
-2 -2
Y-2=3x
/3 /3
(Y-2)/3 = x

     F-¹ (x) = (x-2)/3

Steps
Step One
- Make f(x) become Equal to Y
Step two
- Make X the subject
Step Three
- write the f-¹(x) in terms of x

Question 2

Surds

Answer 2

√a x√b = √ab

√a x √a = a

√a / √b = √a/b

Question 3

Completing the square

Answer 3

X²-2x-2=0

X²-2x=2

(X-1)²-1²=2

(X-1)²-1=2
(X-1)²=3

X=1±√3

Steps

Step one
-Move constant to the right

Step two
-half the nx number (e.g 2x goes to 1) and place inside in the n position (x±n)

Step three
Square the new n value and subtract it from the overall equation e.g (x-1)²-1²=2

Step four
Remove the -n number by adding or subtracting to get to 0 doing the same to the other side.

Step five
Square root both sides removing the (x)²

Step six
Add or subtract the final value in the x bracket, e.g 1±√3=x

Question 4

Circle Theorems

Answer 4

Angle at the center is double the angel at the circumference

Angle in a semi circle is 90*

Angels in the same segment are equal

Opposite angels in cyclic quadrilaterals add to 180

Lengths of tangents are equal if from the same point

Angel between the radium and tangent is always 90

**Alternative segment theorem, The angel between the tangent and the chord is equal to the alternate segment **

Radius may bisect a chord

Question 5

Parts of a circle

Answer 5

Radius
- From the side to the center

Diameter
- From side to the other side through the center point

Circumference
Whole way around the circle

Chord
One side of a circle to another side without going through the center

Arc
A section of the circumference that doesn’t go the full way around

Tangent
Line that touches the circle once and carries on without going inside

Segment
Whole area that is bound by a chord and arc, internal

Sector
Bound by 2 separate radii the area internal

Question 6

Vectors

Answer 6

Vector
- Size and direction e.g length with a direction of facing