Chapter 1 (Trigonometry: Sine and Cosine rules)

Sine Rule

asin A

= bsinB

= csinC

Cosine Rule

a2=b2+c2−2bc cos A

Chapter 2 (Trigonometry)

No notes

Chapter 3 (Vectors)

Equal vectors = Vectors with same magnitude AND direction

Vector addition and subtraction

A⃗B=a B⃗A=−a

B⃗C=b C⃗B=−b

A⃗C=a+b C⃗A=−a+(−b)

Scalar multiplication of vectors

k (ab)=(kakb)Null vector

a+b=0

Colum vector

( xy ) x=distancemoved alongthe x−axisy=distancemoved alongthe y−axis

(ab)+(cd )=(a+cb+d)Magnitude of vector

Magnitude of ( xy )=|( xy )|=√x2+ y2

Position vector = vectors that have their initial positions at the origin

Chapter 4 (Graphs)

No notes

Chapter 5 (Matrices)

Column vector = only has one column

352

Matrices = r x c (r = row, c = column)

3 53 9

= 2 x 2 (2 by 2)

4 1 33 8 5

= 2 x 3 (2 by 3)

Addition and subtraction = Only possible with same kind of Matrices

3 28 6

+6 85 3

= 9 1013 9

8 56 89 4

−1 75 52 4

=7 −21 37 0

3 64 5

+4 5 17 2 5

=N . A

Equal matrices = Matrices that are the same type and have same elements

Zero/Null matrices = 0 00 0

∨0 0 00 0 00 0 0

Identity matrix = 1 00 1

∨1 0 00 1 00 0 1

Scalar multiplication

k 5 74 8

=5k 7k4k 8k

Matrix multiplication

(r 1x c1 ) x (r2 x c2 )=(r 1x c 2)

c 1=r 2(MUST ‼‼)

a bc de f

x g h ij k l

=ag+bj ah+bk ai+blcg+dj ch+dk ci+dleg+ fj eh+ fk ei+ fl

a bc d

xe fg hi j

=N . A

Chapter 6 (Probabilities)

Probability

P (E )= No .of favourable occurencesNo .of equally possible occurences

,E=anything

Independent = the occurrences of one event does not affect the occurrences of another (E.G. The rolling of one die does not affect the result of another die)

Mutually exclusive = the outcomes cannot occur at the same time (E.G. Drawing a red card and a clubs at the same time from a deck of playing cards)