Advanced Higher Maths Formulas

Question 1

Trigonometric Identities

Link between ratios (1)

Includes Cos and Sin

Answer 1

cos^2A + sin^2A = 1

Question 2

Trigonometric Identiteis

Link between ratios (2)

Includes Sin, Cos and Tan

Answer 2

TanA = SinA / CosA

Question 3

Trigonometric Identities

Squared (1)

Includes Cos

Answer 3

Cos^2x = 1/2(1+cos2x)

Question 4

Trigonometric Identities

Squared (2)

Includes Sin and Cos

Answer 4

Sin^2x = 1/2(1-cos2x)

Question 5

Trigonometric Identities

Compound Angle (1)

For Cos

Answer 5

Cos(A(+/-)B) = CosACosB (-/+) SinASinB

Question 6

Trigonometric Identities

Compound Angle (2)

For Sin

Answer 6

Sin(A(+/-)B) = SinACosB (+/-) SinBCosA

Question 7

Trigonometric Identities

Double Angle (1)

For sin

Answer 7

Sin(2A) = 2SinACosA

Question 8

Trigonometric Identities

Double Angle (2)

For Cos

Answer 8

Cos(2A) = cos^2A - sin^2A

Question 9

Trigonometric Identities

Link between ratio (3)

Includes tan and sec

Answer 9

Sec^2A = 1+Tan^2A

Question 10

Exact Values

Sin 0, Cos 0, Tan 0

Answer 10

0, 1, 0

Question 11

Exact Values

Sin π/6, Cos π/6, Tan π/6

Answer 11

1/2, √3/2, 1/√3

Question 12

Exact Values

Sin π/4, Cos π/4, Tan π/4

Answer 12

1/√2, 1/√2, 1

Question 13

Exact Values

Sin π/3, Cos π/3, Tan π/3

Answer 13

√3/2, 1/2, √3

Question 14

Exact Values

Sin π/2, Cos π/2, Tan π/2

Answer 14

1, 0, undefined

Question 15

Exact Values

Sin π, Cos π, Tan π

Answer 15

0, -1, 0

Question 16

Exact Values

Sin 3π/2, Cos 3π/2, Tan 3π/2

Answer 16

-1, 0, undefined

Question 17

Exact Values

Sin 2π, Cos 2π, Tan 2π

Answer 17

0, 1, 0

Question 18

Complex Numebers

Complex Number Formula

Answer 18

z = a + bi

Question 19

Complex Numbers

Modulus

Answer 19

l z l = √a^2+b^2

Question 20

Complex Numbers

Argument

Answer 20

tan θ = b/a

Question 21

Complex Numbers

Conjugate

Answer 21

z^- = a - bi

Question 22

Differentiation

Speed

Parametric Equations

Answer 22

Speed = √(dy/dt)^2 + (dx/dt)^2

Question 23

Differentiation

Gradient (direction of movement)

Parametric Equations

Answer 23

dy/dx = (dy/dt)/(dx/dt)

Question 24

Intergration

Volume of solid of revolution about x axis

Answer 24

V = π ∫ y^2 dx

Question 25

# Intergration Volume of solid of rotation about y axis

Answer 25

V = π ∫ x^2 dy

Question 26

# Properties of Functions Odd function

Answer 26

f(-x) = -f(x)

Question 27

# Properties of functions Even function

Answer 27

f(-x) = f(x)

Question 28

# Sequences and Series Arithmetic Sequence

Answer 28

Un = a + (n-1)d

Question 29

# Sequences and Series Geometric Sequence

Answer 29

Un = ar^n-1

Question 30

# Important Identities Sigma Notation | Sigma notation of 1

Answer 30

Σ1 = n

Question 31

# Maclaurin Series e^x

Answer 31

e^x = 1+x+(x^2/2!)+(x^3)/3!)+...+(x^n/n!)+...

Question 32

# Maclaurin Series Sin x

Answer 32

sin x = x - (x^3/3!) + (x^5/5!) - (x^7/7!) + ...

Question 33

# Maclaurins Series Cos x

Answer 33

Cos x = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + ...

Question 34

# Maclaurin Series tan ^-1 | (NOT AS IMPORTANT)

Answer 34

Tan^-1 = x - (x^3/3) + (x^5/5) - (x^7/7) + ...

Question 35

# Maclaurin Series In(1+x) | (NOT AS IMPORTANT)

Answer 35

In(1+x) = x - (x^2/2) + (x^3/3) - (x^4/4) +...

Question 36

# Vectors, Lines and Planes Parametric form of x

Answer 36

x = x1 + at

Question 37

# Vectors, Lines and Planes Parametric form of y

Answer 37

y = y1 + bt

Question 38

# Vectors, Lines and Planes Parametric form of z

Answer 38

z = z1 + ct

Question 39

# Vectors, Lines and Planes Overall parametric equation

Answer 39

x = a + td

Question 40

# Vectors, Lines and Planes Symmetric form

Answer 40

((x-x1)/a) = ((y-y1)/b) = ((z-z1)/c) = t

Question 41

# Vectors, Lines and Planes Vector equation

Answer 41

x.a = a.n

Question 42

# Vector, Lines and Planes Symmetric/Cartesian

Answer 42

lx + my + nz = k (where k = a.n)

Question 43

# Vectors, Lines and Places Angle between 2 lines

Answer 43

Acute angle between their direction vectors

Question 44

# Vectors, Lines and Planes Angle between 2 planes

Answer 44

Acute angle between their normals

Question 45

# Vectors, Lines and Planes Angle between line and plane

Answer 45

90 - (Acute angle between n and d)

Question 46

# Matricies l a b l l c d l | 2 x 2 Matricies

Answer 46

det A = ad - bc and A^-1 = 1/(ad - bc)

Question 47

# Differential Equations Intergrating factor

Answer 47

μ(x) = e^∫P(x) dx

Question 48

# Differential Equations Main Equation

Answer 48

dy/dx + P(x)y = Q(x)

Question 49

# Differential Equations Solution

Answer 49

μ(x)y = ∫ μ(x)Q(x) dx

Question 50

# Nature of Roots Two real and distinct roots (m and n) | Form of general solution

Answer 50

y = Ae^mx + Be^nx

Question 51

# Nature of Roots Real and equal roots (m) | Form of general solution

Answer 51

y = Ae^mx + Bxe^mx

Question 52

# Nature of Roots Complex conjugate (m = p(+/-) iq) | Form of general solution

Answer 52

y = e^px (Acosq + Bsinqx)

Question 53

# Particular Intergral Sin(ax) or Cos(ax) | If right hand sign contains ... try ...

Answer 53

y = Pcos(ax) + Qsin(ax)

Question 54

# Particular Intergral e^ax | If right hand sign contains ... try ...

Answer 54

y = Pe^ax

Question 55

# Particular Intergral Linear expression y = ax + b | If right hand sign contains ... try ...

Answer 55

y = Px + Q

Question 56

# Particular Intergral Quadratic expression y = ax^2 + bx + c | If right hand sign contains ... try ...

Answer 56

y = Px^2 + Qx + R