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Advanced Higher Maths > Advanced Higher Maths Formulas > Flashcards

Advanced Higher Maths Formulas Flashcards

To memorize the formulas

1
Q

Trigonometric Identities

Link between ratios (1)

Includes Cos and Sin

A

cos^2A + sin^2A = 1

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2
Q

Trigonometric Identiteis

Link between ratios (2)

Includes Sin, Cos and Tan

A

TanA = SinA / CosA

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3
Q

Trigonometric Identities

Squared (1)

Includes Cos

A

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

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4
Q

Trigonometric Identities

Squared (2)

Includes Sin and Cos

A

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

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5
Q

Trigonometric Identities

Compound Angle (1)

For Cos

A

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

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6
Q

Trigonometric Identities

Compound Angle (2)

For Sin

A

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

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7
Q

Trigonometric Identities

Double Angle (1)

For sin

A

Sin(2A) = 2SinACosA

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8
Q

Trigonometric Identities

Double Angle (2)

For Cos

A

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

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9
Q

Trigonometric Identities

Link between ratio (3)

Includes tan and sec

A

Sec^2A = 1+Tan^2A

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10
Q

Exact Values

Sin 0, Cos 0, Tan 0

A

0, 1, 0

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11
Q

Exact Values

Sin π/6, Cos π/6, Tan π/6

A

1/2, √3/2, 1/√3

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12
Q

Exact Values

Sin π/4, Cos π/4, Tan π/4

A

1/√2, 1/√2, 1

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13
Q

Exact Values

Sin π/3, Cos π/3, Tan π/3

A

√3/2, 1/2, √3

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14
Q

Exact Values

Sin π/2, Cos π/2, Tan π/2

A

1, 0, undefined

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15
Q

Exact Values

Sin π, Cos π, Tan π

A

0, -1, 0

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16
Q

Exact Values

Sin 3π/2, Cos 3π/2, Tan 3π/2

A

-1, 0, undefined

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17
Q

Exact Values

Sin 2π, Cos 2π, Tan 2π

A

0, 1, 0

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18
Q

Complex Numebers

Complex Number Formula

A

z = a + bi

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19
Q

Complex Numbers

Modulus

A

l z l = √a^2+b^2

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20
Q

Complex Numbers

Argument

A

tan θ = b/a

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21
Q

Complex Numbers

Conjugate

A

z^- = a - bi

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22
Q

Differentiation

Speed

Parametric Equations

A

Speed = √(dy/dt)^2 + (dx/dt)^2

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23
Q

Differentiation

Gradient (direction of movement)

Parametric Equations

A

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

24
Q

Intergration

Volume of solid of revolution about x axis

A

V = π ∫ y^2 dx

25
Q

Intergration

Volume of solid of rotation about y axis

A

V = π ∫ x^2 dy

26
Q

Properties of Functions

Odd function

A

f(-x) = -f(x)

27
Q

Properties of functions

Even function

A

f(-x) = f(x)

28
Q

Sequences and Series

Arithmetic Sequence

A

Un = a + (n-1)d

29
Q

Sequences and Series

Geometric Sequence

A

Un = ar^n-1

30
Q

Important Identities

Sigma Notation

Sigma notation of 1

A

Σ1 = n

31
Q

Maclaurin Series

e^x

A

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

32
Q

Maclaurin Series

Sin x

A

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

33
Q

Maclaurins Series

Cos x

A

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

34
Q

Maclaurin Series

tan ^-1

(NOT AS IMPORTANT)

A

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

35
Q

Maclaurin Series

In(1+x)

(NOT AS IMPORTANT)

A

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

36
Q

Vectors, Lines and Planes

Parametric form of x

A

x = x1 + at

37
Q

Vectors, Lines and Planes

Parametric form of y

A

y = y1 + bt

38
Q

Vectors, Lines and Planes

Parametric form of z

A

z = z1 + ct

39
Q

Vectors, Lines and Planes

Overall parametric equation

A

x = a + td

40
Q

Vectors, Lines and Planes

Symmetric form

A

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

41
Q

Vectors, Lines and Planes

Vector equation

A

x.a = a.n

42
Q

Vector, Lines and Planes

Symmetric/Cartesian

A

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

43
Q

Vectors, Lines and Places

Angle between 2 lines

A

Acute angle between their direction vectors

44
Q

Vectors, Lines and Planes

Angle between 2 planes

A

Acute angle between their normals

45
Q

Vectors, Lines and Planes

Angle between line and plane

A

90 - (Acute angle between n and d)

46
Q

Matricies

l a b l
l c d l

2 x 2 Matricies

A

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

47
Q

Differential Equations

Intergrating factor

A

μ(x) = e^∫P(x) dx

48
Q

Differential Equations

Main Equation

A

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

49
Q

Differential Equations

Solution

A

μ(x)y = ∫ μ(x)Q(x) dx

50
Q

Nature of Roots

Two real and distinct roots (m and n)

Form of general solution

A

y = Ae^mx + Be^nx

51
Q

Nature of Roots

Real and equal roots (m)

Form of general solution

A

y = Ae^mx + Bxe^mx

52
Q

Nature of Roots

Complex conjugate
(m = p(+/-) iq)

Form of general solution

A

y = e^px (Acosq + Bsinqx)

53
Q

Particular Intergral

Sin(ax) or Cos(ax)

If right hand sign contains … try …

A

y = Pcos(ax) + Qsin(ax)

54
Q

Particular Intergral

e^ax

If right hand sign contains … try …

A

y = Pe^ax

55
Q

Particular Intergral

Linear expression y = ax + b

If right hand sign contains … try …

A

y = Px + Q

56
Q

Particular Intergral

Quadratic expression
y = ax^2 + bx + c

If right hand sign contains … try …

A

y = Px^2 + Qx + R

Advanced Higher Maths (1 decks)

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