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Maths Formulae To Remember > Maths Formulas > Flashcards

Maths Formulas Flashcards

1
Q

Chain rule

A

Dy/dx = dy/du x du/dx

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2
Q

Product rule

A

Dy/dx = u(dv/dx) + v(du/dx). u and v are the constants

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3
Q

Quotient rule

A

dy/dx = v(du/dx) - u(du/dx) all divided by v squared ( remember v is the denominator)

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4
Q

Implicit differentiation

A

f(y) = f’(y) x dy/dx

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5
Q

Reciprocal of dy/dx

A

1/(dx/dy)

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6
Q

Parametric differentiation

A

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

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7
Q

If f’(x) is less than 0, the function is …

A

Decreasing

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8
Q

If f’(x) is = 0, the function is…

A

Stationary

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9
Q

If f’(x) is greater than 0, the function is …

A

Increasing

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10
Q

If f’’(x) is less than 0, the point is…

A

Maximum - also concave

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11
Q

If f’’(x) is =0, the point is

A

A point of inflection

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12
Q

If f’’(x) is greater than 0, the point is…

A

Minimum - is convex

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13
Q

Derivative of e to the power of x

A

E to the power of x

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14
Q

Derivative of ln (x)

A

1/x

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15
Q

Derivative of sinx

A

Cosx

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16
Q

Derivative of cosx

A

-sinx

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17
Q

Derivative of tanx

A

sec squared x

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18
Q

Derivative of secx

A

secxtanx

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19
Q

Derivative of cotx

A

-cosec squared x

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20
Q

Derivative of cosecx

A

-cosecxcotx

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21
Q

How do you work out the other answers for sinx ?

A

180 - x / cos (90-x)

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22
Q

How do you work out the other answers for cosx?

A

360 - x / sin (90-x)

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23
Q

How do you work out the other answers for tanx?

A

X + 180

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24
Q

1 + tan squared x is = to ?

A

Sec squared x

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25
1 + cot squared x is equal to?
Cosec squared x
26
Sin2x double angle formulae?
2sinxcosx
27
Cos2x double angle forumale?
Either cos squared x - sin squared x OR 2cos squared x - 1 OR 1 - 2 sin squared x
28
Tan2x double angle forumale?
2tanx/1- tan squared x
29
F(x) + a transformation
Y- direction moves up a
30
F(x+a) transformation
X direction moves left a (-a)
31
Af(x) transformation
Stretch y-direction by a
32
F(ax) transformation
Stretch x-direction by 1/a
33
-f(x) transformation
Reflection in the x-axis
34
F(-x) transformation
Reflection in the y-axis
35
/f(x)/ transformation
Anything below the x-axis goes up
36
f(/x/) transformation
Anything right of the y-axis goes left
37
Integral of cosx
Sinx
38
Integral of sinx
-cosx
39
Integral of sec squared x
Tanx
40
Integral of secxtanx
Secx
41
Integral of cosec squared x
-cotx
42
Integral of cosecxcotx
-cosecx
43
Integral of f’(ax+b)
1/af(ax+b)
44
Steps for the substitution rule
Find u, find du in terms of dx, change the limits to u
45
Integration by parts formula
uv- integral of (du/dx x v)
46
Parametric integration formula
Integral of y x dx/dt dt, change the limits
47
A to the power of n x A to the power of m
A to the power of n+m
48
A to the power of n/ A to the power of m
A to the power of n-m
49
(A to the power of n) to the power of m
A to the power of n x m
50
A to the power of -n
1/ a to the power of n
51
A to the power of 1/n
A to the root of n
52
A to the power of 0
1
53
Log a x = n
A to the power of x = n
54
Lnxy =
Lnx + lny
55
Ln x/y =
Lnx - lny
56
Lnx to the power of k
Klnx
57
Ln 1/x =
-lnx
58
Lne =
1
59
Ln1 =
0
60
Cosine rule
A squared = b squared + c squared - 2bccosA
61
Sine rule
SinA/a = SinB/b = SinC/c
62
Area of a triangle formula
1/2 x ab x sinC
63
Arc length
R x Theta
64
Area of a sector
1/2 x r squared x theta
65
Segment area
1/2 x r squared x (theta - sin theta )
66
Geometric nth term
Un = a x r to the power of n-1
67
Arithmetic nth term
Un = a + (n-1)d
68
Unit vector =
(1/ magnitude of a) x a
69
Volume of a sphere
4/3 pi x r cubed
70
Volume of a cylinder
Pi x r squared x h
71
Area of a cylinder
2 pi r h + 2 pi r squared
72
Area of a sphere
4 pi r squared
73
Integral of a to the power of x
A to the power of x lna

Maths Formulae To Remember (1 decks)

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