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Mathematics A Level > Core 3 Memorisation > Flashcards

Core 3 Memorisation Flashcards

1
Q

What is domain?

A

This is the values that x can take in f(x).

Usually represented with inequalities.

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2
Q

What is the range?

A

This is the values that the product of f(x) can take.

Usually represented with inequalities.

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3
Q

What does one to one mean?

A

It means that for every value in the domain there is only one value for the range and also for every value of the range there is only one domain

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4
Q

What does many to one mean?

A

This means that values in the range can share different values in the domain and also that values in the domain can share values in the range

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5
Q

What is the transformation of y = f(x) to y = f(x - a) + b?

A

Translation a in x-axis and b in y-axis

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6
Q

What is the transformation of y = f(x) into y = -f(x)?

A

Reflection in the line y = 0

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7
Q

What is the transformation of y = f(x) into y = f(-x)?

A

Reflection in the line x = 0

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8
Q

What is the transformation of y = f(x) into y = df(x)?

A

Stretch, scale factor d, in the y direction

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9
Q

What is the transformation of y = f(x) into y = f(x / d) ?

A

Stretch, scale factor d in the x direction

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10
Q

Does cos^-1(x) = 1 / Cos(x)?

A

No

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11
Q

What is sec(x)?

A

This is 1 / Cos(x)

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12
Q

What is cosec(x)?

A

This is 1 / Sin(x)

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13
Q

What is cot(x)?

A

This is 1 / Tan(x)

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14
Q

What is the equation relating tan to sin and cos?

A

tan(x) = sin(x) / cos(x)

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15
Q

What is the derivative of e^x?

A

y = e^x ==> dy/dx = e^x

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16
Q

What is the derivative of e^kx?

A

y = e^kx ==> dy/dx = ke^kx

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17
Q

What is ∫e^x dx?

A

∫e^x dx ==> y = e^x + c

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18
Q

What is ∫e^kx dx?

A

∫e^kx dx ==> y = 1/k e^kx + c

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19
Q

What is ln(y) = ln(e^x)

A

ln(y) = x

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20
Q

What is the derivative of ln(x)?

A

y = ln(x) ==> dy/dx = 1/x

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21
Q

What is ∫1/x dx?

A

∫1/x dx ==> ln(x) + c

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22
Q

What is e^0?

A

e^0 = 1

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23
Q

What does d(e^kx)/dx equal ?

A

d(e^kx)/dx = ke^kx

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24
Q

What is the derivative of Sine?

A

Cosine

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25
Q

What is the derivative of Cosine?

A
  • Sine
26
Q

What is the derivative of - Sine?

A
  • Cosine
27
Q

What is the derivative of - Cosine?

A

Sine

28
Q

What is the chain rule?

A 
y = ln(u)
u = e^kx + 3

dy/dx = (dy/du) x (du/dx)

29
Q

What is the extended chain rule?

A 
y = ln(u) 
u = e^(v) + 3
v = e^kx + 2

dy/dx = (dy/du) x (du/dv) x (dv/dx)

30
Q

What is dy/dx equal to?

A

dy/dx = 1 /dx/dy

31
Q

What is dx/dy equal to?

A

dx/dy = 1/dy/dx

32
Q

What is the formula for relating sin^2(x) and cos^2(x)?

A

sin^2(x) + cos^2(x) = 1

33
Q

What is the product rule used for?

A

dy/dx(u x v) dx

34
Q

What is the product rule?

A

y = u x v

dy/dx = u(dv/dx) + v(du/dx)

35
Q

What is the quotient rule used for?

A

dy/dx(u / v)

36
Q

What is ∫-cos(x)?

A

-sin(x) + c

37
Q

What is ∫-sin(x)?

A

cos(x) + c

38
Q

What is ∫cos(x)?

A

sin(x) + c

39
Q

What is ∫sin(x)?

A

-cos(x) + c

40
Q

what is ∫sec^2(x)?

A

tan(x) + c

41
Q

What is ∫cos(ax + b)?

A

1/a sin(ax + b) +c

42
Q

What is ∫sin(ax + b)?

A

-1/a cos(ax + b) + c

43
Q

What is ∫sec^2(ax+ b)?

A

1/a tan(ax + b) + c

44
Q

What is ∫cosec(ax)cot(ax)?

A
  • 1/a cosec(ax) + c
45
Q

What is ∫sec(ax)tan(ax)?

A

1/a sec(ax) + c

46
Q

What is ∫cosec^2(ax)?

A

-1/a cot(ax) + c

47
Q

What is ∫f’(x)/f(x)

A

ln |f(x)| + c

48
Q

What is ∫tan(ax)?

A

1/a ln | sec(ax) | + c

49
Q

What is ∫cot(ax)?

A

1/a ln | sin(ax) |

50
Q

What is ∫sec(ax)?

A

1/a ln | sec(ax) + tan(ax) | + c

51
Q

What is ∫cosec(ax)?

A

-1/a ln | cosec(ax) + cot(ax) | + c

52
Q

What is the equation when an area bounded by a curve is rotated 2π radians?

A

V = ∫πy^2 dx

V = ∫π(f(x))^2 dx

53
Q

Sin^2 + Cos^2 = ____

A

Sin^2 + Cos^2 = 1

54
Q

Sin^2 = _ ± ______

A

Sin^2 = 1 - Cos^2

55
Q

1 + Tan^2 = _____

A

1 + Tan^2 = Sec^2

56
Q

Tan^2 = ______ ± _

A

Tan^2 = Sec^2 - 1

57
Q

Sec^2 - Tan^2 = _______

A

Sec^2 - Tan^2 = 1

58
Q

1 + Cot^2 = _____

A

1 + Cot^2 = Cosec^2

59
Q

Cot^2 = _______ ± _

A

Cosec^2 - 1

60
Q

Cosec^2 - Cot^2 = ______

A

Cosec^2 - Cot^2 = 1

61
Q

Tan = ______ / _____

A

Tan = Sin / Cos

62
Q

Cot = ______/______

A

Cot = Cos / Sin

Mathematics A Level (1 decks)

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