Core 3 Memorisation Flashcards
What is domain?
This is the values that x can take in f(x).
Usually represented with inequalities.
What is the range?
This is the values that the product of f(x) can take.
Usually represented with inequalities.
What does one to one mean?
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
What does many to one mean?
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
What is the transformation of y = f(x) to y = f(x - a) + b?
Translation a in x-axis and b in y-axis
What is the transformation of y = f(x) into y = -f(x)?
Reflection in the line y = 0
What is the transformation of y = f(x) into y = f(-x)?
Reflection in the line x = 0
What is the transformation of y = f(x) into y = df(x)?
Stretch, scale factor d, in the y direction
What is the transformation of y = f(x) into y = f(x / d) ?
Stretch, scale factor d in the x direction
Does cos^-1(x) = 1 / Cos(x)?
No
What is sec(x)?
This is 1 / Cos(x)
What is cosec(x)?
This is 1 / Sin(x)
What is cot(x)?
This is 1 / Tan(x)
What is the equation relating tan to sin and cos?
tan(x) = sin(x) / cos(x)
What is the derivative of e^x?
y = e^x ==> dy/dx = e^x
What is the derivative of e^kx?
y = e^kx ==> dy/dx = ke^kx
What is ∫e^x dx?
∫e^x dx ==> y = e^x + c
What is ∫e^kx dx?
∫e^kx dx ==> y = 1/k e^kx + c
What is ln(y) = ln(e^x)
ln(y) = x
What is the derivative of ln(x)?
y = ln(x) ==> dy/dx = 1/x
What is ∫1/x dx?
∫1/x dx ==> ln(x) + c
What is e^0?
e^0 = 1
What does d(e^kx)/dx equal ?
d(e^kx)/dx = ke^kx
What is the derivative of Sine?
Cosine
What is the derivative of Cosine?
- Sine
What is the derivative of - Sine?
- Cosine
What is the derivative of - Cosine?
Sine
What is the chain rule?
y = ln(u) u = e^kx + 3
dy/dx = (dy/du) x (du/dx)
What is the extended chain rule?
y = ln(u) u = e^(v) + 3 v = e^kx + 2
dy/dx = (dy/du) x (du/dv) x (dv/dx)
What is dy/dx equal to?
dy/dx = 1 /dx/dy
What is dx/dy equal to?
dx/dy = 1/dy/dx
What is the formula for relating sin^2(x) and cos^2(x)?
sin^2(x) + cos^2(x) = 1
What is the product rule used for?
dy/dx(u x v) dx
What is the product rule?
y = u x v
dy/dx = u(dv/dx) + v(du/dx)
What is the quotient rule used for?
dy/dx(u / v)
What is ∫-cos(x)?
-sin(x) + c
What is ∫-sin(x)?
cos(x) + c
What is ∫cos(x)?
sin(x) + c
What is ∫sin(x)?
-cos(x) + c
what is ∫sec^2(x)?
tan(x) + c
What is ∫cos(ax + b)?
1/a sin(ax + b) +c
What is ∫sin(ax + b)?
-1/a cos(ax + b) + c
What is ∫sec^2(ax+ b)?
1/a tan(ax + b) + c
What is ∫cosec(ax)cot(ax)?
- 1/a cosec(ax) + c
What is ∫sec(ax)tan(ax)?
1/a sec(ax) + c
What is ∫cosec^2(ax)?
-1/a cot(ax) + c
What is ∫f’(x)/f(x)
ln |f(x)| + c
What is ∫tan(ax)?
1/a ln | sec(ax) | + c
What is ∫cot(ax)?
1/a ln | sin(ax) |
What is ∫sec(ax)?
1/a ln | sec(ax) + tan(ax) | + c
What is ∫cosec(ax)?
-1/a ln | cosec(ax) + cot(ax) | + c
What is the equation when an area bounded by a curve is rotated 2π radians?
V = ∫πy^2 dx
V = ∫π(f(x))^2 dx
Sin^2 + Cos^2 = ____
Sin^2 + Cos^2 = 1
Sin^2 = _ ± ______
Sin^2 = 1 - Cos^2
1 + Tan^2 = _____
1 + Tan^2 = Sec^2
Tan^2 = ______ ± _
Tan^2 = Sec^2 - 1
Sec^2 - Tan^2 = _______
Sec^2 - Tan^2 = 1
1 + Cot^2 = _____
1 + Cot^2 = Cosec^2
Cot^2 = _______ ± _
Cosec^2 - 1
Cosec^2 - Cot^2 = ______
Cosec^2 - Cot^2 = 1
Tan = ______ / _____
Tan = Sin / Cos
Cot = ______/______
Cot = Cos / Sin
