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These are what you are expected to be able to solve BEFORE undergoing university education.

Differential Calculus

$÷{d}{dx}(3⋅(\sin x)²+4⋅(\cos x)³)=?$
$÷{d}{dx}(x⋅\sin x+x²⋅\cos x+x³⋅√x)=?$
$÷{d}{dx}(e^{3⋅x})=?$
$÷{d}{dx}(\ln(1+x))=?$
$÷{d}{dx}(√{\sin x})=?$
$÷{d}{dx}(x^x)=?$

Integral Calculus

$∫(\sin x)²⋅dx=?$
$∫÷{1}{\cos x}⋅dx=?$
$∫(\tan x)⋅dx=?$
$∫\limits_{-÷{π}{2}}^{÷{π}{2}} (\sin x+3⋅\cos x+2⋅\tan x)⋅dx=?$
$∫\limits_{x-1}^{x+1} u^x⋅du=?$
$∫\limits_{1}^{2} e^{x+3}⋅dx=?$
$∫\limits_{0}^{1} (x²+3⋅x+7)⋅dx=?$
$∫\limits_{0}^{1} ({√{x³}}+\sqrt[3]{x}-\sqrt[7]{x⁵})⋅dx$
$∫x^{n²+n}⋅dx=?$
$∫\limits_{-1}^{1} x⋅e^x⋅dx=?$

Annoying Integral Calculus

$∫(\cos x)^3⋅(\sin x)^5⋅dx=?$
$∫\limits_{0}^{1} x²⋅(\ln x)⋅dx=?$
$∫(\ln x)²⋅dx=?$
$∫÷{1}{x⋅\ln x}⋅dx=?$
$∫(\arctan x)⋅dx=?$
$∫e^{√x}⋅dx=?$
$∫÷{1+e^x}{1-e^x}⋅dx=?$

Complex Numbers

in Polar Coordinates = ?
in Polar Coordinates = ?
in Polar Coordinates = ?
graphical
graphical
graphical
$÷{z_1}{z_2}$ graphical
graphical
Solve for z.
Solve for z.
Solve for z.
Solve for z.
Solve for z.

Trigonometry

$\sin 405°=?$
$\cos 405°=?$
$\tan 405°=?$
$\sin -240°=?$
$\cos -240°=?$
$\tan -240°=?$
$\sin ÷{π}{2}=?$
$\cos ÷{π}{2}=?$
$\tan ÷{π}{2}=?$
$\sin ÷{π}{3}=?$
$\cos ÷{π}{3}=?$
$\tan ÷{π}{3}=?$
Simplify $\sin(x-5⋅π)$
Simplify $\tan(x-5⋅π)$
Simplify $\cos(x-÷{π}{2})$
Simplify $\sin(x-÷{π}{2})$

Vector Calculus

Let $a⃗:=\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ .

Let $b⃗:=\begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}$ .

Let $c⃗:=\begin{pmatrix} 7 \\ 8 \\ 9 \end{pmatrix}$ .

What is the angle between and ?
Represent the plane that contains both and by using the normal vector of the plane.
Given a triangle ABC [A(-2,-10), B(8,0), C(-8,8)], determine the height cross points and the equation for the outer circle.

Greek Alphabet

α,Α Alpha
β,Β Beta
γ,Γ Gamma
δ,Δ Delta
ε,Ε Epsilon (there are more)
ζ,Ζ Zeta
η,Η Eta
ϑ,θ,Θ Theta
ι,Ι Iota
κ,Κ Kappa
λ,Λ Lambda
μ,Μ My
ν,Ν Ny
ξ,Ξ Xi
o,O Omikron
π,Π Pi
ρ,Ρ Rho (there are more)
σ,Σ Sigma
τ,Τ Tau
υ,Υ Ypsilon
φ,ϕ,Φ Phi
χ,Χ Chi
ψ,Ψ Psi
ω,Ω Omega

Mathematical Symbols (don't need to know all of them, but at least the names of most)

Nabla
$\quabla$ Quabla
Sum
Integral (continuous sum)
Absolute value
$\field{R}$ Body of real numbers
$\field{C}$ body of complex numbers
for all
there exists
H-bar
vector a
scalar product
expected value (or scalar product)
Laplace
Partial derivation
Product
closed loop integral
Norm (length) of x
infinity
scalar product

Author: FS TPH

Last modification on: Sat, 04 May 2024 .