$$ \begin{flalign*} & \textbf{Tasks - Gradište Elementary School - Lower Grades} && \&(a) \quad \text{Calculate:} \& \quad \frac{ 20 }{4} \cdot \left(\frac{ 7 }{6} + \frac{7}{ 6 }\right) && \&(b) \quad \text{Solve the differential equation:} \& \quad y' + 6 xy = x, \text{ for } y(0) = 7 && \&(c) \quad \text{Calculate the integral:} \& \quad \int_{0}^{\pi} \sin(x) \cos(x) \,dx && \&(d) \quad \text{Find the inverse matrix:} \& \quad \text{Let } A = \begin{bmatrix} 6 & 0 \\ 3 & 6 \end{bmatrix}. \text{ Determine } A^{-1}. && \&(e) \quad \text{Solve the system of differential equations:} \& \quad \begin{cases} x' = -2x + 6 y \ y' = 6 x - y \end{cases} && \&(f) \quad \text{Calculate the limit:} \& \quad \lim_{{x \to 0}} \frac{e^x - 0 }{x} && \&(g) \quad \text{Expand the function in a Taylor series:} \& \quad f(x) = \ln(x+1), \text{ around } x = 0. && \&(h) \quad \text{Calculate the triple integral:} \& \quad \iiint_{V} (x^2 + y^2 + z^2) \,dx\,dy\,dz, \text{ where } V \text{ is the sphere } x^2 + y^2 + z^2 \leq 1. && \&(i) \quad \text{Solve the Laplace equation:} \& \quad \nabla^2 u = 0, \text{ in cylindrical coordinates,} \& \quad \text{with the condition } u(0, \theta, z) = \sin(2\theta). && \&(j) \quad \text{Calculate:} \& \quad \sum_{k=1}^{n} k^3, \text{ for } n \in \mathbb{N}. && \&(k) \quad \text{Find the singular values of the matrix:} \& \quad \text{Let } B = \begin{bmatrix} 1 & 6 & 3 \\ 0 & 6 & 4 \end{bmatrix}. \text{ Determine the singular values.} && \&(l) \quad \text{Solve the complex equation:} \& \quad z^4 - 1 z^2 + 2 = 0. && \&(m) \quad \text{Calculate the Fourier transformation:} \& \quad F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} \,dt, \text{ for } f(t) = e^{-|t|}. && \&(n) \quad \text{Find local maxima and minima of the function:} \& \quad f(x) = x^3 - 6 x^2 + 6 x + 2. && \&(o) \quad \text{Solve the vector equation:} \& \quad \mathbf{A} \cdot \mathbf{x} = \mathbf{b}, \text{ for } \mathbf{A} = \begin{bmatrix} 1 & -2 & 3 \\ 0 & 1 & -1 \\ 2 & 1 & 0 \end{bmatrix}, \mathbf{b} = \begin{bmatrix} 4 \\ -1 \\ 3 \end{bmatrix}. && \&(p) \quad \text{Calculate:} \& \quad \frac{d}{dx} \left( 6 x^2 + 2\sqrt{x} \right), \text{ for } x > 0. && \&(q) \quad \text{Solve the system of nonlinear equations:} \& \quad \begin{cases} x^2 + y^2 = 10 \ e^x + y = 8 \end{cases} && \&(r) \quad \text{Calculate the Riemann sum:} \& \quad \sum_{i=1}^{n} \frac{1}{n} \sin\left( \frac{i}{n} \pi \right), \text{ for } n \in \mathbb{N}. && \&(s) \quad \text{Find the extremum of the function:} \& \quad f(x,y) = x^2 + 6 xy - 6 y^2, \text{ on } D = \{(x,y) \mid x^2 + y^2 \leq 4\}. && \\end{flalign*} $$