1103023903
Level:
A
The graph of \( f' \) is given in figure. Function \( f' \) is the derivative of a function \( f \). Choose which of the following graphs is the graph of \( f \).
A
1103023902
Level:
A
The figure shows the derivative of one of the functions displayed below. Choose the function.
1103023901
Level:
A
The graph of \( f' \) is given in figure. Function \( f' \) is the derivative of a function \( f \). Choose which of the following graphs is the graph of \( f \).
1003020304
Level:
A
Find the solution set of the equation
\[1-\left[4x+3\cdot(x-y)\right]=\frac{1-14x}2-\frac{3-6y}2\]
in \( \mathbb{R}\times\mathbb{R} \).
\( \emptyset \)
\( \left\{[x;y],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{\left[x;\frac13+x\right],x\in\mathbb{R}\right\} \)
\( \left\{\left[x;-\frac13\right],x\in\mathbb{R}\right\} \)
1003020303
Level:
A
Find the solution set of the equation
\[1-\frac{x-2y}4=x+\frac{y+2}2\]
in \( \mathbb{R}\times\mathbb{R} \).
\( \left\{[0;y],y\in\mathbb{R}\right\} \)
\( \left\{[x;y],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{\left[\frac{-4y}5;y\right],y\in\mathbb{R}\right\} \)
\( \{0\} \)
\( \emptyset \)
1003020302
Level:
A
Assuming \( [x;y]\in\mathbb{R}\times\mathbb{R} \), solve the equation
\[ x-y-\frac{x-y}2=\frac{x-y}3 \]
Decide which of the answers below does not express the set of roots.
\( \left\{[x;y],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{[x;x],x\in\mathbb{R}\right\} \)
\( \left\{[y;y],y\in\mathbb{R}\right\} \)
\( \left\{[t;t],t\in\mathbb{R}\right\} \)
1003020301
Level:
A
In \( \mathbb{R}\times\mathbb{R} \), find the solution set of the equation:
\[ 2x-\frac{x+2y}3=2+\frac83y \]
\( \left\{\left[2y+\frac65;y\right],y\in\mathbb{R}\right\} \)
\( \left\{\left[2y+\frac65;\frac x2-\frac35\right],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{\left[\frac{6+6y}5;y\right],y\in\mathbb{R}\right\} \)
\( \emptyset \)
1003028806
Level:
A
Find all the real roots of the equation.
\[ \left(x^4-1\right)\left(x^3-8\right)\left(x^2-2\right)=0 \]
\( \left\{-\sqrt2;-1;1;\sqrt2;2\right\} \)
\( \left\{-2;-1;1;2\right\} \)
\( \left\{-\sqrt2;-1;1;\sqrt2\right\} \)
\( \left\{-\sqrt2;\sqrt2;2\right\} \)
1003028805
Level:
A
Find the sum of all the real roots of the next equation. Multiple roots, if any, count only once.
\[ \left(x^3+8\right)\left(x^2-1\right)\left(x+1\right)=0 \]
\( -2 \)
\( 0 \)
\( 2 \)
\( -3 \)
1003028804
Level:
A
For the next equation, find the sum of all the roots from the set of natural numbers. Multiple roots, if any, count only once.
\[ \left(x^3+1\right)\left(x^2-4\right)=0 \]
\( 2 \)
\( -1 \)
\( 3 \)
\( 1 \)