1003019402
Level:
C
Identify which of the given functions is neither even nor odd.
\( h(x) = \frac{x^3-7}{2x^2} \)
\( f(x) = \frac{x^2+3}{3x^4} \)
\( g(x) = \frac{5x^2-6}{x} \)
\( m(x) = \frac{x^3}{2x^2+5} \)
C
1003019401
Level:
C
Identify which of the given functions is even.
\( m(x)=\frac{x^4-3}{x^2} \)
\( h(x)=\frac{x^3+2}{x^2} \)
\( g(x)=\frac{x^2}{x+1} \)
\( f(x)=\frac{x^3}{x^2-5} \)
1003025504
Level:
C
Find the range of the function \( f(x)=\Bigl|\left(\frac13\right)^x-1\Bigr|\).
\( [ 0,\infty) \)
\( ( 0,\infty) \)
\( (-1,\infty) \)
\( [ -1,\infty) \)
1003025503
Level:
C
Find the domain of the function \( f(x)=\sqrt{3^x}\).
\( (-\infty,\infty) \)
\( (0,\infty) \)
\( [0,\infty) \)
\( (-\infty,0) \)
1103025502
Level:
C
Identify a possible graph of the function \( f(x)=\Bigl|\left(\frac12\right)^x-1\Bigr|\).
1103025501
Level:
C
Identify a possible graph of the function \( f(x)= 2^{|x|}-1\).
1003020901
Level:
C
Let there be vectors: \(\vec{a}=(1,3,-1)\), \(\vec{b}=(0,3,1)\), \(\vec{c}=(-1,2,2)\). Find \(\vec{a}\times\vec{b}\) and \(\left(\vec{a}\times\vec{b}\right)\cdot\vec{c}\).
\(\vec{a}\times\vec{b}=(6,-1,3), \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=-2\)
\(\vec{a}\times\vec{b}=8, \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=(-8,16,16)\)
\(\vec{a}\times\vec{b}=(-6,1,-3), \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=2\)
\(\vec{a}\times\vec{b}=\sqrt{46}, \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=2\)
9000154801
Level:
C
There are six money transports through the Sherwood forest. Robin Hood knows
that two of the transports are secured by soldiers. Find the respective probabilities
that if Robin's band attacks two random transports, then none, one and both
transports will be secured by the soldiers.
\(\frac{6}
{15},\, \frac{8}
{15},\, \frac{1}
{15}\)
\(\frac{3}
{9},\, \frac{5}
{9},\, \frac{1}
{9}\)
\(\frac{1}
{3},\, \frac{2}
{3},\, \frac{2}
{3}\)
\(\frac{1}
{2},\, \frac{1}
{4},\, \frac{1}
{4}\)
9000153901
Level:
C
Find the number of ways how to distribute
\(8\) identical
balls among \(5\)
persons so that each of them gets at least one ball.
\(\left({7\above 0.0pt
3}\right) = 35\)
\(5^{3} = 125\)
\(\left({12\above 0.0pt
5} \right) = 792\)
\(\left({12\above 0.0pt
8} \right) = 495\)
9000153902
Level:
C
Find the number of ways how to distribute
\(8\) identical
balls among \(5\)
persons.
\(\left({12\above 0.0pt
8} \right) = 495\)
\(5^{8} = 390625\)
\(\left({8\above 0.0pt
5}\right) = 56\)
\(\left({12\above 0.0pt
5} \right) = 792\)