9000079202
Level:
B
Find the set \(M\)
of all the real \(x\)
for which the following expression is not a well defined number.
\[
\frac{x - 4}
{x^{3} - 16x}
\]
\(M = \{ - 4;0;4\}\)
\(M = \{ - 4;4\}\)
\(M = \{0;4\}\)
\(M = \{0\}\)
Polynomials and fractions
9000079210
Level:
A
Consider the expression
\[
V (x) = \frac{x}
{x - 1} - \frac{1}
{1 - x}.
\]
Find the correct ordering of the values
\(V (-2)\),
\(V (0)\) and
\(V (2)\).
\(V (0) < V (-2) < V (2)\)
\(V (-2) < V (0) < V (2)\)
\(V (0) < V (2) < V (-2)\)
\(V (2) < V (0) < V (-2)\)
9000079206
Level:
A
Assuming \(x\neq 0\),
\(y\neq 0\),
\(x\neq y\),
simplify the following expression.
\[ {
\frac{1}
{x^{2}} - \frac{1}
{y^{2}}
\over -\frac{1}
{y} + \frac{1}
{x}}
\]
\(\frac{x+y}
{xy} \)
\(-\frac{x+y}
{xy} \)
\(\frac{1}
{y} -\frac{1}
{x}\)
\(\frac{1}
{x} -\frac{1}
{y}\)
9000039301
Level:
B
Given formula for an acceleration of the motion in the form
\[
a = \frac{v - v_{0}}
{t} ,
\]
find the initial velocity \(v_{0}\).
\(v_{0} = v - at\)
\(v_{0} = vat\)
\(v_{0} = v + at\)
\(v_{0} = at - v\)
9000039302
Level:
B
Find \(N\),
the number of the turns, as a function of the other variables in the formula for the
magnetic induction of a solenoid.
\[
B =\mu \frac{NI}
{l}
\]
\(N = \frac{Bl}
{\mu I} \)
\(N = \frac{Bl\mu }
{I} \)
\(N = B -\mu \frac{I}
{l} \)
\(N = \frac{Bl}
{\mu } - I\)
9000039303
Level:
B
Find the time \(t\)
as a function of the other variables in the formula for the distance of a motion in the
form \(s = v_{0}t + s_{0}\).
\(t = \frac{s-s_{0}}
{v_{0}} \)
\(t = \frac{s}
{t+s_{0}} \)
\(t = \frac{s+s_{0}}
{v_{0}} \)
\(t = \frac{v_{0}}
{s-s_{0}} \)
9000039304
Level:
B
Find the focus length \(f\)
as a function of the other variables from the following equation relating this distance with object
and image distances \(a\)
and \(a'\).
\[
\frac{1}
{f} = \frac{1}
{a} + \frac{1}
{a'}
\]
\(f = \frac{aa'}
{a+a'}\)
\(f = \frac{a-a'}
{a+a'}\)
\(f = a + a'\)
\(f = \frac{a}
{a'}\)
9000039305
Level:
B
Find \(m_{1}\)
as a function of the other variables from the following mixing equation.
\[
w_{1}m_{1} + w_{2}m_{2} = w_{3}m_{3}
\]
\(m_{1} = \frac{w_{3}m_{3}-w_{2}m_{2}}
{w_{1}} \)
\(m_{1} = \frac{w_{3}m_{3}w_{2}m_{2}}
{w_{1}} \)
\(m_{1} = \frac{w_{3}m_{3}+w_{2}m_{2}}
{w_{1}} \)
\(m_{1} = \frac{w_{2}m_{2}-w_{3}m_{3}}
{w_{1}} \)