9000010501
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{5}}
\]
\(x\root{3}\of{x^{2}}\)
\(x^{2}\root{3}\of{x^{2}}\)
\(x^{3}\root{3}\of{x^{2}}\)
\(x^{2}\root{5}\of{x^{3}}\)
A
9000010502
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{5}}\cdot \root{3}\of{x^{4}}
\]
\(x^{3}\)
\(\root{3}\of{x^{12}}\)
\(\root{3}\of{x}\)
\(x\root{3}\of{x^{4}}\)
9000010504
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{2}} : \root{3}\of{x}
\]
\(\root{3}\of{x}\)
\(x\)
\(1\)
\(\root{9}\of{x}\)
9000010507
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x^{3} : \root{}\of{x}
\]
\(x^{2}\root{}\of{x}\)
\(x^{3}\root{}\of{x}\)
\(\root{}\of{x^{3}}\)
\(\root{6}\of{x}\)
9000013505
Level:
A
Write the number \(3\root{3}\of{3}\)
in an equivalent form involving just radical of a single number or radical of a single
power.
\(\root{3}\of{81}\)
\(\sqrt{9}\)
\(\root{3}\of{27}\)
\(\root{3}\of{3^{2}}\)
9000008007
Level:
A
Given the functions \(f(x) = -\frac{3}
{x}\)
and \(g(x) = 6\),
solve \(f(x) = g(x)\).
\(-\frac{1}
{2}\)
\(- 2\)
\(3\)
\(6\)
9000007205
Level:
A
Given the linear function
\[
f(x) = -3x + 2
\]
solve the inequality \(f(x)\geq 1\).
\(x\leq \frac{1}
{3}\)
\(x\geq \frac{1}
{3}\)
\(x\leq \frac{2}
{3}\)
\(x\geq 2\)
9000007204
Level:
A
Among the following functions identify an odd function
\(f\) which
satisfies \(f(-2) = 4\).
\(f(x) = -2x\)
\(f(x) = -2x + 1\)
\(f(x) = x + 2\)
\(f(x) = 2x + 8\)
9000007802
Level:
A
Consider linear functions \(f(x) = ax - 2\)
and \(g\colon y = -4x + 3\). Find the value of
the real parameter \(a\) which
ensure that the graphs of \(f\)
and \(g\)
are two parallel lines.
\(- 4\)
\(4\)
\(- 2\)
\(2\)
9000007804
Level:
A
Three of the points \(A = [2;-4]\),
\(B = [0;-3]\),
\(C = [-2;-1]\),
\(D = [-4;1]\) lie on
the graph of the same linear function. Identify these points. (Colinear points.)
\(B\),
\(C\),
\(D\)
\(A\),
\(B\),
\(C\)
\(A\),
\(B\),
\(D\)
\(A\),
\(C\),
\(D\)