2010001002
Level:
A
Given an arithmetic sequence $(a_n)_{n=1}^{\infty}$, where $a_5=\frac54$, $a_k=15$ and the common difference is $\frac{11}{4}$, find $k$.
\(10\)
\(-6\)
\(0\)
\(9\)
\( 6\)
A
2010001001
Level:
A
The \( n \)th term of an arithmetic sequence is \( -70 \), the common difference is \( -6 \) and the first term is \(2\). Find the \(n\).
\( 13\)
\(11\)
\(-11\)
\(-13\)
\(12\)
2000002305
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 3\).
\[\frac{2}{3}x-5= \fbox{$\phantom{5}$}\cdot x-1 \]
\( -\frac{2}{3} \)
\( 6 \)
\( 2 \)
\( \frac{4}{3} \)
2000002304
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 0\).
\[-3x+10= \fbox{$\phantom{5}$}\cdot x-6 \]
such a number does not exist
any real number
\( 16 \)
\( -4 \)
2000002303
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 0\).
\[-3x+10= \fbox{$\phantom{5}$}+2x \]
\( 10 \)
\( 5 \)
\( -10 \)
\( 0 \)
2000002302
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = -2\).
\[-x+10= \fbox{$\phantom{5}$}\cdot x-6 \]
\( -9 \)
\( -8\)
\(2 \)
\( 9\)
2000002301
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 2\).
\[-x+10= \fbox{$\phantom{5}$} \cdot x-6 \]
\( 7 \)
\( 8 \)
\( 2 \)
\( 6 \)
2000002205
Level:
A
Identify the solution set of the following inequality.
\[
|7x+1|+1>0
\]
\( \mathbb{R} \)
\( \emptyset \)
\( \mathbb{R} \setminus \left\{\frac{1}{7}\right\} \)
\( \mathbb{R} \setminus \left\{-\frac{1}{7}\right\} \)
2000002204
Level:
A
Identify the solution set of the following inequality.
\[
-|2x-100|< 0
\]
\( \mathbb{R} \setminus \{50\} \)
\( \mathbb{R} \)
\( \mathbb{R} \setminus \{-50\} \)
\( \{50\} \)
2000002202
Level:
A
Identify the solution set of the following inequality.
\[
|x-25| \leq 0
\]
\( \{25\} \)
\( \emptyset \)
\( \mathbb{R} \setminus \{25\} \)
\( (-\infty;-25) \)