1003057902
Level:
A
The \( 13 \)th term of an arithmetic sequence is \( 64 \) and the \( 21 \)st term is \( 32 \). Find the common difference.
\( -4 \)
\( 4 \)
\( 8 \)
\( -8 \)
\( 2 \)
A
1003057901
Level:
A
The \( 20 \)th term of an arithmetic sequence is \( 150 \) and the common difference is \( 3 \). Find the first term.
\( 93 \)
\( 90 \)
\( 87 \)
\( 210 \)
\( 207 \)
1103080004
Level:
A
The graph of the function \( f \) is given in the figure. Choose the incorrect statement.
\( \lim\limits_{x\rightarrow1^-} f(x) = -1 \)
\( \lim\limits_{x\rightarrow -1} f(x) \) does not exist
\( \lim\limits_{x\rightarrow1^+} f(x) = 0 \)
\( \lim\limits_{x\rightarrow-\infty} f(x) = 1 \)
1103080003
Level:
A
The graph of the function \( f \) is given in the figure. Choose the incorrect statement.
\( \lim\limits_{x\rightarrow \infty} f(x) = -x \)
\( \lim\limits_{x\rightarrow 0^+} f(x) = 0 \)
\( \lim\limits_{x\rightarrow 0^-} f(x) = \infty \)
\( \lim\limits_{x\rightarrow-\infty} f(x) = \infty \)
1103080002
Level:
A
The graph of the function \( f \) is given in the figure. Choose the incorrect statement.
\( \lim\limits_{x\rightarrow-1}f(x) \) does not exist
\( \lim\limits_{x\rightarrow\infty} f(x) = \infty \)
\( \lim\limits_{x\rightarrow0} f(x) = 0 \)
\( \lim\limits_{x\rightarrow-\infty} f(x) = 1 \)
1103080001
Level:
A
The graph of the function \( f \) is given in the figure. Choose the incorrect statement. Dashed lines represent asymptotes of the function $f$.
\( \lim\limits_{x\rightarrow \infty} f(x) = -\infty \)
\( \lim\limits_{x\rightarrow -2^-} f(x) = -\infty \)
\( \lim\limits_{x\rightarrow \infty} f(x) = -2 \)
\( \lim\limits_{x\rightarrow -2} f(x) \) does not exist
1103079904
Level:
A
Given the complex numbers \( u = 1 + 2\mathrm{i} \) and \( v = 2 -\mathrm{i} \), choose the diagram which shows the complex number \( z \), such that \( z = u^2 - v^2 \).
1103079903
Level:
A
The diagram shows in red all the complex numbers \( z \) such that:
\( |z- 1 + \mathrm{i}| = 2 \)
\( |z- 1 - \mathrm{i}| = 2 \)
\( |z + 1 - \mathrm{i}| = 2 \)
\( |z + 1 + \mathrm{i}| = 2 \)
1103079902
Level:
A
The diagram shows in red all the complex numbers \( z \) such that:
\( |z + 1 + 2\mathrm{i}| < 1 \)
\( |z - 1 - 2\mathrm{i}| < 1 \)
\( |z + 1 - 2\mathrm{i}| < 1 \)
\( |z - 1 + 2\mathrm{i}| < 1 \)
1103079901
Level:
A
The diagram shows in red all the complex numbers \( z \) such that:
\( |z + \mathrm{i}| \geq 2 \)
\( |z - \mathrm{i}| \geq 2 \)
\( |z + 1| \geq 2 \)
\( |z - 1| \geq 2 \)