1003099607
Level:
A
Let \( \frac{m}{6-\sqrt6}=\frac{6+\sqrt6}6 \), determine \( m \).
\( m=5 \)
\( m=6 \)
\( m=1 \)
\( m=-5 \)
A
1003099604
Level:
A
Express \( \left(\sqrt2+3\right)^2 \) in the simplest form:
\( 11+6\sqrt2 \)
\( 11 \)
\( 6\sqrt2 \)
\( 5 \)
1003099603
Level:
A
Calculate \( \left(2\sqrt{75}-3\sqrt{48}+2\sqrt{27}\right)^2 \).
\( 48 \)
\( 192 \)
\( 12 \)
\( 60 \)
1003099602
Level:
A
Simplifying \( \frac32\sqrt8 + \sqrt{16} + \sqrt{32} - \frac13\sqrt{18} \) you get:
\( 4+6\sqrt2 \)
\( 4+\sqrt{12} \)
\( 2+\sqrt{56} \)
\( 4+\sqrt{40} \)
1003099601
Level:
A
Given the numbers \( x=1+2\sqrt2 \) and \( y=\sqrt2-1 \), calculate \( xy \).
\( 3-\sqrt2 \)
\( 4-\sqrt2 \)
\( 3 \)
\( -\sqrt2 \)
1003123402
Level:
A
Given the complex number \( b=\sqrt[3]2\cdot\left(\cos\frac56\pi+\mathrm{i}\cdot\sin\frac56\pi\right) \), find the polar form of \( b^9 \).
\( 8\cdot\left(\cos\frac32\pi+\mathrm{i}\cdot\sin\frac32\pi\right) \)
\( 64\cdot\left(\cos\frac12\pi-\mathrm{i}\cdot\sin\frac12\pi\right) \)
\( 8\cdot\left(\cos\frac12\pi-\mathrm{i}\cdot\sin\frac12\pi\right) \)
\( 64\cdot\left(\cos\frac32\pi+\mathrm{i}\cdot\sin\frac32\pi\right) \)
1003123401
Level:
A
Given the complex number \( a =\sqrt3\cdot\left( \cos 225^{\circ} + \mathrm{i}\cdot\sin 225^{\circ}\right) \), find the polar form of \( a^6 \).
\( 27\cdot\left(\cos270^{\circ}+\mathrm{i}\cdot\sin270^{\circ}\right) \)
\( 9\cdot\left(\cos90^{\circ}+\mathrm{i}\cdot\sin90^{\circ}\right) \)
\( 27\cdot\left(\cos90^{\circ}+\mathrm{i}\cdot\sin90^{\circ}\right) \)
\( 9\cdot\left(\cos270^{\circ}+\mathrm{i}\cdot\sin270^{\circ}\right) \)
1003085104
Level:
A
The \( n \)th term of an arithmetic sequence is \( 1-3n \). Find the \( 5 \)th term and the common difference.
\( a_5=-14;\ d=-3 \)
\( a_5=-2;\ d=-3 \)
\( a_5=14;\ d=-3 \)
\( a_5=-14;\ d=3 \)
\( a_5=-2;\ d=3 \)
1003085103
Level:
A
The third term of an arithmetic sequence is \( 3 \) and the common difference is \( 3 \). Find the \(n\)th term.
\( a_n=3n-6 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n-3 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n \text{ for all } n\in\mathbb{N} \)
\( a_n=3n+3 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n+6 \text{ for all } n\in\mathbb{N} \)
1003085102
Level:
A
The first term of an arithmetic sequence is \( 6 \) and the sixth term is \( 1 \). Find the recursive formula for the sequence.
\( a_1=6;\ a_{n+1}=a_n-1 \text{ for all } n\in\mathbb{N} \)
\( a_1=6;\ a_{n+1}=a_n+1 \text{ for all } n\in\mathbb{N} \)
\(a_1=1;\ a_{n+1}=a_n+5 \text{ for all } n\in\mathbb{N} \)
\( a_1=1;\ a_{n+1}=a_n-5 \text{ for all } n\in\mathbb{N} \)