Daily Math · 2026-05-18

Question 1

A finite group of prime order $p$ is necessarily:

Accepted Answer

Take any $g 
e e$. The subgroup $\langle g angle$ has order dividing $p$. It's not $1$ (since $g 
e e$), so it has order $p$, i.e. $\langle g angle = G$. So $G$ is cyclic, hence abelian.

Answer

non-abelian

Answer

non-cyclic

Answer

cyclic and abelian

Answer

has $|G|$ subgroups

Question 2

The solution set of $x^2 > 9$ in $\mathbb{R}$ is:

Accepted Answer

$x^2 > 9 \Leftrightarrow |x| > 3 \Leftrightarrow x < -3$ or $x > 3$. Solution: $(-\infty, -3) \cup (3, +\infty)$.

Answer

$(-3, 3)$

Answer

$[-3, 3]$

Answer

$(-\infty, -3) \cup (3, +\infty)$

Answer

$(-\infty, -3] \cup [3, +\infty)$

Question 3

Let $\vec{a}$ and $\vec{b}$ be two non-collinear vectors. Find $m \in \mathbb{R}$ so that $\vec{u} = 3\vec{a} - (m + 1)\vec{b}$ and $\vec{v} = (m - 1)\vec{a} - 5\vec{b}$ are collinear.

Accepted Answer

$3 \cdot (-5) = (m - 1)\,(-(m+1))$, i.e. $-15 = -(m-1)(m+1) = 1 - m^2$, so $m^2 = 16$ and $m \in \{-4, 4\}$.

Answer

$\{-4\}$

Answer

$\{4\}$

Answer

$\{-4, 4\}$

Answer

$\{-2, 8\}$

Problems & worked solutions

Problem 1 — Groups

Problem 2 — Elementary Functions

Problem 3 — Vectors in the Plane