Daily Math · 2026-05-21

Question 1

The solution set of $2^{x} < 8$ is:

Accepted Answer

$2^x < 2^3 \Leftrightarrow x < 3$, i.e. $x \in (-\infty, 3)$.

Answer

$(-\infty, 3]$

Answer

$(3, +\infty)$

Answer

$(-\infty, 3)$

Answer

$[3, +\infty)$

Question 2

For $A = \begin{pmatrix} 1 & 1 \ 0 & 1 \end{pmatrix}$, the matrix $A^2$ equals:

Accepted Answer

$A^2 = \begin{pmatrix} 1 + 0 & 1 + 1 \ 0 + 0 & 0 + 1 \end{pmatrix} = \begin{pmatrix} 1 & 2 \ 0 & 1 \end{pmatrix}$.

Answer

$\begin{pmatrix} 1 & 1 \ 0 & 1 \end{pmatrix}$

Answer

$\begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}$

Answer

$\begin{pmatrix} 1 & 2 \ 0 & 1 \end{pmatrix}$

Answer

$\begin{pmatrix} 2 & 2 \ 0 & 2 \end{pmatrix}$

Question 3

Three numbers in arithmetic progression have sum $15$ and the sum of their squares is $83$. The largest of them is:

Accepted Answer

Set the terms as $5 - r,\, 5,\, 5 + r$. Then $(5-r)^2 + 25 + (5+r)^2 = 50 + 2r^2 + 25 = 83$, so $2r^2 = 8 \Rightarrow r = 2$. The largest term is $5 + 2 = 7$.

Answer

$5$

Answer

$6$

Answer

$7$

Answer

$8$

Problems & worked solutions

Problem 1 — Powers, Radicals, Logarithms

Problem 2 — Matrices

Problem 3 — Arithmetic Sequences