For A = 1 1; 0 1, the matrix A^2 equals:

A^2 = 1 + 0 1 + 1; 0 + 0 0 + 1 = 1 2; 0 1.

Daily Math Problems — May 21, 2026: Powers, Radicals, Logarithms, Matrices, Sequences

dailymath

Problems & worked solutions

RO M1

Problem 1 — Powers, Radicals, Logarithms

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

Show answer & worked solution

A. $(- \infty, 3]$
B. $(3, + \infty)$
C. $(- \infty, 3)$ ✓ correct
D. $[3, + \infty)$

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

RO M1

Problem 2 — Matrices

For $A = (\begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array})$ , the matrix $A^{2}$ equals:

Show answer & worked solution

A. $(\begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array})$
B. $(\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array})$
C. $(\begin{array}{cc} 1 & 2 \\ 0 & 1 \end{array})$ ✓ correct
D. $(\begin{array}{cc} 2 & 2 \\ 0 & 2 \end{array})$

$A^{2} = (\begin{array}{cc} 1 + 0 & 1 + 1 \\ 0 + 0 & 0 + 1 \end{array}) = (\begin{array}{cc} 1 & 2 \\ 0 & 1 \end{array})$ .

RO M1

Problem 3 — Arithmetic Sequences

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

Show answer & worked solution

A. $5$
B. $6$
C. $7$ ✓ correct
D. $8$

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

Problems & worked solutions

RO M1

Problem 1 — Powers, Radicals, Logarithms

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

Show answer & worked solution

A. $(- \infty, 3]$
B. $(3, + \infty)$
C. $(- \infty, 3)$ ✓ correct
D. $[3, + \infty)$

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

RO M1

Problem 2 — Matrices

For $A = (\begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array})$ , the matrix $A^{2}$ equals:

Show answer & worked solution

A. $(\begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array})$
B. $(\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array})$
C. $(\begin{array}{cc} 1 & 2 \\ 0 & 1 \end{array})$ ✓ correct
D. $(\begin{array}{cc} 2 & 2 \\ 0 & 2 \end{array})$

$A^{2} = (\begin{array}{cc} 1 + 0 & 1 + 1 \\ 0 + 0 & 0 + 1 \end{array}) = (\begin{array}{cc} 1 & 2 \\ 0 & 1 \end{array})$ .

RO M1

Problem 3 — Arithmetic Sequences

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

Show answer & worked solution

A. $5$
B. $6$
C. $7$ ✓ correct
D. $8$

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