Daily Math Problems — June 21, 2026: Combinatorics, Financial Mathematics, Calculus

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Problems & worked solutions

RO M1

Problem 1 — Binomial Theorem

The expansion of $(a + b)^2$ is:

Show answer & worked solution

A. $a^2 + b^2$
B. $a^2 - 2ab + b^2$
C. $a^2 + 2ab + b^2$ ✓ correct
D. $2(a + b)$

The binomial formula gives $(a + b)^2 = a^2 + 2ab + b^2$ .

RO M1

Problem 2 — Financial Mathematics

An item priced at $\$80$ is on sale at a $25\%$ discount. The sale price is:

Show answer & worked solution

A. $\$55$
B. $\$60$ ✓ correct
C. $\$65$
D. $\$75$

Discount $= 20$ . Sale price $= 80 - 20 = \$60$ .

RO M1

Problem 3 — Asymptotes

The slant asymptote of $f(x) = \dfrac{2x^2 + 3x + 1}{x - 1}$ as $x \to \pm\infty$ is:

Show answer & worked solution

A. $y = 2x$
B. $y = 2x + 3$
C. $y = 2x + 5$ ✓ correct
D. $y = x + 1$

$\dfrac{2x^2 + 3x + 1}{x - 1} = 2x + 5 + \dfrac{6}{x - 1}$ . As $x \to \pm\infty$ , the remainder vanishes, leaving the slant asymptote $y = 2x + 5$ .

Problems & worked solutions

RO M1

Problem 1 — Binomial Theorem

The expansion of $(a + b)^2$ is:

Show answer & worked solution

A. $a^2 + b^2$
B. $a^2 - 2ab + b^2$
C. $a^2 + 2ab + b^2$ ✓ correct
D. $2(a + b)$

The binomial formula gives $(a + b)^2 = a^2 + 2ab + b^2$ .

RO M1

Problem 2 — Financial Mathematics

An item priced at $\$80$ is on sale at a $25\%$ discount. The sale price is:

Show answer & worked solution

A. $\$55$
B. $\$60$ ✓ correct
C. $\$65$
D. $\$75$

Discount $= 20$ . Sale price $= 80 - 20 = \$60$ .

RO M1

Problem 3 — Asymptotes

The slant asymptote of $f(x) = \dfrac{2x^2 + 3x + 1}{x - 1}$ as $x \to \pm\infty$ is:

Show answer & worked solution

A. $y = 2x$
B. $y = 2x + 3$
C. $y = 2x + 5$ ✓ correct
D. $y = x + 1$

$\dfrac{2x^2 + 3x + 1}{x - 1} = 2x + 5 + \dfrac{6}{x - 1}$ . As $x \to \pm\infty$ , the remainder vanishes, leaving the slant asymptote $y = 2x + 5$ .