Daily Math · 2026-05-12

Question 1

The value of $\cos\dfrac{\pi}{4}$ is:

Accepted Answer

$\cos\dfrac{\pi}{4} = \sin\dfrac{\pi}{4} = \dfrac{\sqrt{2}}{2}$.

Answer

$\dfrac{1}{2}$

Answer

$\dfrac{\sqrt{2}}{2}$

Answer

$\dfrac{\sqrt{3}}{2}$

Answer

$1$

Question 2

In $\mathbb{Z}_8$, the additive inverse of $\hat{3}$ is:

Accepted Answer

$3 + 5 = 8 \equiv 0 \pmod{8}$, so the inverse is $\hat{5}$.

Answer

$\hat{3}$

Answer

$\hat{0}$

Answer

$\hat{5}$

Answer

$\hat{8}$

Question 3

For which value of $a$ does $f(x) = x^3 - 3ax + 1$ have a local minimum at $x = 2$?

Accepted Answer

$f'(x) = 3x^2 - 3a$, so $f'(2) = 12 - 3a = 0 \Rightarrow a = 4$. Check: $f''(x) = 6x$, so $f''(2) = 12 > 0$, confirming a local minimum.

Answer

$a = 1$

Answer

$a = 2$

Answer

$a = 3$

Answer

$a = 4$

Problems & worked solutions