Daily Math · 2026-05-25

Question 1

The equation of the line through $A(0, 1)$ and $B(2, 5)$ is:

Accepted Answer

Slope $= 2$. The line through $(0, 1)$: $y - 1 = 2(x - 0) \Rightarrow y = 2x + 1$.

Answer

$y = x + 5$

Answer

$y = 2x - 1$

Answer

$y = 2x + 1$

Answer

$y = -2x + 5$

Question 2

$\displaystyle\int x \cos x \, dx$ equals:

Accepted Answer

$u = x$, $du = dx$, $v = \sin x$. $\int x \cos x \, dx = x \sin x - \int \sin x \, dx = x \sin x + \cos x + C$.

Answer

$\dfrac{x^2}{2} \cos x + C$

Answer

$-x \sin x + \cos x + C$

Answer

$x \sin x + \cos x + C$

Answer

$\sin x - x \cos x + C$

Question 3

The value of $\cos	frac{2\pi}{5} + \cos	frac{4\pi}{5} + \cos	frac{6\pi}{5} + \cos	frac{8\pi}{5}$ is:

Accepted Answer

The fifth roots of unity sum to $0$. Subtracting the root $1$ leaves a sum of $-1$, and taking real parts gives $\cos	frac{2\pi}{5}+\cos	frac{4\pi}{5}+\cos	frac{6\pi}{5}+\cos	frac{8\pi}{5}=-1$.

Answer

$-1$

Answer

$0$

Answer

$1$

Answer

$-	frac{1}{2}$

Problems & worked solutions

Problem 1 — Lines in the Plane

Problem 2 — Antiderivatives

Problem 3 — Trigonometry