ACT Math Practice Question #2122 (Hard) | Test Citadel
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ACT Math Difficulty: Hard

Digital ACT Math Practice Question #2122

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

For what values of $x$ in the interval $0 \le x < 2\pi$ does $2\sin^2 x - \sin x - 1 = 0$?
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Test $x = \pi/2$: $\sin(\pi/2) = 1 \implies 2(1)^2 - 1 - 1 = 0$. Choice must include $\pi/2$! That eliminates B, D, and E.

Masterclass Solution & Distractor Trap Analysis

Factor the quadratic in terms of $\sin x$: $(2\sin x + 1)(\sin x - 1) = 0$. Thus $\sin x = 1$ or $\sin x = -\frac{1}{2}$. In $[0, 2\pi)$: $\sin x = 1 \implies x = \frac{\pi}{2}$. $\sin x = -\frac{1}{2} \implies x = \frac{7\pi}{6}, \frac{11\...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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