Daily Practice Questions

Explanation: The phrase "dusty backstage corner" serves as a simile indicating that the author's memories have become neglected and forgotten over time, much like items left undisturbed in a dusty area. This imagery emphasizes that she has not thought of the events described in the passage for some time, making (G) the correct choice. The other options are incorrect because the dustiness refers to the state of her memory, not her physical location backstage or her current inability to recall the performance at all.

Explanation: Set up two equations: $M = 2R$ for the current ratio, and $M - 3 = R + 2$ for the ages three years ago. Substitute $2R$ for $M$ in the second equation to get $2R - 3 = R + 2$. Solving yields $R = 5$. A common error is to ignore the time shift, leading to an incorrect ratio; always adjust both variables by the same number of years when comparing past or future states.

Explanation: To find the number of unique $x$-intercepts, identify where the graph crosses the $x$-axis. The provided graph shows the curve intersecting the horizontal axis at three distinct points. Each intersection represents a unique real root of the function. While the graph may appear complex, counting the visible crossings yields exactly three locations. Answer (D) is a common trap if you mistakenly count local extrema or other features, but only axis intersections count as intercepts.

Explanation: The linear acceleration of the center of mass is found using the relationship $a = r\alpha$, where $\alpha$ is the angular acceleration. Given the angular position function $\theta = 4t^2$, the angular velocity is $\omega = d\theta/dt = 8t$ and the angular acceleration is $\alpha = d\omega/dt = 8 \text{ rad/s}^2$. At $t=1$, this constant angular acceleration of $8 \text{ rad/s}^2$ yields a linear acceleration of $a = (2 \text{ m})(8 \text{ rad/s}^2) = 16 \text{ m/s}^2$.

Explanation: The question asks for data that weakens an economist's claim about pyramid schemes, and choice (D) is correct because it provides statistical evidence showing that the vast majority of participants lose money, directly contradicting any argument suggesting these schemes are broadly profitable. Choices (A) and (B) actually strengthen a positive view of the scheme by highlighting profits for initiators or large groups, while choice (C) describes a specific negative outcome for latecomers but lacks the comprehensive statistical weight of choice (D) to effectively refute a general claim about participant success rates.

Explanation: 16. (E) The speaker explains in lines 12–13: “It is in a spirit of curiosity . . . that I approach the subject of teaching poetry.” He also wants to know more about the young people, their teachers, and the current teaching methods (lines 13–15).