# Sample Page

## Verbal

A meteor stream is composed of dust particles that have been ejected from a parent comet at a variety of velocities. These particles follow the same orbit as the parent comet, but due to their differing velocities they slowly gain on or fall behind the disintegrating comet until a shroud of dust surrounds the entire cometary orbit. Astronomers have hypothesized that a meteor stream should broaden with time as the dust particles’ individual orbits are perturbed by planetary gravitational fields. A recent computer-modeling experiment tested this hypothesis by tracking the influence of planetary gravitation over a projected 5,000-year period on the positions of a group of hypothetical dust particles. In the model, the particles were randomly distributed throughout a computer simulation of the orbit of an actual meteor stream, the Geminid. The researcher found, as expected, that the computer model stream broadened with time. Conventional theories, however, predicted that the distribution of particles would be increasingly dense toward the center of a meteor stream. Surprisingly, the computer model meteor stream gradually came to resemble a thick walled, hollow pipe.

Whenever the Earth passes through a meteor stream, a meteor shower occurs. Moving at a little over 1,500,000 miles per day around its orbit, the Earth would take, on average, just over a day to cross the hollow, computer-model Geminid stream if the stream were 5,000 years old. Two brief periods of peak meteor activity during the shower would be observed, one as the Earth entered the thick-walled “pipe” and one as it exited. There is no reason why the Earth should always pass through the stream’s exact center, so the time interval between the two bursts of activity would vary from one year to the next.

Has the predicted twin-peaked activity been observed for the actual yearly Geminid meteor shower? The Geminid data between 1970 and 1979 show just such a bifurcation, a secondary burst of meteor activity being clearly visible at an average of 19 hours(1,200,000 miles)after the first burst. The time intervals between the bursts suggest the actual Geminid stream is about 3000 years old.

1. Which of the following is an assumption underlying the last sentence of the passage?

A. In each of the years between 1970 and 1979, the Earth took exactly 19 hours to cross the Geminid meteor stream.
B. The comet associated with the Geminid meteor stream has totally disintegrated.
C. The Geminid meteor stream should continue to exist for at least 5, 000 years.
D. The Geminid meteor stream has not broadened as rapidly as the conventional theories would have predicted.
E. The computer-model Geminid meteor stream provides an accurate representation of the development of the actual Geminid stream.

## Math

Original問題のquestion poolのうちの一部の問題を記載させて頂きます。

### Basic/Intermediate

1. 因数分解: $$6x^2-29x+20$$
2. y=-3x+1のgraphを書きなさい。xが-3以上2以下の時のyのrangeを求めなさい。
3. a and bが共に5で割り切れる時cが5で割り切れる理由を説明しなさい。$$c=3a+2b$$

1. Calculate x: $$\sqrt{x^{2}+\sqrt{x}}+x-1=0$$
2. Determine a and b: The tens and unit digit of two-digit number (ab) is switched to (ba), and the two values meets the following equation.$$\sqrt{ab+ba} \ and \ \sqrt{ba-ab} \ are \ both \ integers.$$