The SAT is the best known and most widely used college admissions test in existence. Not all schools require students to take the SAT before applying, but most do. Doing well on the exam is of critical importance to every high school student who hopes to go on to attend college. A low score can have very damaging consequences, from disqualifying a student when it comes to receiving scholarship funds all the way down to preventing a student from being accepted into even second or third tier schools. On the other hand, those who do very well on the SAT tend to get accepted into better colleges and universities while receiving many more scholarship offers, including full four year scholarships.

The SAT is officially called the SAT Reasoning Test, but most people simply call it the SAT. It consists of three sections – Mathematics, Critical Reading, and Writing. Test takers have three hours and forty-five minutes to complete the exam. Scores range from a possible 200, which is essentially a 0, to a perfect score of 2400, or 800 on each section.

The exam is given seven times a year – January, March or April, May, June, October, November, and December. There is a fee to take the exam, which is $50 as of this writing. Students need to take the SAT well in advance of starting the college application process, in order to make sure their scores are available to the admissions committees when they begin considering applications. It’s also necessary to register well ahead of time for the desired test date. Late registration is available, but at a much higher cost. Scores are available around three weeks after the test for those who choose online access; paper scores are mailed around six weeks after the test.

Each year well over a million people take the SAT test, with an average score of about 1500, or around 500 for each of the three sections. Most colleges and universities that require applicants to take the exam publish information on their website to give applicants an idea of what kind of score they’ll need to win admission – the average score of the entire student body, the average score of the top and bottom 25th percentiles, the absolute highest score, etc. This information can be quite useful, as it gives an applicant a very good idea of just what kind of score it takes to get into a particular school. Knowing this information is one thing; actually achieving the score is another. That’s why it’s vitally important to be thoroughly prepared when taking the SAT.

## SAT Practice Questions

**1. What is the area of an isosceles triangle inscribed in a circle of radius r if the base of the triangle is the diameter of the circle?**

- r
^{2} - 2r
^{2} - πr
^{2} - 2πr

**2. A sailor judges the distance to a lighthouse by holding a ruler at arm’s length and measuring the apparent height of the lighthouse. He knows that the lighthouse is actually 60 feet tall. If it appears to be 3 inches tall when the ruler is held 2 feet from his eye, how far away is it?**

- 60 feet
- 120 feet
- 240 feet
- 480 feet
- 960 feet

**3. If p and n are positive consecutive integers such that p > n, and p + n = 15, what is the value ofn?**

- 5
- 6
- 7
- 8
- 9

**4. Forty students in a class take a test that is graded on a scale of 1 to 10. The histogram in the figure shows the grade distribution, with the x-axis representing the grades and the y-axis representing the number of students obtaining each grade. If the mean, median, and modal values are represented by n, p, and q, respectively, which of the following is true?**

- n > p > q
- n > q > p
- q > p > n
- p > q > n
- q > n > p

**5. Referring again to the figure for Question 18, if the top 10% of students are to receive a grade of A, what is the minimum test score required to get an A?**

- 10
- 9
- 8
- 7
- 6

**6. If x and y are positive integers, which of the following expressions is equivalent to (xy)^{7y} – (xy)^{y} ?**

*(xy)*^{6y}*(xy)*^{7y-1}*(xy)*[^{y}*(xy)*-1]^{7}*(xy)*[^{y}*(xy)*-1]^{6y}*(xy)*^{7y}

*Questions 7-10 are based on the following passage.*

Zakov arrived at the prison shortly before noon, having dropped Ludmilla off at the train station beforehand. He was relieved to find that Gorkhi had gone, for he found the chief to be a bit bombastic, and was disposed to conduct the interrogation without him if he could. He was fortunate in that one of Gorkhi’s men recognized him and let him in to see the prisoner.

He found the student sitting on the floor of a damp cell. The only illumination came from a small window set high in the concrete wall. Nasadev raised red-rimmed eyes when the door opened, amid a clatter of keys and bolts, and Zakov found himself again amazed at the lad’s homeliness, rendered even more pathetic by features wet and swollen from weeping. Somewhat discomfited by his own reaction, he forced a smile.

The young man attempted to rise, but was hindered by the shackles about his ankles.

“Please, remain seated,” offered Zakov quickly, and joined him on the earthen floor. “Ludmilla delivered your note. Just what kind of trouble are you in?”

“They are saying that I killed Olga,” the youth replied, his face contorted in a grimace. “As if I could! I adored her,” he cried. “But things look rather bleak for me, the way they found my knife. Only you can help me, sir. I know your reputation. Please help me, sir! Not for myself, but for my family. This will destroy them…” His tears welled up again, and he sniffled and dabbed vainly at his cheeks with his dirty sleeve.

Zakov looked at him sympathetically. Ludmilla had told him the student was pathetic, and she was right: the ordinary face, the weak chin, now damp with tears and perspiration, made him seem a most unlikely suitor. He must have been deeply hurt by Olga’s rejection. And she, delicate, spirited and appealing, must have found his attentions tedious and annoying, the more so since he had neither fortune nor prospects. Had she derided him, mocked him, gone too far setting trial to his devotion until he killed her?

“What made the police suspect you?” he asked.

“They talked to some of the other students, and my name came up.” Nasadev was almost whining. “One of them found a letter I had written, but never sent. He told the others. It made me angry, but I guess it was foolish of me to think that such a girl could ever like someone like me. But she was nice to me, nonetheless. She told me about the play she was writing, and how she hoped to go to Moscow.”

Zakov found that his heart went out to the poor, infatuated youth. But pity was not enough to resolve the charges the student faced.

“So the other students mentioned your name,” he continued. “That explains why the police spoke to you, but it’s not enough for them to bring charges. What else happened?”

Nasadev replied plaintively, fixing Zakov with an imploring look. “We had a quarrel. In the park. The day before they found her. Someone must have heard us and they told the police. They came and searched my room in the dormitory, found my diary, some other letters I had written.”

“What was the quarrel about?”

Nasadev hesitated, would not meet Zakov’s eye. “I had asked her to marry me. I know it was crazy…how could I support her? But I was afraid she would stop seeing me, that someone else would come along and I would lose her.”

“And what did she say?” Zakov knew the answer already, but he had to ask.

“She turned me down. She didn’t laugh at me, but she turned me down. And that was in my diary, too.” Nasadev was practically inaudible.

Zakov stayed a while longer, asked a few more questions. A deep sadness seemed to fill his heart as he regarded the small cell and its single miserable occupant. Finally, with a shiver, he called for Gorkhi’s man to open the door and he left.

**7. Zakov thought that Gorkhi, the police chief, was**

- considerate
- pretentious
- enthusiastic
- moderate
- uncooperative

**8. The passage suggests that Nasadev’s cell**

- was modern
- had only a bed in it
- was spacious
- was unfurnished
- smelled badly

**9. Nasadev’s frame of mind during the interview can best be described as**

- resigned
- courageous
- determined
- desperate
- calculating

**10. Nasadev’s look, when he replies to Zakov’s question (Line 79) implies that he is**

- begging for help
- about to collapse
- looking for words
- exhausted
- unable to think clearly

### Essay

Time – 25 minutes

*Consider the issue presented below:*

A study conducted by a non-profit foundation examined teenagers’ socializing on the Internet. The study found that most teenagers turn on their computers as soon as they return home from school every day, and that they use myspace and similar sites, as well as instant messaging, to stay in touch with their circle of friends almost constantly throughout the day. Since many parents believe that internet socializing is a waste of time, the teenagers were subject to many restrictions, but they usually found ways to circumvent these rules.

*Assignment:*

Should internet socializing by teenagers be restricted? Write an essay developing your point of view on this issue. Support your position with evidence from your reading, experience, and personal observations.

## Answers and Explanations

1. **A: **The area of a triangle equals half the product of base times height. Since the base passes through the center, we have base = 2*r* and height = *r*, so that the area *A* is *A* = *r × 2r* / 2 = *r ^{2}*

2. **D: **The ratio of the ruler’s height to the distance from eye to ruler, which is the tangent of the angle subtended at the eye by the ruler’s height, must be the same as the ratio of the lighthouse’s height to its distance, which is the tangent of the same angle. Since 3 inches is ¼ foot, we have ¼/2=60/D, and solving for D gives D= 2×60/¼ = 4 × 120 = 480 feet

3. **C: **This can be solved as two equations with two unknowns. Since the integers are consecutive with *p > n*, we have *p – n* = 1, so that *p* = 1 + *n*, Substituting this value into *p* + *n* = 15 gives 1 + 2*n* = 15, or *n* = 14/2 = 7.

4. **A: **The mean, or average of the distribution can be computed by multiplying each grade by the number of students obtaining it, summing, and dividing by the total number of students. Here, *n* = 4.2. The median is the value for which an equal number of students have received higher or lower grades. Here, *p* = 4. The mode is the most frequently obtained grade, and here, *q* = 3.

5.** D: **10% of the tested population of 40 students is 4 students. Four students got grades of 7 or higher.

6.** D: **Remember that when you multiply like bases, you add the exponents, and when you divide like bases, you subtract the exponents. (*xy*)^{7y}-(*xy*)^{y} = (*xy*)^{y} [(*xy*)^{7y-y}-1] = (*xy*)^{y} [(*xy*)^{6y}-1]

7.** B: **Gorkhi is described in line 6 as a bit bombastic. A bombastic individual is one who is overbearing and pretentious.

8.** D: **Line 13 tells us that Zakov found the student on the floor.

9.** D:** Nasadev is described as whining, with his eyes red from crying, and concerned that his troubles will affect his family.

10.** A: **The student regards Zakov with an imploring look. To implore is to beg.