【SAT备考】SAT数学真题内容介绍

10月的SAT考试将近，以下是新通外语整理的SAT考试数学真题介绍，考生可以作为练习，提前熟悉考题

1. A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out

A.4 feet

B.5 feet

C.6 feet

D.7 feet

E.8 feet

2.Read the following SAT test question, then click on a button to select your answer.

A train traveling 60 miles per hour for 1 hour covers the same distance as a train traveling 30 miles per hour for how many hours?

A.3

B.2

C.1

D.1/2

E.1/3

3. Read the following SAT test question, then click on a button to select your answer.

At Central High School, the math club has 15 members and the chess club has 12 members. If a total of 13 students belong to only one of the two clubs, how many students belong to both clubs?

A.2

B.6

C.7

D.12

E.14

4. Read the following SAT test question, then click on a button to select your answer.

On a number line, x represents a number that is within 2 units of 12. Which of the following describes this relationship?

A.|x + 2| < 12

B.|x + 12| < 2

C.|x – 2| < 12

D.|x – 12| < 2

E.|12 – 2| < x

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Answers:

1. Correct Answer: E

* Here's Why:

The ladder, the wall, and the ground form a right triangle with a 25-foot hypotenuse. At first, the bottom of the ladder is 7 feet from the base of the building, so one leg of the right triangle measures 7 feet; the length of the other leg, x, can be found by solving 72 + x2 = 252, which is the Pythagorean theorem. From this, you can figure out that the other leg measures 24 feet.

After the ladder slips down 4 feet, the 24-foot leg of the right triangle becomes 20 feet long. The other leg then has to be 15 feet long. This length is found by solving 202 + y2 = 252, which is again the Pythagorean theorem.

Since the distance between the bottom of the ladder and the base of the building increases from 7 feet to 15 feet, the amount that the bottom of the ladder slides out is 8 feet.

* Difficulty: Hard

* Question Type: Standard Multiple Choice(Mathematics)

2. Correct Answer: B

* Here's Why:

When the speed of a train in miles per hour is multiplied by the travel time in hours, the distance traveled by the train is obtained. The distance that the first train travels is 60 miles per hour times 1 hour, which is 60 miles. Using the variable x for the travel time, in hours, of the second train, the distance that the second train travels is 30 miles per hour times x hours, which is 30x miles. Since the two trains travel the same distance, 60 = 30x, which gives x = 2 hours, the travel time of the second train.

* Difficulty: Easy

* Question Type: Standard Multiple Choice(Mathematics)

3. Correct Answer: C

* Here's Why:

Let n stand for the number of students who belong to both clubs. The 15 members of the math club can be broken down into two groups: those who are in both clubs (there are n students in this category) and those who are in the math club only (there are 15 – n students in this category).

The 12 members of the chess club can also be broken down into two groups: n students who are in both clubs and 12 – n students who are in the chess club only.

Since a total of 13 students belong to only one of the two clubs, you know that (15 – n) + (12 – n) = 13. Solving this equation gives n = 7, so 7 students belong to both clubs.

* Difficulty: Medium

* Question Type: Standard Multiple Choice(Mathematics)

4. Correct Answer: D

* Here's Why:

The distance between x and 12 is |x – 12|. If x is within 2 units of 12, then the distance between x and 12 is less than 2. Therefore, this relationship is represented by |x – 12| < 2.

* Difficulty: Hard

* Question Type: Standard Multiple Choice(Mathematics) 

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