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# GRE辅导：ETS官方GRE数学样题

2020-01-09 18:27:30

GRE考试分为Verbal Reasoning(文字推理)，Quantitative Reasoning(定量推理)和Analytical Writing(分析性写作)三个部分。而申请美国研究生，每个专业的要求不是一样的。申请EE(电气工程)项目对于Quantitative 的要求很高(基本要求满分170)，对Verbal和Analytical Writing要求会低一些;而申请Education(教育学)对Verbal和Analytical Writing的要求高，反而对Quantitative并不怎么看重。 This document includes figures, which appear on screen. Following each figure on screen is text describing that figure. Readers using visual presentations of the figures may choose to skip parts of the text describing the figure that begin with “Begin skippable figure description” and end with “End skippable figure description.”

Mathematical Equations and Expressions

This document includes mathematical equations and expressions. Some of the mathematical equations and expressions are presented as graphics. In cases where a mathematical equation or expression is presented as a graphic, a verbal presentation is also given and the verbal presentation comes directly after the graphic presentation. The verbal presentation is in green font to assist readers in telling the two presentation-modes apart. Readers using audio alone can safely ignore the graphical presentations, and readers using visual presentations may ignore the verbal presentations.

Introduction

The revised Quantitative Reasoning section contains four types of questions: Multiple-choice Questions — Select One Answer Choice

These questions are multiple-choice questions that ask you to select only one answer choice from a list of five choices.

Sample Questions Directions: Select a single answer choice. Sample question 1 below is based on figure 1.

Figure 1

Begin skippable figure description.

Figure 1 is a circle with center C.Two diameters of the circle are drawn, dividing the circle into 4 sectors. Two nonadjacent sectors are shaded, and the central angle of one of the unshaded sectors measures 160 degrees.

End skippable figure description.

1. Figure 1 above shows a circle with center C and radius 6. What is the sum of the areas of the two shaded regions?

A.7.5 pi

B. 6 pi

C.4.5 pi

D.4 pi

E. 3 pi

Multiple-choice Questions — Select One or More Answer Choices

Numeric Entry Questions

Quantitative Comparison Questions

Each question appears either independently as a discrete question or as part of a set of questions called a Data Interpretation set. All of the questions in a Data Interpretation set are based on the same data presented in tables, graphs, or other displays of data. Below are descriptions, directions, and samples of each type of question.

Multiple-Choice Questions — Select One Answer Choice

Sample question 2 below is based on figure 2.

Figure 2

Begin skippable figure description.

Figure 2 shows the graph in the x y plane of the function f of x = the absolute value of 2x, end absolute value, + 4. There are equally spaced tick marks along the x axis and along the y axis. The first tick mark to the right of the origin, and the first tick mark above the origin, are both labeled 1.

The graph of the function f is in the shape of the letter V. It is above the x axis and is symmetric with respect to the y axis.

The lowest point on the graph of f is the point 0 comma 4 on the y axis.

Going leftward from the point 0 comma 4 the graph of fis a line that slants upward, passing through the point negative 2 comma 8.

Going rightward from the point 0 comma 4 the graph of f is a line that slants upward, passing through the point 2 comma 8.

End skippable figure description. 2. Figure 2 above shows the graph of a function f, defined by

f of x = the absolute value of 2x, end absolute value, + 4 for

all numbers x. For which of the following functions g defined for all numbers x does the graph of g intersect the graph of f? A. g of x = x minus 2

B.

C.

D.

E.

Answer: E (g of x = x + 3 g of x = 2x minus 2 g of x = 2x + 3 g of x = 3x minus 2 g of x = 3x minus 2)

Multiple-Choice Questions — Select One or More Answer Choices

These questions are multiple-choice questions that ask you to select one or more answer choices from a list of choices. A question may or may not specify the number of choices to select.

Sample Questions

Directions: Select one or more answer choices according to the specific question directions.

If the question does not specify how many answer choices to select, select all that apply.

The correct answer may be just one of the choices or may be as many as all of the choices, depending on the question.

No credit is given unless you select all of the correct choices and no others. If the question specifies how many answer choices to select, select exactly that number of choices.

1. Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The average (arithmetic mean) salary is \$25,000 for the employees in Department X and is \$35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees in the company? Indicate all such amounts.

A. \$26,000

B. \$28,000

C. \$29,000

D. \$30,000

E. \$31,000

F. \$32,000

G. \$34,000

Answer: A (\$26,000) and B (\$28,000)

2. If f, g, and h are positive integers, f is a factor of g, and g is a factor of h, which of the following statements must be true? Indicate all such statements.

A. f is a factor of

B. f is a factor of gh. C. f is a factor of h minus g. g squared), B (f is a factor of gh.), and g squared. Answer: A (f is a factor of

C (f is a factor of h minus g)

Numeric Entry Questions

Questions of this type ask you either to enter the answer as an integer or a decimal in a single answer box or to enter it as a fraction in two separate boxes — one for the numerator and one for the denominator. In the computer-administered test, the computer mouse and keyboard are used to enter the answer.

Sample Questions

Directions: Enter your answer in the answer box(es) below the question. Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Fractions do not need to be reduced to lowest terms. = 10 to the power negative 1, what is the value of

open parenthesis, x + the fraction 1 over x, close parenthesis,

times, open parenthesis, 1 over x , close parenthesis?

2. A university admitted 100 students who transferred from other institutions. Of these students, 34 transferred from two-year community colleges, 25 transferred from private four-year institutions, and the rest transferred from public four-year institutions. If two different students are to be selected at random from the 100 students, what is the probability that both students selected will be students who transferred from two-year community colleges? Quantitative Comparison Questions

Questions of this type ask the examinee to compare two quantities — Quantity A and Quantity B — and then determine which of four statements describes the comparison.

Sample Questions

Directions: Compare Quantity A and Quantity B, using the additional information given, if any. Select one of the following four answer choices.

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

A symbol that appears more than once in a question has the same meaning throughout the question.

1. Quantity A:

Quantity B: x squared + 1 2x, minus 1

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

Answer: A (Quantity A is greater.)