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GRE数学课件


* Arithmetic * Algebra

算术、计算 代数

* Geometry
* Data Analysis

几何
数据分析

* Arithmetic
1 integers positive negative zero
add subtract

multiply divide sum difference product factor divisor multiple least common multiple greatest common divisor/factor quotient remainder even/odd integer prime number

* Arithmetic
? Which of the following could be the remainder when four consecutive positive integers are each divided by 3? ? A. 1,2,3,1 ? B. 1,2,3,4 ? C. 0,1,2,3 ? D. 0,1,2,0 ? E. 0,2,3,0

* Arithmetic
? Three individuals contributed $800 each toward the purchase of a computer.if they bought the computer on sale for $1950 plus 10 percent sales tax,how much money should be refunded to each individual? ? A.$65 B.$85 C.$150 ? D.$195 E.$255

* Arithmetic
? 1,234,…1,920,21…,484,950 ? The integer above is formed by writing the integers from 1 to 50,in older,next to each other.if the integer is read from left to right,what is the 50th digit from the left? ? A.0 B.1 C.2 D.3 E.9

* Arithmetic
? How many integers greater than 20 and less than 30 are each the product of exactly two different numbers,both of which are prime? ? A.zero B.one C.two ? D.three E.four

* Arithmetic

? The figure above shows the remaining pieces of a paper chain from which a section has been removed. the first link of the original chain was red and the colors of the links formed the repeating pattern of red (R), yellow (Y), green (G), white (W) and blue (B) from left to right. which of the following could be the number of links in the section that was removed? ? A.60 B.61 C.62 D.63 E.64

* Arithmetic
? In the figure above,three wires are braided.that is,by starting in the orderA,B,C,the outer left wire A is brought over wire B to the middle position.forming the order shown in step 1,then the outer right wire C is brought the new middle position shown in step 2.and so on,alternately bringing each new left and new each right wire to the middle.at what numbered step does the braid first repeat the original order A,B,C? ? A.3 B.4 C.5 D.6 E.7

* Arithmetic
? A secretary typed 6 letters,each of which had either 1 or 2 pages.if the secretary typed 10 pages in all,how many of the letters had 2 pages? ? A.1 B.2 C.3 D.4 E.5

* Arithmetic
2 fractions numerator 分子 denominator 分母
rational numbers reciprocal mixed number

* Arithmetic
3 exponents and roots
base exponent squaring square root cube root fourth root odd-order roots even-order roots

* Arithmetic
? If i= ?1 ,for which of the folloeing values of n does i n ? (?i)n have a positive value? ? A.23 B.24 C.25 ? D.26 E.27

* Arithmetic
4 decimals 小数、十进制数 terminate repeat

5 real number number line interval 区间

absolute value

* Arithmetic
? 5.101001000100001… ? The decimal number above consists of only 1’s and 0’s to the right of the decimal point.the first 1 is followed by one 0, the second 1 is followed by two 0’s, the third 1 is followed by three 0’s,and so on . what is the total number of 0’s between 98th and the 101st 1 in this decimal number? ? A.288 B.291 C.294 D.297 E.300

* Arithmetic
6 ratio proportion percent
percent increase percent decrease 7 Sequence arithmetic Sequence geometric Sequence

* Arithmetic
? If United States imports increased 20 percent and export decreased 10 percent during a certain year,the ratio of imports to exports at the end of the year was how many times the ratio at the beginning of the year? ? A. 12/11 B. 4/3 C.11/8 ? D. 3/2 E.2

* Arithmetic
? 一个电影院,第一排有16个位置,每后一 排多两个,最后一排64,问总共多少位置 ?

? 一个球落下弹回原高度75%,到第三次落 地共旅程为2146CM,问最初高度?

* Arithmetic
? n, __, 2n, __ ? The first number in the sequence above is n,and each number after the first is p units greater than the previous number.in terms of p,what is the sixth number in the sequence ? A.3p B.4p C.5p D.6p E.7p

* Arithmetic
? In a list of numbers,the first number is 3.the second is 4.and each subsequent number is the sum of all the proceeding numbers in the list.if the 20th number in the list is x.what is the 25th number in the list? ? A.7X B.16X C.32X ? D.35X E.161X

* Arithmetic
? 3, 5, -5,… ? The first term in the sequence of numbers show above is 3.each even-numbered term is 2 more than the previous term and each odd-numbered term,after the first, is -1 times the previous term .for example,the second term is 3+2,and the third term is(?1) ? 5.what is the 55th term of the sequence? A.-5 B.-3 C.-1 D.3 E.5

* Algebra
1 operations with algebraic expressions
constant variable coefficient equation solutions a linear equation in two variables quadratic

* Algebra
2 rules of exponents 3 solving linear equations
4 solving quadratic equations quadratic formula factoring 5 solving linear inequalities 6 functions domain range

* Algebra
7 applications

e.g. Ellen has received the following scores on 3 exams:82,74,and 90.What score will Ellen need to receive on the next exam so that the average score for the 4 exams will be 85
e.g. In a driving competition, Jeff and Dennis drove the same course at average speeds of 51 miles per hour and 54 miles per hour, respectively. If it took Jeff 40 minutes to drive the course, how long did it take Dennis?

* Geometry
interest——simple interest compound interest principal annually quarterly monthly e.g. A college student expects to earn at least $1000 in interest on an initial investment of $20000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

* Algebra
8 translation the graph of h(x)+c is the graph of h(x) shifted upward by c units shifted downward shifted to the left shifted to the right

* Geometry
1 lines and angles
point line plane line segment endpoint angles vertex midpoint

intersection obtuse angle

opposite angles = vertical angles right angle acute angle

* Geometry
2 triangles interior angles equilateral triangle

isosceles triangle
right triangle legs hypotenuse pythagorean theorem congruent triangles similar triangles

* Geometry
? In △PQR above, QS ? 1
QV
QS 1 ? QV 3

3

and

PT 3 ? . PR 4

what is the

value of the fraction
area?PST area?PQR

* Geometry
3 quadrilaterals rectangle square

parallelogram
trapezoid 4 circles center radius diameter chord circumference arc central angle sector

a tangent to a circle point of tangency

* Geometry
? In the figure show above,lengthsAB,BD, and CDare all 3 2 units.angles Aand C are both 450 .what is the perimeter of ABCD? What is the area of ABCD?

3 2

* Geometry
? In the figure above,ABCD is a rectangle with BC=4 and AB=6 ? Points P,Q,and R are different points on a line (not shown) that is parallel to AD.points P and Q are symmetric about line AB and points Q and R are symmetric about line CD.what is the length of PR? ? A.6 B.8 C.10 D.12 E.20

* Geometry
? In the figure show above,A is center of a circle whose area is 25 ? .B and C are points on the circle.the measure of angle ABC is 450.what is the length of line segment BC?

450

* Geometry
? In the figure above,O is the center of the circle and arc SRT has length 2? ,if the circumference of the circle is 12? ,what is the value of x+y? ? A.60 B.90 C.120 D.150 ? E.it cannot be determined from the information given.

* Geometry

? A circle of radius ? rolls to the right along the line shown above without slipping.in the starting position,point Aon the circle touches the line for the first time at point 0 on the line. At what point on the line will point A touch the line for the fourth time? ? A.12 B.10 C.8 D.6 E.4

2

* Geometry
5 polygons regular polygon (n-2)(180°) 6 three-dimensional figures rectangular solid faces edge vertex cube volume surface area circular cylinder lateral surface perimeter area

* Geometry
? In the stop sign shown in the figure above,all sides have equal length and all angles have equal measure.if the figure could be rotated 225 degrees in a counterclockwise direction,point G would be in the position of point ? A. I B.J C.K D.L E.M

* Geometry
? The figure above shows a cylinder with radius 2 and hight 5.if points A and B lie on the circumference or the top and bottom of the cylinder,respectively,what is the greatest possible straight-line distance between A and B? ? A.3 B.5 C.7 D. 29 E. 41

* Geometry
? In a plane ,two regions, S and T, are called “unlinked” if (1)S has no points in common with T. ? (2)any line segment that can be drawn with both endpoints in S has no points in common with any line segment that can be draw with both endpoints in T. ? Which of the following shows a pair of regions that are unlinked?

* Geometry
7 coordinate geometry rectangular coordinate system xy-coordinate system xy-plane x-axis y-axis quadrants I, II, III, IV x-coordinate y-coordinate origin graph of an equation——linear equation slope x-intercepts y-intercepts parallel lines perpendicular lines

* Geometry
? In the xy-plane,point R(2,3) and point S(5,6) are two vertices of triangle RST.if the sum of the slopes of the sides of the triangle is 1,which of the following angles could be a right angle? ? 1.R 2.S 3.T ? A.none B.1only C.3only ? D.1and3 only E.1,2and3

* Geometry
7 coordinate geometry line of symmetry (y=2x+5 & x=2y+5)

graph of an equation——quadratic equation parabola vertex graph of an equation——circle point(a,b) radius r

* Geometry
? The figure above shows the graph of a quadratic function f that has a minimum at the point (1,1).if f(b)=f(3),which of the following could be the value of b? ? A.-3 B.-2 C.-1 ? D. 1 E.5

* Geometry
? Point O has coordinates (0,0),point P lies on the graph y ? 6 ? x2 ,and point B has of coordinates (2 3,0) .if OP=BP,the area of triangle OPB is ? A.1.7 B.3.0 C.3.5 ? D.4.7 E.5.2

* Geometry
? The figure above shows the graphs of y=x^2 and y=ax^2 for some constant a.if the length of PQ is equal to 6,what is the value of a?
? A.6 D.15 B.9 C.12 E.18

* Geometry
? In the xy-plane above , point Q and S are the centers of the circles , which are tangent to the x-axis . what is the slope of line QS? ? A.1/8 B.1/4 C.1/2 ? D.7/8 E.1

* Data Analysis
1 graphical methods for describing data frequency distributions
Number of children 0 1 2 3 4 5 Total

Frequency
3 5 7 6 3 1 25

Number of children 0 1 2 3 4 5 Total

Relative Frequency 12% 20% 28% 24% 12% 4% 100%

* Data Analysis
Number of siblings per student in a preschool class
Number of Siblings Number of Students

0
1 2 3

3
6 2 1

? The table above shows how many students in a class of 12 preschoolers had 0,1,2,or 3 siblings.later,a new student joined the class,and the average(arithmetic mean) number of siblings per students became equal to the median number of siblings per student.how many siblings did the new students have? ? A.0 B.1 C.2 D.3 E.4

* Data Analysis
1 graphical methods for describing data bar graphs

* Data Analysis
1 graphical methods for describing data segmented bar graphs

* Data Analysis
1 graphical methods for describing data bar graphs

* Data Analysis
1 graphical methods for describing data circle graphs

* Data Analysis
1 graphical methods for describing data scatterplot

* Data Analysis
1 graphical methods for describing data time plots

* Data Analysis
2 numerical methods for describing data measures of central tendency arithmetic mean——average weighted mean median mode
2,4,4,5,7,7,7,7,7,7,8,8,9,9,9,9,

* Data Analysis
2 numerical methods for describing data measures of position quartiles first quartile Q1 second quartile Q2=M third quartile Q3 percentiles P1 P2……P99 Q1=P25 Q2=P50=M Q3=P75
2,4,4,5,7,7,7,7,7,7,8,8,9,9,9,9,

* Data Analysis
2 numerical methods for describing data measures of dispersion range = G - L outliers inter-quartile range = Q3 - Q1 boxplots box-and-whisker plots

2,4,4,5,7,7,7,7,7,7,8,8,9,9,9,9,

* Data Analysis
2 numerical methods for describing data standard deviation
Six hundred applicants for several post office jobs were rated on a scale from 1 to 50 points. The ratings had a mean of 32.5 points and a standard deviation of 7.1 points. How many standard deviations above or below the mean is a rating of 48 points? A rating of 30 points? A rating of 20 points? 48 points is 15.5 points above the mean, or approximately 2.2 standard deviations above the mean.

* Data Analysis
3 counting methods
sets members elements finite infinite empty set nonempty set subset intersection union Venn diagram

* Data Analysis
? 最近演了3部电影。调查了100个人,其中20人看 了所有3部,10人什么都没看。看了每部电影的 人数分别为:47,48,55。问:只看了2部的人 数? A 20, B 30, C 40, D 70, E 90。

* Data Analysis
3 counting methods
multiplication principle Suppose that a computer password consists of four characters such that the first character is one of the 10 digits from 0 to 9 and each of the next 3 characters is any one of the uppercase letters from 26 letters of the English alphabet. How many different passwords are possible?

* Data Analysis
? If p,r,and s are three different prime numbers greater than 2,and n=p×r×s,how many positive factors,including 1 and n,does n have?

* Data Analysis
3 counting methods
permutations and factorials combinations

? 有两个老师三个学生排队,老师只能在最 前或最后,有多少种排法? ? 6本书其中 paper book 4 本,hard book 2本 .求取3本至少1本hard book, 有多少种取法 ?

* Data Analysis
? ◎ ☆ ◆ ㊣ ⊙ ? If the 5 cards show above are placed in a row so that ◆ is never at either end ,how many different arrangements are possible?

* Data Analysis
4 probability outcome

sample space

event

P(E)

P∩E P∪E mutually exclusive

* Data Analysis
? On Monday,Anderson High School’s basketball team will play the team from Baker High School.On Wednesday, Baker’s team will play the team from Cole High School.On Friday, Cole will play Anderson.in each game,either team has a 50 percent chance of winning. ? (a)what is the probability that Anderson will win both its game? ? (b)what is the probability that Baker will lose both its game? ? (c)what is the probability that Anderson will win both its game and Baker will lose both its game?

* Data Analysis
on the desk show above, a player spins the arrow twice .the fraction a is formed, where a b is the number of the sector where the arrow stops after the first spin and b is the number is the sector where the arrow stops after the second spin . on every spin, each of the numbered sectors has an equal probability of being the sector on which the arrow stops. a what is the probability that the fraction is b greater than 1? ? A. B. 16 C. D. 20 E. 21

15 36

36

18 36

36

36


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