有代表性的数学题

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1.y=2x
2
+7x – 3

x y
2.
The figure above shows the graph of a function f, defined by f(x)=|2x|+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(x)x–2
B g(x)x3
C g(x)2x – 2
D g(x)2x3
E g(x)3x – 2
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


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E $$31,000
F $$32,000
G $$34,000
g alone at its constant rate, machine A produces k car parts in 10
minutes. Working alone at its constant rate, machine B produces k car parts
in 15 minutes. How many minutes does it take machines A and B, working
simultaneously at their respective constant rates, to produce k car parts?
____________minutes
5.
1)If the dollar amount of sales at Store P was $$800,000 for 2006, what was
the dollar amount of sales at that store for 2008 ?
A $$727,200
B $$792,000
C $$800,000
D $$880,000
E $$968,000
2)At Store T, the dollar amount of sales for 2007 was what percent of the
dollar amount of sales for 2008 ?
Give your answer to the nearest 0.1 percent.
___________%
3)Which of the following statements must be true?
Indicate all such statements.
A For 2008 the dollar amount of sales at Store R was greater than that at
each of the other four stores.
B The dollar amount of sales at Store S for 2008 was 22 percent less
than that for 2006.
C The dollar amount of sales at Store R for 2008 was more than 17
percent greater than that for 2006.
6.A certain store sells two types of pens: one type for $$2 per pen and the
other type for $$3 per pen. If a customer can spend up to $$25 to buy pens at


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the store and there is no sales tax, what is the greatest number of pens the
customer can buy?
A 9
B 10
C 11
D 12
E 20
7.A list of numbers has a mean of 8 and a standard deviation of 2.5. If x is a
number in the list that is 2 standard deviations above the mean, what is the
value of x ?
x=______
ncy Distribution for List X
Number 1 2 3 5
Frequency 10 20 18 12
Frequency Distribution for List Y
Number 6 7 8 9
Frequency 24 17 10 9
List X and list Y each contain 60 numbers. Frequency distributions for each list are
given above. The average (arithmetic mean) of the numbers in list X is 2.7, and the
average of the numbers in list Y is 7.1. List Z contains 120 numbers: the 60 numbers
in list X and the 60 numbers in list Y.
Quantity A Quantity B
The average of the 120numbers in list Z The median of the 120 numbers in list Z
figure above shows the graph of the function f in the xy-plane. What is
the value of f ( f (–1)) ?
A –2
B –1
C 0
D 1
E 2
weight, liquid A makes up 8 percent of solution R and 18 percent of solution S.
If 3 grams of solution R are mixed with 7 grams of solution S, then liquid A accounts
for what percent of the weight of the resulting solution?
A 10%
B 13%
C 15%
D 19%
E 26%


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the 700 members of a certain organization, 120 are lawyers. Two members of
the organization will be selected at random. Which of the following is closest to the
probability that neither of the members selected will be a lawyer?
A 0.5
B 0.6
C 0.7
D 0.8
E 0.9
k lies in the xy-plane. The x-intercept of line k is –4, and line k passes through
the midpoint of the line segment whose endpoints are (2, 9) and (2, 0). What is the
slope of line k ?
Give your answer as a fraction._______
13.
In the course of an experiment, 95 measurements were recorded, and all of the
measurements were integers. The 95 measurements were then grouped into 7
measurement intervals. The graph above shows the frequency distribution of the 95
measurements by measurement interval.
Quantity A Quantity B
The average (arithmetic The median of the 95
mean) of the 95 measurements
Measurements
random variable X is normally distributed. The values 650 and 850 are at the
60th and 90th percentiles of the distribution of X, respectively.
Quantity A Quantity B
The value at the 75
th
750


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percentile of the
distribution of X
1+x+x
2
+x
3
=60, then the average (arithmetic mean) of x, x
2
, x
3
, and
x
4
is equal to which of the following?
A 12x
B 15x
C 20x
D 30x
E 60x

16.
Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The
coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6).
What are the coordinates of point R ?
A (3, 2)
B (3, 3)
C (4, 4)
D (5, 2)
E (6, 2)
S be the set of all positive integers n such that n2 is a multiple of both
24 and 108. Which of the following integers are divisors of every integer n
in S ?
Indicate all such integers.


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A 12
B 24
C 36
D 72
range of the heights of the female students in a certain class is 13.2 inches,
and the range of the heights of the male students in the class is 15.4inches.
Which of the following statements individually provide(s) sufficient additional
information to determine the range of the heights of all the students in the class?
Indicate all such statements.
A The tallest male student in the class is 5.8 inches taller than the tallest female
student in the class.
B The median height of the male students in the class is 1.1 inches greater than the
median height of the female students in the class.
C The average (arithmetic mean) height of the male students in the class is 4.6 inches
greater than the average height of the female students in the class.
19.A random variable Y is normally distributed with a mean of 200 and a standard
deviation of 10.
Quantity A Quantity B
The probability of the event 16
that the value of Y is
greater than 220
a graduating class of 236 students, 142 took algebra and 121 took chemistry.
What is the greatest possible number of students that could have taken both
algebra and chemistry?__________students
total amount that Mary paid for a book was equal to the price of the book
plus a sales tax that was 4 percent of the price of the book. Mary paid for the book
with a $$10 bill and received the correct change, which was less than $$3.00. Which of
the following statements must be true?
Indicate all such statements.
A The price of the book was less than $$9.50.
B The price of the book was greater than $$6.90.
C The sales tax was less than $$0.45.


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of the following statements individually provide(s) sufficient additional
information to determine the area of triangle ABC above? Indicate all such
statements.
A DBC is an equilateral triangle.
B ABD is an isosceles triangle.
C The length of BC is equal to the length of AD.
D The length of BC is 10.
E The length of AD is 10
fabric needed to make 3 curtains sells for $$8.00 per yard and can be
purchased only by the full yard. If the length of fabric required for each
curtain is 1.6 yards and all of the fabric is purchased as a single length,
what is the total cost of the fabric that needs to be purchased for the 3
curtains?
A $$40.00
B $$38.40
C $$24.00
D $$16.00
E $$12.80
fabric needed to make 3 curtains sells for $$8.00 per yard and can be
purchased only by the full yard. If the length of fabric required for each
curtain is 1.6 yards and all of the fabric is purchased as a single length,
what is the total cost of the fabric that needs to be purchased for the 3
curtains?
A $$40.00
B $$38.40
C $$24.00
D $$16.00
E $$12.80


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the xy-plane, the point with coordinates (–6, –7) is the center of circle C.
The point with coordinates (–6, 5) lies inside C, and the point with
coordinates (8, –7) lies outside C. If m is the radius of C and m is an
integer, what is the value of m ?
m =_____
is the least positive integer that is not a factor of 25! and is not a
prime number?
A 26
B 28
C 36
D 56
E 58
27If 1 is expressed as a terminating decimal, how many nonzero digits
1[(2
11
)(5
17
)]
will the decimal have?
A One
B Two
C Four
D Six
E Eleven
hundred insects were weighed, and the resulting measurements, in
milligrams, are summarized in the boxplot below.
(a) What are the range, the three quartiles, and the interquartile range of the
measurements?
(b) If the 80th percentile of the measurements is 130 milligrams, about how
many measurements are between 126 milligrams and 130 milligrams?



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figure shows a normal distribution with mean m and standard deviation d,
including approximate percents of the distribution corresponding to the six regions
shown.
Suppose the heights of a population of 3,000 adult penguins are approximately
normally distributed with a mean of 65 centimeters and a standard deviation of 5
centimeters.
(a) Approximately how many of the adult penguins are between 65 centimeters and
75 centimeters tall?
(b) If an adult penguin is chosen at random from the population, approximately what
is the probability that the penguin’s height will be less than 60 centimeters? Give
your answer to the nearest 0.05
机经题:
8月
5选1
1. 3个数的平均数是30,把这3个数翻倍之后也加在这个list中。问加进去后,
6个 数的平均数是多少。

2. 一个矩形里有个圆,圆外的面积涂阴影,圆面积是阴影面积的一半,求矩形
面积与圆面积的比例。
补充:好像还有个答案是(0,-50)

3. 哪个选项满足-f(x)=f(x)? 然后给了一些函数表达式。爆简单吧~~

4. 本金是a(给了具体数的,忘了),单利,年利率r%,一个月后利息是a100,
求r。

5. 1-9这9个整数中选2个,选中的都是3的倍数的概率。



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6. x<0, 0
7. 某次测验,7 0分以上的有75%,85分以下的60%,求70到85分的人占总数
的百分比(应该是35%)

8. The average test score of 2 boys is 75 and that of 3 girls is 95. What is the total
average score of 5 people?

5选多
1. 一串数的range(极差)是21,求这串数中最小、最大值的可能组合。(秒杀,right?)

2. 坐标系中的一个圆,半径为50,圆心在原点,选哪些点在圆上。(30,40)OK,
(14,48)OK, 还有个选项也是可以的,忘了
还有好多是跟在图表后出的,不好描述。。。

3. ,好像是一个学校里有38是 女生,有150是生物系学生,问该校可能有几名
学生。(其实就是找能够8和50的公倍数)

Questions 4 ~6
显示关于Professor, assistant, researcher的salary的柱状图。
4. What is the median salary of assistant?
我选择了45-50之间的值。

5. What percent of total salary of professor is more than 100?
我选择了3%部分和14%的和值17%

6. If the average salary between 50~120 is x and that of more than 120
is y of professor, what is the total salary? (the percent of till 120
is 86%)
我选择0.86x + 0.14y.


AB值大小比较 (选项A: A>B, B: B>A, C: A=B, D: 大小关系不确定)
1. 17除以某个数余2,这个数叫A,B是4(我选D,A可以是3或5)

2. y方开根号=8, A=3^2y, B=3^(-2y) (选D,y可以是正负8)

3.数列首项a1是(1-12^2), an=(1-1(n+1)^2)*前一项(算下来就是a1=34,


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a2=89*34......) A是a5, B是12 (选A,a5=712)

4.
nk = 37

Column A
nk + kn

5.
A line passes (4, 6), (-6, 5)

Column A
The slope of the line A

6.
2
Column A Column B
The median of 5 integers The range of 5 integers

7.
F(x) : 2x + 4y = 6 and G(x) : 4x + 2y = 10. F(x) and G(x) intersect at a point (a, b)

Column A Column B
A b

8.
When 15 is divided by z, remainder is 2

Column A Column B
z 3





Column B
-1
Column B
1






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9.
In the figure above, This is regular hexagon

Column A Column B
The length of AB The length of CD

10.







Column A
The sum of a + b +c


11.
0 < x < 1 and n > 1

Column A
nx


12.
The mean of 600 females is 80 and standard deviation is 5. 86 is k
th
percentile
The mean of 400 males is 75 and standard deviation is 3. 81 is n
th
percentile

Column A Column B
k n



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Column B
180°
Column B
N




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13.


In the figure above, the line passes (0, 0) (4, -4)

Column A Column B
lal lbl


14.
x = y2

Column A
y + (x2)

15.
Column A
(5n - 3)3
Column B
(5n - 1)2
Column B
1.25y

16. 有一射击队,人数600人,对其射击结果打分,结果服从正 态分布,得到算
数平均分为84分,标准方差为5,假定分数大于90分的概率为k%; 另一射击队,
人数400人,对其射击结果打分,结果服从正态分布,得到算数平均分为80分,
标准方差为 3,假定分数大于86分的概率为n%; 问k和n谁大?(具体数据记
不清了,但就是这样的题目)

17. 已知P1=34;Pn=(1-(1(n-1)2))*Pn-1 (n≥2)。问P8 和 12的大小?



数值填空
1. 3个不同的整数相加是76,x是3数中最大的,求x的最小值 (我填的是27)

2.( 原题不是这么说的,而是给了一个图再描述,信息提取出来是这样滴)x、y
两个角,相加180度,x 是y的2.5倍+12,求x

3. 7个队伍比赛,第一轮中,每个队跟其余6个队都各赛3场,求第一轮中总的


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比赛场数

4. 一个比赛有七个人参与,规定每两个人组队完成一个游戏。如果在 一轮比赛
中,每个人都要和另外一个人组队,每个队要进行三个游戏,那么问最终这一轮
比赛后 ,一共进行了多少个游戏?


不确定题型
1. A衣服买了100件 ,B衣服买了150件,A衣服的单价比B衣服便宜30美元,
总共花了10500块,问A衣服的单价 是多少?

2. |x| + |y| = 6, 这个方程式在坐标上所围成的图形宽是多少?

3. 7. In 1981 Ms. Jones paid 20 percent less in federal taxes than in 1980, and in 1982
she paid 30 percent more in 1981. In 1982 Ms. Jones paid what percent less or more
in federal taxes than in 1980?

4.△ABC is right triangle and angle B,D are right angles , ∠BAC = 30˚, AC = 4, what is
the length of BD?


5. Y = ?


6. The average of set A consisting 30 integers is 30. If the value of each components
of set A is twice and appended to the original set A, what is the average of new set
consisting 60 integers?



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7. From 6 boys and 3 girls, 2 people are selected. What is the probability that two
selected are girls?

8. 变化率最大的是?

A
B
C
D
E

Questions 9 ~ 11
1990
$$84
$$82
$$87
$$100
$$46
2000
$$90
$$88
$$80
$$90
$$50

A=4%, B=7%, C=8%, D=12%, E=23%, F = 46%
(Total = 30 billion, *1 billion = 109)

9. What is the central angle of the potion 12%?

10. What amount of total is difference between B and D? (in billion)

11. What fraction of the others is E?

12. Which of followings is f(-x) = -f(x)?
A) x3(x2+1) B) x4 + x2 C) x2(x + x2) D) x3(x2 + x)


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13. If the value of a solution of 8x2+2x+k is 12, what is the other solution?

14. What is the median of 10, 10, 8, 8, 8, 12, 12?

15. 连续扔硬币六次,同一面不连续出现的概率有多少?

16. 把圆形蛋糕分成8份时, 把sector shape cake的central angle设为 x,分成
12份时sector shape cake的central angle设为Y时,xy=?

17. The three vertexes of a rectangle are (0, 4), (0, -3), (7, -3), what is the perimeter
of the rectangle?

18.

Number 1 2 5 7 1 4


Score x 1 2 1 3 2

If the average score of 20 cards is 2, what is the value of x?

19. If x + y ≤ 11, what is the greatest value of x*y? (x and y are positive integers)

20. In a rectangle of which width and height is 10 and 12 each, a circle is located. If
the diameter of the circle is 8, what is the area of the rectangle except the circle?

21. x and y are positive integers greater than 1. If 4x + 12y = 100 and x < y, what is
the value of x?

22. one-fifth of 1% of x = ? (In terms of x)
9月
1. 六个连续的奇数(整数)相加,不可能得到以下哪个结果

2. 一个等腰直角三角形里面镶嵌一个正方形,图画的不好,差不多是这样,正
方形的底边是 个三角形的斜边是重合,并且是斜边的13。已知三角形面积是r,
求1这个小三角面积

3. V1: 一个数把它的三角形向右移六次,得到的数是原来这个数的倒数的九倍,
求这个 数,好像是这个,记得不太清楚了。


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V2:一个数的小数点向右移动六位后得到的数与原数的倒数的3倍还是多少相
等,求这个 数,最后结果是0.003。 中间的关系是怎么着我也忘了,看清题,
认识倒数(reciprocal)就能做对。

4. x的平方<36 让我们比较 x的最大值跟最小值的差与12的大小 应该是等


5. 给了一个表格,表示一二三四年级的人数,一个教授要建一个小 组,从二三
四年级中各选相应的人数,用乘法计算就对了。

6. 一道图表题给的 一个大学的藏书的来源,好像是四个书店,第二个图是某一
个书店卖给这个大学的书中不同种类书的数量 。 需要注意的是,图中列出的并
不是所有图书的种类而是部分图书种类,因此给出的这些书的总数小于 这个书店
卖给大学的书,要用第一个表中的数据,题目中有一个好像用到了,但是即使没
注意到 这个问题也不一定做错。

7. 比较25的九次方的倒数 与 625的4次方还是几次方的 最后两个结果是相
等的

8. 有个等腰直角三 角形内嵌正方形的题,开始还没想到,后来才想起来。问一
个三角形的面积占总面积的比例。

9. 还有一个是正方形绕一点旋转,对着那点绕成的圆面积

10. 一道图表分 析题,提供了一个柱面图,显示了几年间某公司在欧洲分部和美
国分部的年收入情况,出了三道题,
其中有一个概念没搞懂:。

11. 三角型三边长5,6,8,问你5,6边夹的那个角和90度比较

12. 一个数列是S(n+1)=(13)Sn,问你S(11)和S(28)(3^17)的关系

13. 投资$$96,000,simple annual interest,第一个月拿了$$960利息,问年利息多少

14. 一个班75%的同学分数在70分以上,60%的同学分数在85分以下,问70~
85分之间的比例



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15. 有一个圆心在坐标系原点的圆,再画一条slope是12的直线,问第一象限交
点的坐标
数轴上有两个负数,三个正数,任取三个,问取到不同三个正数的概率

16. -1
17. 已知三个不等正整数之和为76,问其中最大的一个数a,它最小的可能值是多
少.这题是填空题. 三角形
10月
1. 整体数学比我3年前在国内考笔考的时候难多了。第一个Q一上来就吓 了我
一跳,一开始就是standard deviation,然后概率、组合、解析几何都考到了,而
且不只出现一次。

2. 是一个正五边形,它的边长是另一个正五边形边长的两倍,问小的那个正五
边形是大的正 五边形的几分之几。
11月
1,有复利、等比数列,统计方面的比较多,比如range 中位数平均数什么的。
每个Q平均有一个统计图的大题,要答3到4道题,难度不大,但很费时间。还有一个算cube的容积什么的

2,还有那个example 4.2.9,还有OG最后那个模考练习里面也有一题,具体哪题
忘掉

3,有一道,10,20,30 ,x,50,60,70,问平均数和x比大小。

4,还有一个8、6、5、7忘了是不是这些数了,说他们组成的四位数一共可以是
20个,从小到大 排列问……失忆……,好像是那个特定的数排第几个。

5,invest多少钱,simple interest rate,求单个月的利息是多少

6,五边形,A、B、C三个内角是270度,问D、E加起来多少度。答案270

7,根号x方=9,问2的负x次方和2的x次方作比较。选D吧

8,特别说一下正态分布题目,没有专门考到,倒是涉及median的好几道

9,问了好多rectangular, median, possible max&min, trapezoid的,还有个直方图
我貌似看见所有人都有得做


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10,有道给了一组四个数,都是80左右的,另外一组是这四个数都减去一个x,
问两组的方差大小,当然是一样啦

11,我考到的数列题挺多,有道是An=12A(n- 1)+4,A1=0,问A100接近多少,答案
是8
有道45度等腰直角三角形面积题和一 个正八边形的外接圆的圆心到各个边的角
度问题,67.5度答案

12,输入题一道 一个数小数点右移六位,这个数等于原数的倒数乘以九,原数
是多少 0.003无误

13,还有道percentile的题,得分Y是52 X是64的pe rcentile,10000学生做200
道题,答案记得选A,好像是说Y得分比X少,这道有点疑 惑性

14,新G中出现了中国学生不太熟悉的唯一知识点应该是normal distribution,
在OG的289页,考前一定要记得看的









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