SAT数学难题汇总及答案
x^2 表示 x 的平方， =！表示不等于。 pi 表示圆周率
类型 1 ：
20.The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set
(A)25
(B)26
(C)50
(D)51
(E)52
14.Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible
16. Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z
(A)x + y + k
(B)x + y - k
(C)x + y + 2k
(D)x + y - 2k
(E)2x + 2y - 2k
20.There are 75 more women than men enrolled in Linden College. If there are n men enrolled, then, in terms of n, what percent of those enrolled are men
17.A merchant sells three types of clocks that chime as indicated by the check marks
in the table above. What is the total number of chimes of the inventory of clocks in
the 90-minute period from 7:15 to
8:45
is never at eithe end, how 18. If the 5 cards shown above are placed in a row so
many different arrangements are possible
20.When 15 is divided by the positive integer k, the remainder is 3. For how many
different values of k is this true
(A)One
(B)Two
(C)Three
(D)Four
(E)Five
17.On the number line above, there are 9 equal intervals between 0 and 1. What is
the value of x
19.If a, b. c, and f are four nonzero numbers, then all of the following
proportions are equivalent
EXCEPT (A)
a/f=b/c
(B)f/c=b/a
(C)c/a=f/b
(D)a/c=b/f
(E)af/bc=1
/1
8. If a and b are positive integers and what is the value of ab
(A) 6
(B)12
(C)18
(D)24
(E)36
16. After the first term, each term in a sequence is3 greater than1/3of the preceding term. If t is the first term of the sequence and t=!0. what is the ratio
of the second term to the first term
15. The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job.
The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible
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
18. If the sum of the consecutive integers from-22 to x, inclusive, is 72,
what is the value of x (A) 23
(B) 25
(C) 50
(D) 75
(E) 94
17. For all positive integers j and k. let j \R\ k be defined as the whole number
remainder when j is divided by k. If 13 \R\k = 2, what is the value of k
19, In a set of eleven different numbers, which of the following CANNOT affect
the value of the median
(A)Doubling each
number
(B) Increasing each number by
10
(C)Increasing the smallest number only
(D) Decreasing the largest
number only (E) Increasing the
largest number only
15.A store charges $28 for a certain type of sweater. This price is 40 percent more
than the amount it costs the store to buy one of these sweaters. At an end-of-season
sale, store employees can purchase any remaining sweaters at 30 percent off the store's cost How much would it cost an employee to
purchase a sweater of this type at
this sale (A) $
(B)
$ (C)$ (D)
$ (E) $
and Corinne stand back-to-back. They each take 10 steps in opposite directions away from each other and stop. Alice then turns around, walks toward Corinne. and reaches her in 17 steps. The length of one of Alice's steps is how many times the length of one of Corinne's steps (All of Alice's steps are the same length and all of Corinne's steps are the same length.)
14.If n and p are integers greater than 1 and if p is a factor of both n +3 and
n + 10. what is the value of p
(A) 3
(B)7
(C)10
(D)13
(E)30
16.In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5to 2. How many pounds of cashews will there be in 4 pounds of this mixture
14.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
20.If k is a positive integer, which of the following must represent an even
integer that is twice the value of an odd integer
(A) 2k
(B) 2k + 3
(C)2k+ 4
(D)4k+1
(E)4k+ 2
类型 2 ：
18. The shaded region in the figure above is bounded by the x‐ axis, the line x
=4, and the graph of y = f(x).If the point (a, b) lies in the shaded region,
which of the following must be true
I. a < 4II. b
III. b < f(a) (A) I
< a
only
(B)III only
(C)I and II
only (D) I and
III only(E)
I. II, and III
19.At a bottling company,machine A fills, a bottle with spring water and machine B accepts
the bottle
only if the number of fluid ounces 117
12
1
If machine B accepts a and
is between88
bottle containing n fluid ounces,which of the following describes all possible values of n
7.Dwayne has a newspaper route for which he collects k dollars each day. From this
amount he pays out k/3 dollars per day for the cost of the papers, and he saves the rest of the money. In terms of k, how many days will it take Dwayne to save $1,000
17. In the xy-coordinate plane, the graph of x = y*y -4 intersects line l at (0, p)
and (5, t). What is the greatest possible value of the slope of l
18.Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning
14. If (a + b)^ = (a - b) ^, which of the following must be
true (A) b = 0
(B) a + b = 1
(C) a - b = 1
(D)a^2 + b^2 = 1
(E)a^2 - b^2 = 1
15.The figure above shows the graphs of y = x*x and y = a - x*x
for some constant
a. If the length of
PQ is equal to 6, what is the value
of a (A) 6
(B)9
(C)12
(D)15
18.During a sale, a customer can buy one shirt for x dollars. Each additional shirt the customer buys costs z dollars less than the first shirt. For example, the cost of the second shirt is x - z dollars. Which of the following represents the customer's cost, in dollars, for n shirts bought during this sale
16. Let the function h be defined by h(x) = 14 + x^2/4. If h(2m) = 9m, what is one possible value of m
16. If x is an integer greater than 1 and if y = x + 1/x, which of the following
must be true I. y =! x II. y is an integer.III. xy > x^2
(A)I only
(B)III only
(C)I and II
only (D) I and
III only (E) I,
II, and III
6. If m and k are positive and 10(m^2)*k^-1= 100m, what is m^-1! in
terms of k (A) k/10
(B)k/90
(C)k^10 (D)
1/10k
(E)1/90k
8. 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
16. If a + 2b is equal to 125 percent of 4b, what is the value of a/b
's biology experiment involved timing 12 hamsters in a maze. Each hamster received at
least one practice before being timed. The scatter plot above shows the time took to complete the maze and the corresponding number of practices that each hamster received. Based on the data, which of the following functions best relationship between t, the number of seconds to complete the maze, and p, the number of practices each hamster models the
(A)t(p) = 44
(B)t(p) = p
(C)t(p)=
44p
(D)t(p)=
p/44 (E) t(p)=
p+ 44
20. For all numbers .t and v. let the operation□ be defined by x□v = xy - y If a and b re positive integers, which of the following can be equal to zero
I.a
□b
II. (a + b)
□b IIl.a
□(a + b) (A)
I only
(B)II only
(C)IIl
only (D) I and ll (E) I and IIl
18.In the figure above, ABCD is a rectangle. Points A and C lie on the graph of y
= p*x^3, where p is a constant. If the area of ABCD is 4, what is the value of p
19. If k, n, x, and y are positive numbers satisfying x ^(-4/3)=k^-2 and y^(4/3) = n^2, what is
(xy)^(-2/3 in terms of n and k
(A) 1
(B)
1/2 (C) 3/2
(D)6/5
(E)3
8. The price of ground coffee beans is d dollars for 8 ounces and each ounce makes c
cups of brewed coffee. In terms of c and d. what is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee
15.Ifx^2-y^2 = 10 and x +y = 5. what is the
value of x - y
18. The average (arithmetic mean) of the test scores of a class of p students is 70.
and the average of the test scores of a class of n students is 92. When the scores of
both classes are combined, the average score is 86. What is the value of
p/n
1.正整数n有奇数个因子,则n为完全平方数 2.因子个数求解公式:将整数n分解为质因子乘积形式,然后将每个质因子的幂分别加一相乘.n=a*a*a*b*b*c则因子个数=(3+1)(2+1)(1+1) eg. 200=2*2*2 * 5*5 因子个数=(3+1)(2+1)=12个 3.能被8整除的数后三位的和能被8整除;能被9整除的数各位数的和能被9整除.能被3整除的数,各位的和能被3整除. 4.多边形内角和=(n-2)x180 5.菱形面积=1/2 x 对角线乘积 6.欧拉公式：边数=面数+顶点数-2 8.三角形余玄定理 C2=A2+B2-2ABCOSβ,β为AB两条线间的夹角 9.正弦定理:A/SinA=B/SinB=C/SinC=2R(A,B,C是各边及所对应的角,R是三角形外接圆的半径) 10.Y=k 1X+B 1 ,Y=k 2 X+B 2 ，两线垂直的条件为K 1 K 2 =-1 11.N的阶乘公式: N!=1*2*3*....(N-2)*(N-1)*N 且规定0!=1 1!=1 Eg:8!=1*2*3*4*5*6*7*8 12. 熟悉一下根号2、3、5的值 sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236 13. ...2/3 as many A as B: A=2/3*B ...twice as many... A as B: A=2*B 14. 华氏温度与摄氏温度的换算 换算公式:(F-32)*5/9=C PS.常用计量单位的换算:（自己查查牛津大字典的附录吧）
练习题: 1：还有数列题：a1=2，a2=6，a n=a n-1/a n-2，求a150. 解答: a n=a n-1/a n-2,所以a n-1=a n-2/a n-3,带入前式得a n=1/a n-3,然后再拆一遍得到a n=a n-6,也就是说,这个数列是以6为周期的,则a150=a144=...=a6,利用a1,a2可以 =1/3. 计算出a 6 如果实在想不到这个方法,可以写几项看看很快就会发现a150=a144,大胆推测该数列是以6为周期得,然后写出a1-a13(也就是写到你能看出来规律),不难发现a6=a12,a7=a13,然后那,稍微数数,就可以知道a150=a6了,同样计算得1/3. 2：问摄氏升高30度华氏升高的度数与62比大小. key:F=30*9/5=54<62 3：那道费波拉契数列的题:已知,a1=1 a2=1 a n=a n-1+a n-2，问a1,a2,a3,a6四项的平均数和a1,a3,a4,a5四项的平均数大小比较。 解答:费波契那数列就是第三项是前两项的和,依此类推得到a1-a6为: 1 1 2 3 5 8 13 21 a1+a2+a3+a6=12, a1+a3+a4+a5=11,所以为大于. 4：满足x^2+y^2<=100的整数对（x,y）有多少？ key: 按照X的可能情况顺序写出: X= Y= 11-9 21-9 31-9 41-9 51-8 61-8 71-7 81-6 91-4 ＝>My answer:加起来=69 5：24，36，90，100四个数中,该数除以它的所有的质因子，最后的结果是质数的是那个：Key:90
2017年全国硕士研究生入学统一考试 数学二真题分析 （word 版） 一、选择题：1～8小题，每小题4分，共32分，下列每小题给出的四个选项中，只有一项符合题目要求的，请将所选项前的字母填在答题纸．．． 指定位置上. （1） ）若函数10(),0x f x ax b x ?->?=??≤? 在0x =处连续，则（ ） (A)12ab = (B)12ab =- (C)0ab = (D)2ab = 【答案】A 【解析】001112lim lim ,()2x x x f x ax ax a ++→→-==Q 在0x =处连续11.22b ab a ∴=?=选A. （2）设二阶可导函数()f x 满足(1)(1)1,(0)1f f f =-==-且''()0f x >，则（ ） 【答案】B 【解析】 ()f x 为偶函数时满足题设条件，此时01 10()()f x dx f x dx -=??，排除C,D. 取2()21f x x =-满足条件，则()112112()2103 f x dx x dx --=-=-
【答案】D 【解析】特值法：（A ）取n x π=，有limsin 0,lim n n n n x x π→∞→∞ ==，A 错； 取1n x =-，排除B,C.所以选D. （4）微分方程的特解可设为 （A ）22(cos 2sin 2)x x Ae e B x C x ++ （B ）22(cos 2sin 2)x x Axe e B x C x ++ （C ）22(cos 2sin 2)x x Ae xe B x C x ++ （D ）22(cos 2sin 2)x x Axe e B x C x ++ 【答案】A 【解析】特征方程为：2 1,248022i λλλ-+=?=± 故特解为：***2212(cos 2sin 2),x x y y y Ae xe B x C x =+=++选C. （5）设(,)f x y 具有一阶偏导数，且对任意的(,)x y ，都有(,)(,)0,0f x y f x y x y ??>>??，则 （A ）(0,0)(1,1)f f > （B ）(0,0)(1,1)f f < （C ）(0,1)(1,0)f f > （D ）(0,1)(1,0)f f < 【答案】C 【解析】(,)(,)0,0,(,)f x y f x y f x y x y ??>
新SAT 数学OG 数学题目详细讲解 第一题: Content: Heart of Algebra Key: B Objective: You must make a connection between the graphical form of a relationship and a numerical description of a key feature. Explanation: Choice B is correct. The slope of a line can be determined by finding the difference in the y-coordinates divided by the difference in the x-coordinates for any two points on the line. Using the points indicated, the slope of line l is - 3/2. Translating line l moves all the points on the line the same distance in the same direction, and the image will be a line parallel to ￡. Therefore, the slope of the image is also - 3/2. 第二题：
Content: Passport to Advanced Math Key: A Objective: You must complete operations with multipleterms and manipulate an equation to isolate the variable of interest. Explanation: Choice A is correct. Multiplying both sidesof the equation by the denominators of the rational expressions in the equation gives 2y = 4a - 4. You should then divide both sides by 2 to isolate the y variable, yielding the equation y = 2a - 2. 第三题： Content: Heart of Algebra Key: D Objective: You must interpret the slope of an equationin relation to the realworld situation it models. Also, when themodels are created from data, you must recognize that these models only estimate the independent variable, y, for a given value of x. Explanation: Choice D is correct. When an equation is written in the form y = mx + b, the coefficient of the x-term (in this case 0.8636) is theslope. The slope of this linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x). 第四题：
SAT数学真题精选 1. If 2 x + 3 = 9, what is the value of 4 x – 3 ? (A) 5 (B) 9 (C) 15 (D) 18 (E) 21 2. If 4(t + u) + 3 = 19, then t + u = ? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 3. In the xy-coordinate (坐标) plane above, the line contains the points (0,0) and (1,2). If line M (not shown) contains the point (0,0) and is perpendicular （垂直）to L, what is an equation of M? (A) y = -1/2 x (B) y = -1/2 x + 1 (C) y = - x (D) y = - x + 2 (E) y = -2x 4. If K is divisible by 2,3, and 15, which of the following is also divisible by these numbers? (A) K + 5 (B) K + 15 (C) K + 20 (D) K + 30 (E) K + 45 5. There are 8 sections of seats in an auditorium. Each section contains at least 150 seats but not more than 200 seats. Which of the following could be the number of seats in this auditorium? (A) 800 (B) 1,000 (C) 1,100 (D) 1,300 (E) 1,700 6. If rsuv = 1 and rsum = 0, which of the following must be true? (A) r < 1 (B) s < 1 (C) u= 2 (D) r = 0 (E) m = 0
SAT数学历年真题精选1 以下是小编给大家整理的SAT数学历年真题精选1，需要的同学赶快下载全篇吧。 1. 如果x = 4，下面哪一个是最大的值。 2. 火车A,B, 和C 同时以不同的速度经过一个火车站。火车A的速度是火车B的速度的三倍，然后火车C的速度是火车A的速度的两倍。如果火车B的速度是每小时7英里，请问火车C的速度是多少每小时多少英里? 3. 如果x，5x，和6x 的平均值是8，那x的值是多少? 4. 一个图标上不能有两个同样x坐标的点 哪一个图标符合上面所提的要求? 5.上面这个venn图解展示了在30个上科学的学生中学习蝴蝶,学习蝗虫,两个一起学习或者是两个都没有学习的学生人数。只学习蝴蝶的学生占总人数的多少百分比? 6.在上面的图标里，AB = CD。t的数值是多少? 7. 如果3x2 = 4y = 12, 那么x2y 的数值是多少? 8. 在上面的图解里，圆圈都是相切的和紧紧挨着的(tangent)。圆圈A的圆心也是最大的那个圆圈的圆心。如果圆圈A的半径是2，圆圈B的半径是4，还有圆圈C的半径是4，那么最大的那个圆圈的半径是多少? 9. 在上面的图标里，线上所有的标记都是相等的。那么x的数值是多少? 10. 在上面的图标里，x的数值是多少? 11. 当整数k 除以7以后，余数是6. 那K+2 除以7的余数是多少? 12. 上面的图表展示了一个关于每深入海洋15英尺所对应的气压的函数。如果每深入海洋1英尺，海洋的气压增长是同样的话，那下面哪一个图表符合上面的数据。 13. 在一数列里，第一个数字是1. 如果每后面一个数是前面一个数乘以-2 的乘积，那么这一串数字的第六个数是什么? 14. 如果(2x - 5)(2x +5)= 5，那么4x2的值是多少? 15. A点的坐标是(p，r)，然后|p| > |r|. 下面哪一个会是直线AB的斜度? 16. 如果3a + 4b = b，下面哪一个一定等于6a + 6b?
2014年全国硕士研究生入学统一考试数学二试题 一、选择题:1:8小题,每小题4分,共32分.下列每题给出的四个选项中,只有一个选项符合题目要求的,请将所选项前的字母填在答题纸．．． 指定位置上. (1) 当0x +→时，若ln (12)x +α ，1 (1cos )x -α 均是比x 高阶的无穷小，则α的取值范围是( ) (A) (2,)+∞ (B) (1,2) (C) 1 (,1)2 (D) 1(0,)2 (2) 下列曲线中有渐近线的是 ( ) (A) sin y x x =+ (B) 2 sin y x x =+ (C) 1 sin y x x =+ (D) 21sin y x x =+ (3) 设函数()f x 具有2阶导数，()(0)(1)(1)g x f x f x =-+，则在区间[0,1]上 （ ） (A) 当()0f x '≥时，()()f x g x ≥ (B) 当()0f x '≥时，()()f x g x ≤ (C) 当()0f x ''≥时，()()f x g x ≥ (D) 当()0f x ''≥时，()()f x g x ≤ (4) 曲线2 2 7 41 x t y t t ?=+??=++??上对应于1t =的点处的曲率半径是 （ ） (A) 50 (B) 100 (C) (D)(5) 设函数()arctan f x x =，若()()f x xf '=ξ，则2 2 lim x x →=ξ （ ） (A)1 (B) 2 3 (C) 12 (D) 13 (6) 设函数(,)u x y 在有界闭区域D 上连续，在D 的内部具有2阶连续偏导数，且满足20 u x y ?≠??及22220u u x y ??+=??，则 （ ） (A)(,)u x y 的最大值和最小值都在D 的边界上取得 (B) (,)u x y 的最大值和最小值都在D 的内部上取得 (C) (,)u x y 的最大值在D 的内部取得，最小值在D 的边界上取得
SAT数学难题汇总及答案 x^2 表示x 的平方，=！表示不等于。pi 表示圆周 率 类型1： 20. The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set? (A) 25 (B) 26 (C) 50 (D) 51 (E) 52 14. Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible? 16. Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z ? (A) x + y + k (B) x + y - k (C) x + y + 2k (D) x + y - 2k (E) 2x + 2y - 2k 20. There are 75 more women than men enrolled in Linden College. If there are n men enrolled, then, in terms of n, what percent of those enrolled are men?
2006年数学（二）考研真题及解答 一、填空题 （1）曲线4sin 52cos x x y x x += -的水平渐近线方程为 . （2）设函数23 1sin ,0, (), x t dt x f x x a x ?≠? =??=? ? 在0x =处连续，则a = . （3）广义积分 22 (1) xdx x +∞=+? . （4）微分方程(1) y x y x -'= 的通解是 . （5）设函数()y y x =由方程1y y xe =-确定，则0 A dy dx == . （6）设矩阵2112A ?? = ?-?? ，E 为2阶单位矩阵，矩阵B 满足2BA B E =+，则B = . 二、选择题 （7）设函数()y f x =具有二阶导数，且()0,()0f x f x '''>>，x ?为自变量x 在0x 处的增量，y ?与dy 分别为()f x 在点0x 处对应的增量与微分，若0x ?>，则 （A ）0.dy y <
SAT数学常见解题方法 众所周知，解sat数学题，需要有一定的技巧、方法。了解这些方法，不仅能够提高做题效率，更能保障做题的质量。接下来，文都国际教育小编给大家介绍几种常见的解题方法，以供大家参考，能够在日后的答题中对大家有所帮助。 sat数学解题方法一：最小值代入法 例1：If n is an even integer, which of the following must be an odd integer? a) 3n - 2 b) 3(n + 1) c) n - 2 d) n/3 e) n/2 解答： 答案是(B)。当你不能确定未知数有几个值时，尽管使用最小值代入检验这个解答sat数学题的方法。在这里，你可以设n等于2。而当n = 2时, 3(n + 1) = 9. 问题迎刃而解。如果你没有把握的话可以再试几个数。 sat数学解题方法二：特殊值法 例题：xy=x+y. If y>2, what are all possible values of x that satisfy the equation above? A. x<0, B. 0 解答：y>2,不妨假设它为3，3x=x+3,x=3/2,一目了然D即为正确选项。 sat数学解题方法三：巧解法 例题：At a certain diner, Joe orders 3 doughnuts and a cup of coffee and is charged $2.25. Stella orders 2 doughnuts and a cup of coffee and is charged $1.70. What is the price of 2 doughnuts? A. $ 0.55 B. $ 0.60 C. $ 1.10 D. $ 1.30 E. $ 1.80
SAT数学历年真题整理 SAT数学历年真题整理!在SAT数学考试中，有些题目虽然简单，但是确是考生们容易丢分的题目。因此小编在这里为大家整理了这些易错题目，希望对大家接下来的SAT数学备考有更好的帮助。 原题如下： If j, k, and n are consecutive integers such that 0 < j < k < n and the units (ones) digit of the product jn is 9, what is the units digit of k? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 针对此题，SAT考试专家给予了详细讲解：相当多的学生可能首先是没有读懂这道题，units digit指的是我们说的“位”，ones的意思是“个位”。这道题还原成中文意思是：如果j，k和n是三个连续整数且满足0 < j < k < n这一条件，同时j与n相乘所得的积个位数是9，请问k这个数字的个位数是多少?答案是从0～4这五个连续数字中进行选择。 译成中文后，这是一个需要灵活思维的题目。两个正整数相乘所得的积个位数是9，那么这两个数字(j和n)的个位数只有两种组合可能，分别是3和3，1和9。由于j，k，n，三个数字是连续整数，j和n当中有一个k，那么只有可能k是以0为个位数的数字。比如j=9，k=10，n=11，就满足了题目中所提到的条件。显然答案是A。
在SAT考试中对于美国学生比较难的数学问题对于中国学生来说通常是比较容易的，毫无疑问是中国学生的优势所在。 在日常教学中发现中国学生在SAT数学题上通常遇到两大障碍：第一，是由于对英语数学词汇和表达不熟悉，造成题目理解的困难或错误;第二，SAT数学题多需要巧妙的思维，而非复杂的运算。实际上，在与中国SAT学生交流的过程中，经常会说的一句话是“SAT 数学题是脑筋急转弯”，意思就是题目经常需要学生有巧妙的思维，而不见得是复杂的计算能力。 相对而言SAT数学题的知识难度对于中国学生并不高，关键在于熟悉数学的英语词汇和表达，多用灵活的思路，经过系统的学习和练习，就完全可以拿到很高的分数。 以上就是为大家整理的“SAT数学历年真题整理”，希望通过上述内容的整理，能够帮助大家更好地来备考SAT考试，在接下里的考试中能够取得高分成绩!
2019全国研究生招生考试数学二真题及答案解析 一、选择题 1.当0→x 时，若x x tan -与k x 是同阶无穷小，则=k A.1. B. 2. C. 3. D. 4. 2.）（π202≤≤+=x x cos x sin x y 的拐点 A.??? ? ?2,2ππ B.()2,0 C.()2,π D.??? ? ?-23,23ππ 3.下列反常积分收敛的是（） A.dx xe x ?+∞ -0 B.dx xe x ? +∞ -02 C. dx x x ? +∞ +0 2 1arctan D. dx x x ? +∞ +0 21 4.c ,b ,a ,x C C y ce by y a y x -x x 则的通解为已知e )e (21++==+'+'' 的值为（ ） A.1,0,1 B.1,0,2 C.2,1,3 D.2,1,4 5.已知积 分区域???? ?? ≤+=2πy x |y ,x D ） （，dxdy y x I D ??+=221， dxdy y x I D ??+=222sin ，(dxdy y x I D )cos 1223??+-=，试比较321,,I I I 的大小 A.123I I I << B.321I I I << C.312I I I << D.132I I I << 6.已知)()(x g x f 是二阶可导且在a x =处连续，请问)()(x g x f 相切于a 且曲率相等是 0)() ()(lim 2 =--→a x x g x f a x 的什么条件 A.充分非必要条件 B.充分必要条件 C.必要非充分条件 D.既非充分又非必要条件 7.设A 是四阶矩阵，* A 是A 的伴随矩阵，若线性方程组0=Ax 的基础解系中只有2个向量，则* A 的秩是
新SAT数学考点的大汇总 SAT数学是SAT考试的一部分，那在备考的时候，有哪些考点需要我们注意呢？下面三立小编为你带来新SAT数学考点的大汇总，希望对你有所帮助，更多资讯请访问三立在线教育，专业老师为你在线解答相关疑问。 1识别反映现实生活场景的不等式中的数学记号是否正确。 2读懂和理解问卷调查中统计出来的数据，并运用样本规模和误差率之间的关系来解决问题。 3读懂数据，并能从中获取信息。 4在给定语境中解释斜线斜率代表的意思。 5根据斜线做出预测，并流畅地阅读图表和处理十进制数字。 6建立一个反映现实情境的线性表达式。 7理解展示变量关系的图形的概念。 8读懂双项表格中的信息，并能够判断表格中任意两个类别变量之间的特定关系。 9将已知的复合不等式变换形式，并找到一个满足所有条件的值。 10理解背景信息中蕴藏的概念，从表格中提取相关信息，并运用这些信息形成或比较相关的量。 11根据一个随机抽样做出推断，对一个人口参数进行预估。 12理解一个反应现实情境的表达式或方程式，并能根据情景对全部或部分表达式进行解释。 13评估两类人群的平均值，从而判定两类人群综合的平均值的约束条件。
14运用一项科学研究的内容来评估，其研究结果是否适用被试人群，或者研究内容和结果之间是否存在因果关系。存在因果关系的条件为，从被试人群中任意抽样，因果关系都应用于抽样人群。 15判断反映现实情境的指数关系式的数学记号是否正确。 16运用空间推理和几何逻辑，根据给定信息来推导选项中的哪个关系是可能的。学生必须用数学记号来表达直线分割出的部分之间的关系。 17建一个反映现实情境的方程。 18建一个反映现实情境的线性方程组。 19建一个反映现实情境的线性方程。 20解读描绘每年海牛平均增长数量的散点图中直线斜率的意义，同时要考虑数轴的刻度。 21整合图表和文字信息，并能判断哪些信息与答案相关。 22运用单位速率(数据传输速率)，并能够进行千兆和兆的，以及时间单位的转换。 23通过变换一个方程式，带入另一个方程式中，从而解出一个未知数。 24理解体积、密度等概念之间的联系，以及重要的几何定理如勾股定理和体积公式。 25运用线性方程式来对两个币种的汇率进行转换。 26在给定情境下，利用汇率转换的信息和所提供的限定条件来判定一个有用的数值。
1. How long will Lucy have to wait before for her $2,500 invested at 6% earns $600 in simple interest? A. 2 years B. 3 years C. 4 years D. 5 years E. 6 years 2. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? A. 4 B. 8 C. 12 D. 13 E. 16 3. If r = 5 z then 15 z = 3 y, then r = A. y B. 2 y C. 5 y D. 10 y E. 15 y 4. What is 35% of a number if 12 is 15% of a number? A. 5 B. 12 C. 28 D. 33 E. 62 5. A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price? A. $1800 B. $1900 C. $2000 D. $2100 E. $2200 6. A car dealer sells a SUV for $39,000, which represents a 25% profit over the cost. What was the cost of the SUV to the dealer? A. $29,250
2017考研数学二真题及答案解析 一、选择题（本题共8小题，每小题4分，满分32分） （1）若函数?? ? ??≤>-=0,,0,cos 1)(x b x ax x x f 在0=x 处连续，则（ ） )(A 21= ab 。 )(B 2 1-=ab 。 )(C 0=ab 。 D (2=ab 。 【答案】)(A 【解】a ax x f x 21 cos 1lim )00(0=-=++→，b f f =-=)00()0(， 因为)(x f 在0=x 处连续，所以)00()0()00(-==+f f f ，从而2 1 = ab ，应选)(A 。 （2）设二阶可导函数)(x f 满足1)1()1(=-=f f ，1)0(-=f ，且0)(>''x f ，则（ ） ) (A ? ->1 10)(x f 。 ) (B ? -<1 1 0)(x f 。 )(C ??->10 1 )()(dx x f x f 。 )(D ??-<1 1 )()(dx x f x f 。 【答案】)(B 【解】取12)(2 -=x x f ，显然 ? -<1 1 0)(x f ，应选)(B 。 （3）设数列}{n x 收敛，则 （ ） )(A 当0sin lim =∞ →n n x 时，0lim =∞ →n n x 。 )(B 当0)||(lim =+∞ →n n n x x 时，0lim =∞ →n n x 。 )(C 当0)(lim 2 =+∞ →n n n x x 时，0lim =∞→n n x 。)(D 当0)sin (lim =+∞→n n n x x 时，0lim =∞ →n n x 。 【答案】)(D 【解】令A x n n =∞ →lim ，由0sin )sin (lim =+=+∞ →A A x x n n n 得0=A 。 （4）微分方程)2cos 1(842x e y y y x +=+'-''的特解可设为=* y （ ） )(A )2sin 2cos (22x C x B e Ae x x ++。 )(B )2sin 2cos (22x C x B xe Axe x x ++。 )(C )2sin 2cos (22x C x B xe Ae x x ++。)(D )2sin 2cos (22x C x B xe Axe x x ++。
SAT数学真题精选 1 2 1. If 2 x + 3 = 9, what is the value of 4 x – 3 ? 3 (A) 5 (B) 9 (C) 15 (D) 18 (E) 21 2. If 4(t + u) + 3 = 19, then t + u = ? 4 5 (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 6 3. In the xy-coordinate (坐标) plane above, the line contains the points 7 (0,0) and (1,2). If line M (not shown) contains the point (0,0) and is 8 perpendicular （垂直） to L, what is an equation of M? 9 (A) y = -1/2 x 10 (B) y = -1/2 x + 1 11 (C) y = - x 12 (D) y = - x + 2 13 (E) y = -2x 14 4. If K is divisible by 2,3, and 15, which of the following is also 15 divisible by these numbers? 16 (A) K + 5 (B) K + 15 (C) K + 20 (D) K + 17 30 (E) K + 45 18 5. There are 8 sections of seats in an auditorium. Each section contains at least 150 seats but not more than 200 seats. Which of the following could 19 20 be the number of seats in this auditorium?
1..【分析】本题属基本题型，幂指函数的求导（或微分）问题可化为指数函数求导或 取 对 数 后 转 化 为 隐 函 数 求 导 . 【详解】方法一：x x y )sin 1(+==)sin 1ln(x x e +，于是 ] sin 1cos )sin 1[ln()sin 1ln(x x x x e y x x +? ++?='+， 从而 π =x dy =.)(dx dx y ππ-=' 方法二：两边取对数，)sin 1ln(ln x x y +=，对x 求导，得 x x x x y y sin 1cos )sin 1ln(1+++='， 于是 ] sin 1cos )sin 1[ln()sin 1(x x x x x y x +? ++?+='，故 π =x dy =.)(dx dx y ππ-=' 【评注】幂指函数的求导问题，既不能单纯作为指数函数对待，也不能单纯作为幂函数，而直接运用相应的求导公式. 2..【分析】本题属基本题型，直接用斜渐近线方程公式进行计算即可. 【详解】因为a= ,1) 1(lim )(lim 2 3=+=+∞→+∞ →x x x x x f x x []23)1(lim )(lim 2 32 3= -+=-=+∞ →+∞ →x x x ax x f b x x ， 于是所求斜渐近线方程为 . 23 +=x y 【评注】如何求垂直渐近线、水平渐近线和斜渐近线，是基本要求，应熟练掌握。这 里应注意两点：1）当存在水平渐近线时，不需要再求斜渐近线；2）若当∞→x 时，极限 x x f a x ) (lim ∞ →=不存在，则应进一步讨论+∞→x 或-∞→x 的情形，即在右或左 侧是否存在斜渐近线，本题定义域为x>0，所以只考虑+∞→x 的情形. 3..【分析】作三角代换求积分即可. 【详解】令t x sin =，则
SAT数学最难的3大知识点之数据分析篇（内含例题详解）这是一篇关于SAT数学中数据分析的知识贴,文章比较长，但它一定有用。相信备考的宝宝们吃透这篇文章，就可以在SAT数学分数上一个新高度。 数据分析（Data Analysis）一直是SAT数学中比较麻烦的一道题，数据比较多，看起来比较头痛。那么如何来好好做完这道题呢？下文将带你好好走一遍知识点~ 1、什么是数据分析? 数据分析涉及到一系列的动作。首先要通过一定的方法采集数据(Data Collection)并且记录下来。然后对采集的数据进行过滤整理，找到其背后的整体趋势，从而可以辨别数据的真伪好坏，也能对事物的未来趋势做出预测。为了总结和预测，我们采用了数据分析(Data Analysis)。 2、数据分析中经常用到的图表有哪些? 以下列出统计和数据分析中经常用到的图表。记住：具体的某个个体数字并不是非常重要，重要的是整体的趋势。对于这些图表的解释如果让学生觉得陌生，那么建议该学生跟着统计老师好好补习一下。 (1)表格Table：对于数据的详细记录。如下图所示。
(2)柱状图Bar Graph/Histogram：看整体的趋势。 (3)线形图LineGraph：线形图表明了事物发展的总体趋势，通常而言，如果线的形状可以用某种方程来模拟，我们的数学分析就具有了预测的特征。 如下图： 红线是normal distribution，蓝线是logistic regression。如果可以进一步确定这两条线各自的重要参数，就可以通过已知来推知未知。 (4)饼状图piechart：主要体现的是比重proportion或者百分比percentage。大多数时候，饼状图并不体现绝对数值，只是对于不同事物的比重进行一个比较。
x^2表示x的平方，=！表示不等于。pi表示圆周率 类型1： 20. The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set? (A) 25 (B) 26 (C) 50 (D) 51 (E) 52 14. Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible? 16. Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z ? (A) x + y + k (B) x + y - k (C) x + y + 2k (D) x + y - 2k (E) 2x + 2y - 2k 20. There are 75 more women than men enrolled in Linden College. If there are n men enrolled, then, in terms of n, what percent of those enrolled are men?
2015年全国硕士研究生入学统一考试 数学二试题及答案解析 一、选择题：（1~8小题,每小题4分，共32分。下列每题给出的四个选项中，只有一个选项是符 合题目要求的。） (1)下列反常积分中收敛的是 (A)∫√x 2 (B)∫lnx x +∞2 dx (C)∫1xlnx +∞ 2 dx (D) ∫x e x +∞2dx 【答案】D 。 【解析】题干中给出4个反常积分，分别判断敛散性即可得到正确答案。 ∫x 2 =2√x|2+∞ =+∞； ∫lnx x +∞2dx = ∫lnx +∞ 2d(lnx) =1 2(lnx)2 | 2 +∞=+∞； ∫1xlnx +∞ 2dx =∫1 lnx +∞2d(lnx)=ln?(lnx)|2+∞=+∞； ∫x e x +∞2 dx =?∫x +∞ 2 de ?x =?xe ?x |2+∞ +∫e ?x +∞2 dx =2e ?2?e ?x |2 +∞ =3e ?2， 因此(D)是收敛的。 综上所述，本题正确答案是D 。 【考点】高等数学—一元函数积分学—反常积分 (2)函数f (x )=lim t→0 (1+ sin t x )x 2 t 在(-∞,+∞)内 (A)连续 (B)有可去间断点 (C)有跳跃间断点 (D)有无穷间断点
【答案】B 【解析】这是“1∞”型极限，直接有f (x )=lim t→0 (1+ sin t x )x 2t =e lim t→0x 2t (1+ sin t x ?1)=e x lim t→0sint t =e x (x ≠0), f (x )在x =0处无定义， 且lim x→0 f (x )=lim x→0 e x =1,所以 x =0是 f (x )的可去间断点，选B 。 综上所述，本题正确答案是B 。 【考点】高等数学—函数、极限、连续—两个重要极限 (3)设函数f (x )={ x αcos 1x β ,x >0， 0,x ≤0 (α>0,β>0).若f ′(x )在x =0处连续，则 (A)α?β>1 (B)0<α?β≤1 (C)α?β>2 (D)0<α?β≤2 【答案】A 【解析】易求出 f′(x )={αx α?1cos 1 x β+βx α?β?1sin 1 x β,x >0， 0,x ≤0 再有 f +′(0 )=lim x→0 + f (x )?f (0) x =lim x→0 + x α?1 cos 1 x β={0, α>1, 不存在，α≤1， f ?′(0)=0 于是，f ′(0)存在?α>1，此时f ′(0)=0. 当α>1时，lim x→0 x α?1cos 1 x β=0， lim x→0 βx α?β?1 sin 1 x β={0, α?β?1>0, 不存在，α?β?1≤0， 因此，f′(x )在x =0连续?α?β>1。选A 综上所述，本题正确答案是C 。 【考点】高等数学—函数、极限、连续—函数连续的概念，函数的左极限和右极限