(2021年整理)SAT数学真题精选
sat最难数学题
sat最难数学题（实用版）目录1.SAT 简介2.SAT 数学考试的难度和范围3.SAT 最难数学题的特点4.如何准备和应对 SAT 最难数学题5.结论正文1.SAT 简介SAT（Scholastic Assessment Test）是美国大学入学考试委员会（College Board）主办的一项全球性的大学入学考试，也被称为“美国高考”。
这项考试旨在评估学生在阅读、写作和数学方面的能力，以帮助大学招生官判断学生的学术潜力。
2.SAT 数学考试的难度和范围SAT 数学考试主要包括两个部分：数学（Math）和数学 2（Math 2）。
数学部分主要考察学生的基本数学知识，如代数、几何、统计和数据分析等。
数学 2 部分则更侧重于考察学生的高等数学知识，如微积分、三角函数和复数等。
SAT 数学考试的难度相对较高，尤其是对于非英语国家的学生来说，因为考试语言是英语。
不过，通过系统的学习和练习，大多数学生都可以逐步提高自己的数学水平。
3.SAT 最难数学题的特点SAT 最难数学题通常具有以下特点：- 题目复杂：最难的数学题往往需要学生运用多个数学知识点，进行繁琐的计算和推理。
- 考查能力：这类题目旨在考查学生的逻辑思维能力、分析问题和解决问题的能力，而不仅仅是计算能力。
- 时间紧张：由于题目难度高，学生在解答这类题目时往往需要花费较长时间，而考试时间有限，这使得最难数学题更加具有挑战性。
4.如何准备和应对 SAT 最难数学题要想成功应对 SAT 最难数学题，学生需要：- 扎实掌握数学知识点：学生需要系统地学习 SAT 数学考试所涵盖的知识点，确保自己在面对各种题目时都有足够的知识储备。
- 提高解题技巧：学生需要通过大量的练习，熟悉各类题型的解题方法，提高自己的解题速度和准确率。
- 增强心理素质：面对难度较大的数学题，学生需要保持冷静，避免因为紧张而影响自己的发挥。
- 合理分配时间：在考试中，学生需要合理分配时间，尽量确保有足够的时间解答最难的数学题。
sat数学试题
sat 数学试题SAT 数学题分成了选择题和计算题，相对于 SAT 数学选择题，答案还有一些提示的作用， SAT 数学计算题就需要大家自己进行解答了。
下面为大家推荐的这道 SAT 数学计算题是非常 典型的代数方程类的题目，大家一起来看看吧。
What value of satisfies both of the equations above?The correct answer is1/2 or .5 Explanation Difficulty: MediumSince, the value of iseither or .ORThe two values of that satisfy the firstequation are and .Since, the value of iseither or .ORThe two values of that satisfy thesecond equation are and . You are asked to find the value of thatsatisfies both equations. That value is . The answer can be entered in the grid as or .下面是两道 SAT 数学练习题，都是选择题，后 面附有答案及其解析。
SAT 数学练习题可以让 大家更快更好的了解 SAT 数学考试的出题方式 以及应对方式。
下面是详细内容，我们一起来看 一下这些 SAT 数学练习题的吧。
1、 Cone A has volume 24. When its radius and height are multiplied by the same factor, the cone’s surface area doubles. What is Cone A’s new volume?(A) (B)48(C) (D)96 (E)Not enough information to tell 2、 A rectangle stands so that its 6 inch side lies flat against the ground. If the rectangle is rotated around the axis of one of its two 4 inch sides, what is the volume of the resulting cylinder? (A)24Ï€ (B)36Ï€ (C)64Ï€ (D)96Ï€ (D)144Ï€ Answers 1、 C The formula for a cone’s surface area is πr2 + πrl. A cone’s volume is 1/ 3πr2h. So if the dimensions of a cone are multiplied by the same factor, a,then its surface area multiplies by the square of that factor. If the dimensions of acone are multiplied by the same factor, the volume becomes multiplied by the cube ofthat factor:In general, for solids, if each dimensionof a cone is multiplied by the same factor,the solid’s surface area is multiplied by thesquare of that factor, and its volumeincreases by the cube of that factor. If thesurface area of Cone A doubles, itsdimensions are multiplied by a factor of Thus, the cone’s volume is multiplied by afactor of isCone A’s new volume2、 E If the rectangle is rotated about a side of length 4, then the height of the cylinder will be 4 and the radius will be 6.Once you visualize the cylinder, you can plug in the values for the volume of a cylinder:一道 SAT 数学题(抛物线)天道留学 时间：2011-08-26点击：26 次下面是一道关于抛物线的 SAT 数学题及其 解法的内容，非常详细。
最新sat数学考试试题资料
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) 212. If 4(t + u) + 3 = 19, then t + u = ?(A) 3 (B) 4 (C) 5 (D) 6 (E) 73. 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 = -2x4. 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 + 455. 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) 1,7006. 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 = 07. The least integer of a set of consecutive integers (连续整数) is –126. if the sum of these integers is 127, how many integers are in this set?(A) 126 (B) 127 (C) 252 (D) 253 (E) 2548. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 200 seniors, 300 juniors, and 400 sophomores who applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2 time; and each sophomore’s name, 1 times. If a student’s name is chosen at random from the names in the lottery, what is the probability that a senior’s name will be chosen?（A）1/8 (B) 2/9 (C) 2/7 (D) 3/8 (E) 1/2Question #1: 50% of US college students live on campus. Out of all students living on campus, 40% are graduate students. What percentage of US students are graduate students living on campus?(A) 90% (B) 5% (C) 40% (D) 20% (E) 25% Question #2: In the figure below, MN is parallel with BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC?(A) 5/9 (B) 2/3 (C) 4/9 (D) 1/2 (E) 2/9Question #3: If a2 + 3 is divisible by 7, which of the following values can be a?(A)7 (B)8 (C)9 (D)11 (E)4Question #4: What is the value of b, if x = 2 is a solution of equation x2 - b · x + 1 = 0?(A)1/2 (B)-1/2 (C)5/2 (D)-5/2 (E)2Question #5: Which value of x satisfies the inequality | 2x | < x + 1 ?(A)-1/2 (B)1/2 (C)1 (D)-1 (E)2Question #6: If integers m > 2 and n > 2, how many (m, n) pairs satisfy the inequality m n < 100?(A)2 (B)3 (C)4 (D)5 (E)7Question #7: The US deer population increase is 50% every 20 years. How may times larger will the deer population be in 60 years ?(A)2.275 (B)3.250 (C)2.250 (D)3.375 (E)2.500 Question #8: Find the value of x if x + y = 13 and x - y = 5.(A)2 (B)3 (C)6 (D)9 (E)4Question #9:US UK Medals3 2 gold1 4 silver4 1 bronzeThe number of medals won at a track and field championship is shown in the table above. What is the percentage of bronze medals won by UK out of all medals won by the 2 teams?(A)20% (B)6.66% (C)26.6% (D)33.3% (E)10%Question #10: The edges of a cube are each 4 inches long. What is the surface area, in square inches, of this cube?(A)66 (B)60 (C)76 (D)96 (E)65Question #1: The sum of the two solutions of the quadratic equation f(x) = 0 is equal to 1 and the product of the solutions is equal to -20. What are the solutions of the equation f(x) = 16 - x ?(a) x1 = 3 and x2 = -3 (b) x1 = 6 and x2 = -6(c) x1 = 5 and x2 = -4 (d) x1 = -5 and x2 = 4(e) x1 = 6 and x2 = 0Question #2: In the (x, y) coordinate plane, three lines have the equations:l1: y = ax + 1l2: y = bx + 2l3: y = cx + 3Which of the following may be values of a, b and c, if line l3 is perpendicular to both lines l1 and l2?(a) a = -2, b = -2, c = .5 (b) a = -2, b = -2, c = 2(c) a = -2, b = -2, c = -2 (d) a = -2, b = 2, c = .5(e) a = 2, b = -2, c = 2Question #3: The management team of a company has 250 men and 125 women. If 200 of the managers have a master degree, and 100 of the managers with the master degree are women, how many of the managers are men without a master degree? (a) 125 (b) 150 (c) 175 (d) 200 (e) 225 Question #4: In the figure below, the area of square ABCD is equal to the sum of the areas of triangles ABE and DCE. If AB = 6, then CE =(a) 5 (b) 6 (c) 2 (d) 3 (e) 4Question #5:If α and β are the angles of the right triangle shown in the figure above, then sin2α + sin2β is equal to:(a) cos(β) (b) sin(β) (c) 1 (d) cos2(β) (e) -1 Question #6: The average of numbers (a + 9) and (a - 1) is equal to b, where a and b are integers. The product of the same two integers is equal to (b - 1)2. What is the value of a?(a) a = 9 (b) a = 1 (c) a = 0 (d) a = 5 (e) a = 11Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)? (A) x = 1 (B)x1 = 1, x2 = -1(C)x1 = 1, x2 = 0 (D)x = 0(E)x = -1Question #2: What is the length of the arc AB in the figure below, if O is the center of the circle and triangle OAB is equilateral? The radius of the circle is 9(a) π(b) 2 ·π(c) 3 ·π(d) 4 ·π(e) π/2 Question #3: What is the probability that someone that throws 2 dice gets a 5 and a 6? Each dice has sides numbered from 1 to 6.(a)1/2 (b)1/6 (c)1/12 (d)1/18 (e)1/36 Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He bikes from A to B at a speed of 15 miles/hour while his return speed is 10 miles/hour. What is the distance between the 2 towns?(a)11 miles (b)18 miles (c)15 miles (d)12 miles (e)10 miles Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1. What is the height of C2?(a)2·a /π(b)a / π(c)a / (2·π) (d)a / π(e)a + πQuestion #6: How many integers x are there such that 2x < 100, and at the same time the number 2x + 2 is an integer divisible by both 3 and 2?(a)1 (b)2 (c) 3 (d) 4 (e)5Question #7: sin(x)cos(x)(1 + tan2(x)) =(a)tan(x) + 1 (b)cos(x)(c)sin(x) (d)tan(x)(e)sin(x) + cos(x)Question #8: If 5xy = 210, and x and y are positive integers, each of the following could be the value of x + y except:(a)13 (b) 17 (c) 23 (d)15 (e)43Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y?(a)11 (b)17 (c)13 (d)15 (e) 9Question #10: The inequality |2x - 1| > 5 must be true in which one of the following cases?I. x < -5 II. x > 7 III. x > 01.Three unit circles are arranged so that each touches the other two. Find the radii ofthe two circles which touch all three.2.Find all real numbers x such that x + 1 = |x + 3| - |x - 1|.3.(1) Given x = (1 + 1/n)n, y = (1 + 1/n)n+1, show that x y = y x.(2) Show that 12 - 22 + 32 - 42 + ... + (-1)n+1n2 = (-1)n+1(1 + 2 + ... + n).4.All coefficients of the polynomial p(x) are non-negative and none exceed p(0). Ifp(x) has degree n, show that the coefficient of x n+1 in p(x)2 is at most p(1)2/2.5.What is the maximum possible value for the sum of the absolute values of thedifferences between each pair of n non-negative real numbers which do not exceed 1?6.AB is a diameter of a circle. X is a point on the circle other than the midpoint of thearc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show that the line PQ, the tangent at X and the line AB are concurrent.7.Four points on a circle divide it into four arcs. The four midpoints form aquadrilateral. Show that its diagonals are perpendicular.8.Find the smallest positive integer b for which 7 + 7b + 7b2 is a fourth power.9.10.Show that there are no positive integers m, n such that 4m(m+1) = n(n+1).11.ABCD is a convex quadrilateral with area 1. The lines AD, BC meet at X. Themidpoints of the diagonals AC and BD are Y and Z. Find the area of the triangle XYZ.12.A square has tens digit 7. What is the units digit?13.Find all ordered triples (x, y, z) of real numbers which satisfy the following systemof equations:xy = z - x - yxz = y - x - zyz = x - y - z。
2021年SAT II Subject Test Math (Level 2)考试题库
2021年SAT II Subject Test Math （Level 2）考试题库【历年真题＋章节题库＋模拟试题】目录•第一部分历年真题o数及其运算真题精选及详解o代数和函数真题精选及详解o几何和测量真题精选及详解o数据分析、统计和概率真题精选及详解•第二部分章节题库o第1章数及其运算（Number and Operations）o第2章代数和函数（Algebra and Function）o第3章几何和测量（Geometry and Measurement）o第4章数据分析、统计和概率（Data Analysis, Statistics, and Probability）•第三部分模拟试题o SAT II Subject Test Math （Level 2）模拟试题及详解（一）o SAT II Subject Test Math （Level 2）模拟试题及详解（二）内容简介SAT II Subject Test Math （Level 2）考试题库包括历年真题、章节练习和模拟试题三部分。
具体如下：第一部分为历年真题。
精选SAT II Subject Test Math （Level 2）真题，考生既可以体验真实考试，也可以测试自己的水平。
每道真题均提供名师详细解析。
第二部分为章节练习。
遵循SAT官方网站有关SAT考试的要求，按照最新真题题型的章目编排，共分为四章：数及其运算（Number and Operations）、代数和函数（Algebra and Function）、几何和测量（Geometry and Measurement）、数据分析、统计和概率（DataAnalysis, Statistics, and Probability）。
第三部分为模拟试题。
由SAT II Subject Test Math考试辅导名师根据SAT IISubject Test Math考试的命题规律进行考前预测，其试题数量、试题难度完全仿真最新真题。
sat数学考试试题
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）212。
If 4（t + u）+ 3 = 19, then t + u = ？(A）3 (B) 4 （C）5 （D) 6 （E) 73. 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 = —2x4。
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 + 455. 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) 1，7006。
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 7。
sat数学考试精彩试题
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) 212. If 4(t + u) + 3 = 19, then t + u = ?(A) 3 (B) 4 (C) 5 (D) 6 (E) 73. 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 = -2x4. 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 + 455. 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) 1,7006. 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 = 07. The least integer of a set of consecutive integers (连续整数) is –126. if the sum of these integers is 127, how many integers are in this set?(A) 126 (B) 127 (C) 252 (D) 253 (E) 2548. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 200 seniors, 300 juniors, and 400 sophomores who applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2 time; and each sophomore’s name, 1 times. If a student’s name is chosen at random from the names in the lottery, what is the probability that a senior’s name will be chosen?（A）1/8 (B) 2/9 (C) 2/7 (D) 3/8 (E) 1/2Question #1: 50% of US college students live on campus. Out of all students living on campus, 40% are graduate students. What percentage of US students are graduate students living on campus?(A) 90% (B) 5% (C) 40% (D) 20% (E) 25% Question #2: In the figure below, MN is parallel with BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC?(A) 5/9 (B) 2/3 (C) 4/9 (D) 1/2 (E) 2/9Question #3: If a2 + 3 is divisible by 7, which of the following values can be a?(A)7 (B)8 (C)9 (D)11 (E)4Question #4: What is the value of b, if x = 2 is a solution of equation x2 - b · x + 1 = 0?(A)1/2 (B)-1/2 (C)5/2 (D)-5/2 (E)2Question #5: Which value of x satisfies the inequality | 2x | < x + 1 ?(A)-1/2 (B)1/2 (C)1 (D)-1 (E)2Question #6: If integers m > 2 and n > 2, how many (m, n) pairs satisfy the inequality m n < 100?(A)2 (B)3 (C)4 (D)5 (E)7Question #7: The US deer population increase is 50% every 20 years. How may times larger will the deer population be in 60 years ?(A)2.275 (B)3.250 (C)2.250 (D)3.375 (E)2.500 Question #8: Find the value of x if x + y = 13 and x - y = 5.(A)2 (B)3 (C)6 (D)9 (E)4Question #9:The number of medals won at a track and field championship is shown in the table above. What is the percentage of bronze medals won by UK out of all medals won by the 2 teams?(A)20% (B)6.66% (C)26.6% (D)33.3% (E)10%Question #10: The edges of a cube are each 4 inches long. What is the surface area, in square inches, of this cube?(A)66 (B)60 (C)76 (D)96 (E)65Question #1: The sum of the two solutions of the quadratic equation f(x) = 0 is equal to 1 and the product of the solutions is equal to -20. What are the solutions of the equation f(x) = 16 - x ?(a) x1 = 3 and x2 = -3 (b) x1 = 6 and x2 = -6(c) x1 = 5 and x2 = -4 (d) x1 = -5 and x2 = 4(e) x1 = 6 and x2 = 0Question #2: In the (x, y) coordinate plane, three lines have the equations:l1: y = ax + 1l2: y = bx + 2l3: y = cx + 3Which of the following may be values of a, b and c, if line l3 is perpendicular to both lines l1 and l2?(a) a = -2, b = -2, c = .5 (b) a = -2, b = -2, c = 2(c) a = -2, b = -2, c = -2 (d) a = -2, b = 2, c = .5(e) a = 2, b = -2, c = 2Question #3: The management team of a company has 250 men and 125 women. If 200 of the managers have a master degree, and 100 of the managers with the master degree are women, how many of the managers are men without a master degree? (a) 125 (b) 150 (c) 175 (d) 200 (e) 225 Question #4: In the figure below, the area of square ABCD is equal to the sum of the areas of triangles ABE and DCE. If AB = 6, then CE =(a) 5 (b) 6 (c) 2 (d) 3 (e) 4Question #5:If α and β are the angles of the right triangle shown in the figure above, then sin2α + sin2β is equal to:(a) cos(β)(b) sin(β)(c) 1 (d) cos2(β)(e) -1 Question #6: The average of numbers (a + 9) and (a - 1) is equal to b, where a and b are integers. The product of the same two integers is equal to (b - 1)2. What is the value of a?(a) a = 9 (b) a = 1 (c) a = 0 (d) a = 5 (e) a = 11Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)? (A) x = 1 (B)x1 = 1, x2 = -1(C)x1 = 1, x2 = 0 (D)x = 0(E)x = -1Question #2: What is the length of the arc AB in the figure below, if O is the center of the circle and triangle OAB is equilateral? The radius of the circle is 9(a) π(b) 2 ·π(c) 3 ·π(d) 4 ·π(e) π/2 Question #3: What is the probability that someone that throws 2 dice gets a 5 and a 6? Each dice has sides numbered from 1 to 6.(a)1/2 (b)1/6 (c)1/12 (d)1/18 (e)1/36 Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He bikes from A to B at a speed of 15 miles/hour while his return speed is 10 miles/hour. What is the distance between the 2 towns?(a)11 miles (b)18 miles (c)15 miles (d)12 miles (e)10 miles Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1. What is the height of C2?(a)2·a /π(b)a / π(c)a / (2·π) (d)a / π(e)a + πQuestion #6: How many integers x are there such that 2x < 100, and at the same time the number 2x + 2 is an integer divisible by both 3 and 2?(a)1 (b)2 (c) 3 (d) 4 (e)5Question #7: sin(x)cos(x)(1 + tan2(x)) =(a)tan(x) + 1 (b)cos(x)(c)sin(x) (d)tan(x)(e)sin(x) + cos(x)Question #8: If 5xy = 210, and x and y are positive integers, each of the following could be the value of x + y except:(a)13 (b) 17 (c) 23 (d)15 (e)43Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y?(a)11 (b)17 (c)13 (d)15 (e) 9Question #10: The inequality |2x - 1| > 5 must be true in which one of the following cases?I. x < -5 II. x > 7 III. x > 01.Three unit circles are arranged so that each touches the other two. Find the radii ofthe two circles which touch all three.2.Find all real numbers x such that x + 1 = |x + 3| - |x - 1|.3.(1) Given x = (1 + 1/n)n, y = (1 + 1/n)n+1, show that x y = y x.(2) Show that 12 - 22 + 32 - 42 + ... + (-1)n+1n2 = (-1)n+1(1 + 2 + ... + n).4.All coefficients of the polynomial p(x) are non-negative and none exceed p(0). Ifp(x) has degree n, show that the coefficient of x n+1 in p(x)2 is at most p(1)2/2.5.What is the maximum possible value for the sum of the absolute values of thedifferences between each pair of n non-negative real numbers which do not exceed 1?6.AB is a diameter of a circle. X is a point on the circle other than the midpoint of thearc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show that the line PQ, the tangent at X and the line AB are concurrent.7.Four points on a circle divide it into four arcs. The four midpoints form aquadrilateral. Show that its diagonals are perpendicular.8.Find the smallest positive integer b for which 7 + 7b + 7b2 is a fourth power.9.Show that there are no positive integers m, n such that 4m(m+1) = n(n+1).10.ABCD is a convex quadrilateral with area 1. The lines AD, BC meet at X. Themidpoints of the diagonals AC and BD are Y and Z. Find the area of the triangle XYZ.11.A square has tens digit 7. What is the units digit?12.Find all ordered triples (x, y, z) of real numbers which satisfy the following systemof equations:xy = z - x - yxz = y - x - zyz = x - y - z。
sat数学试卷真题2021电子版
sat数学试卷真题2021电子版1、的值为（）[单选题] *A.-2B. 0C. 1(正确答案)D. 22、在0°~360°范围中，与645°终边相同的角是（）[单选题] * 285°(正确答案)-75°295°75°3、45、下列说法错误的是（）[单选题] *A．三角形的高、中线、角平分线都是线段B．三角形的三条中线都在三角形内部C．锐角三角形的三条高一定交于同一点D．三角形的三条高、三条中线、三条角平分线都交于同一点(正确答案)4、39．若（x﹣3）（2x+1）＝2x2+ax﹣3，则a的值为（）[单选题] *A．﹣7B．﹣5(正确答案)C．5D．75、5．如果某商场盈利万元，记作万元，那么亏损万元，应记作（??）[单选题] * A-8B-8万元(正确答案)C.8万元D.86、21．在﹣5，﹣2，0，这四个数中最小的数是（）[单选题] *A．﹣5(正确答案)B．﹣2C．0D．7、20.下列函数为既不是奇函数，也不是偶函数的是（）. [单选题] *A.?（x）＝x5+3(正确答案)B.?（x）＝x-4C.?（x）＝3x+4x2D.?（x）＝√(1-x^2 )8、已知sina<0且cota＞0，则是（）[单选题] *A、第一象限角B、第一象限角C、第三象限角(正确答案)D、第四象限角9、6、已知点A的坐标是，如果且，那么点A在（）[单选题] *x轴上y轴上x轴上，但不能包括原点(正确答案)y轴上，但不能包括原点10、已知二次函数f（x）=2x2-x+2，那么f（1）的值为（）。
[单选题] * 12283(正确答案)11、12．如图，将一块三角形纸片剪去一部分后，发现剩余阴影部分的纸片周长要比原三角形纸片的周长大，能正确解释这一现象的数学知识是（）[单选题] *A．直线没有端点，向两端无限延伸B．两点之间，线段最短(正确答案)C．经过一点有无数条直线D．两点确定一条直线12、29．已知2a＝5，2b＝10，2c＝50，那么a、b、c之间满足的等量关系是（）[单选题] *A．ab＝cB．a+b＝c(正确答案)C．a：b：c＝1：2：10D．a2b2＝c213、4．同一条直线上三点A，B，C，AB＝4cm，BC＝2cm，则AC的长度为（）[单选题] *A．6cmB．4cm或6cmC．2cm或6cm(正确答案)D．2cm或4cm14、6．数学文化《九章算术》中注有“今两算得失相反，要令正负以名之”，意思是：今有两数，若其意义相反，则分别叫做正数与负数．若向西走9米记作米，则米表示（）[单选题] *A向东走5米(正确答案)B向西走5米C向东走4米D向西走4米15、18.下列关系式正确的是(? ) [单选题] *A.-√3∈NB.-√3∈3C.-√3∈QD.-√3∈R(正确答案)16、4．在﹣，，0，﹣1，4，π，2，﹣3，﹣6这些数中，有理数有m个，自然数有n 个，分数有k个，则m﹣n﹣k的值为（）[单选题] *A．3(正确答案)B．2C．1D．417、7．一条东西走向的道路上，小明向西走米，记作“米”，如果他向东走了米，则可记作（）[单选题] *A-2米B-7米C-3米D+7米(正确答案)18、390°角是（）[单选题] *A、第一象限角(正确答案)B、第二象限角C、第三象限角D、第四象限角19、的单调递减区间为（）[单选题] *A、（-1,1）(正确答案)B、（-1,2）C、（-∞，-1）D、（-∞，+∞）20、23.将x-y-6=0改写成用含x的式子表示y的形式为（）[单选题] *A. x=y+6B. y=x-6(正确答案)C. x=6-yD. y=6=x21、函数y=kx（k是不为0的常数）是（）。
时代焦点出品—SAT数学练习题精选(附解析)
时代焦点出品—SAT数学练习题精选（附解析）下面是6道SAT数学练习题的内容， SAT数学练习题可以帮助大家更快更好的解答SAT数学题，可以帮助大家熟悉SAT数学词汇，掌握解题技巧，非常有用。
大家一起来练习一下吧，不是很难。
1.The histogram above shows the distribution of 31 black cherry trees, by height. For example, the leftmost bar represents the black cherry trees that are at least 60 feet, but not less than 65 feet, in height. Based on the histogram, which of the following can be the average (arithmetic mean) height of the 31 black cherry trees?Answer Choices(A) 70 feet(B) 72 feet(C) 74 feet | 4008-657-088SAT满分老师为你保驾护航，更多TOEFL，SAT资讯，常青藤名校申请请关注新浪微博：@许轶老师_时代 | 4008-657-088SAT 满分老师为你保驾护航，更多TOEFL，SAT 资讯，常青藤名校申请请关注新浪微博：@许轶老师_时代 (D) 78 feet (E) 80 feet2.In the figure above, O is the center of the circle and triangle A B O is equilateral. If the sides of triangle A B O are of length 6, what is the length of line B C?(A) 3 times square root 3 (B) 4 times square root 3 (C) 6 times square root 3 (D) 9 (E) 123.When the positive integer n is divided by 5, the remainder is 0. What is the remainder when 3n is divided by 5? (A) 0 (B) 1 (C) 2 (D) 3 | 4008-657-088SAT满分老师为你保驾护航，更多TOEFL ，SAT 资讯，常青藤名校申请请关注新浪微博：@许轶老师_时代 (E) 44.A 6-sided number cube, with faces numbered 1 through 6, is to be rolled twice. What is the probability that the number that comes up on the first roll will be less than the number that comes up on the second roll? (A) 1 over 4 (B) 1 over 3 (C) 5 over 12 (D) 7 over 12 (E) 1 over 25.The quadratic function is graphed in the -plane above. Iffor all values of , which of the following could be the coordinates of point?(A)(B)(C)(D)(E)6.In a certain lawn-mower factory, 0.06 percent of all mowers produced are defective. On the average, there will be 3 defective mowers out of how many produced?(A) 500(B) 1800(C) 5000(D) 18000(E) 50000Explanation1.The correct answer is CThe histogram does not give the recorded heights for each cherry tree, but rather the intervals in which the heights lie. Thus, to find possible values for the average (arithmetic mean) height, one can find lower and upper bounds for the average height by calculating the averages of lower and upper interval bounds of the histogram with the frequencies given. A lower bound for the average, found by using the value at the left endpoint of the interval, | 4008-657-088SAT满分老师为你保驾护航，更多TOEFL ，SAT资讯，常青藤名校申请请关注新浪微博：@许轶老师_时代is feet, andso feet would be an upper bound for the average height. Therefore, the average height of the 31 black cherry trees can be between 72.74 feet and 77.74 feet. Of the choices given, only 74 feet can be a possible value for the average height of the 31 black cherry trees.2.The correct answer is CChoice (C) is correct. Since triangle A B O is equilateral, each of its angles has measure60 degrees. It follows that angle B O C has measure 120 degrees. Since line O B and line O C are radii of the same circle, they are of equal length, and so delta O C B is isosceles. Hence angle O B C and angle O C B each have measure 30 degrees. Thus angle A B C has measure 60 degrees + 30 degrees = 90 degrees, and so triangle A B C is a 30 degrees minus 60 degrees minus 90 degrees right triangle. Since line A B, the side opposite the 30 degrees angle in triangle A B C, is of length 6, it follows that line B C, the side opposite the 60 degrees angle, is of length 6 times square root 33.The correct answer is AChoice (A) is correct. When the positive integer n is divided by 5, the remainder is 0. It follows that n is a multiple of 5. Therefore, 3n is also a multiple of 5, and so the remainder when 3n is divided by 5 is likewise 0.4.The correct answer is CThe outcome space for this experiment is the set of all orderedpairs where represents the first number that comes up, and represents the second one. Since and can take all the valuesthrough , there will be a total of possible outcomes. The outcomes canbe represented in a table as shown: Among all the | 4008-657-088SAT 满分老师为你保驾护航，更多TOEFL ，SAT 资讯，常青藤名校申请请关注新浪微博：@许轶老师_时代pairs , are pairs for which . So remaining pairs will have . Notice that the number of pairs forwhichis the same with the number of pairs for which . Therefore the number of pairs for which , is (half of ). Then the probability that is equalto .5.The correct answer is CThe fact that for all values of means that the point is the maximum of the quadratic function, so must be the vertex of the parabola. The parabola intersects the-axis at the points and,so must be halfway between and. Therefore,. Of the choices, the only one with-coordinate equal to is. Therefore, could be the coordinates of point.6.The correct answer is CRecall that 0.06 percent means 0.06 out of every 100, or 6 out of every 10000. The question asks for an equivalent ratio: 3 out of how many. The ratio 6 out of 10000 can be reduced (by dividing both members by 2) to 3 out of 5000.以上就是这6道精选SAT数学练习题的全部内容。
sat最难数学题
sat最难数学题【原创版】目录1.SAT 数学考试简介2.SAT 数学中最难的题目类型3.如何应对 SAT 数学难题正文【SAT 数学考试简介】SAT（Scholastic Assessment Test）是美国大学入学考试，其中的数学部分对于很多学生来说是一大挑战。
SAT 数学主要包括三个部分：问题解决、数据分析和数学知识。
这些问题涉及到代数、几何、统计学、概率、三角学等多个数学领域。
【SAT 数学中最难的题目类型】在 SAT 数学中，最难的题目类型通常包括以下几种：1.复杂几何问题：这类问题涉及到多边形、圆形等几何图形的计算，需要掌握复杂的几何知识。
2.代数问题：这类问题涉及到方程、不等式、函数等代数知识，需要具备较强的代数运算能力。
3.数据分析和概率问题：这类问题需要学生对数据进行分析、解释和推理，涉及到图表解读、概率计算等技能。
4.混合题型：这类问题通常会结合多个数学领域的知识，需要学生具备较强的综合运用能力。
【如何应对 SAT 数学难题】面对 SAT 数学难题，学生可以采取以下策略：1.扎实掌握基础知识：要想在 SAT 数学中取得好成绩，首先要扎实掌握基础知识，这样才能在遇到难题时游刃有余。
2.提高解题技巧：通过大量练习，学生可以总结出适合自己的解题方法和技巧，提高解题效率。
3.增强阅读理解能力：SAT 数学题目通常包含较长的题干，学生需要具备较强的阅读理解能力，才能准确把握题目要求。
4.保持冷静：遇到难题时，学生要保持冷静，分析题目的关键信息，尝试从不同角度去解决。
5.合理安排时间：在考试中，要合理安排时间，遇到难题时可以先跳过，等其他题目完成后再回来解决。
总之，要想在 SAT 数学考试中应对难题，需要扎实的基础知识、良好的解题技巧和阅读理解能力，以及冷静应对的心态。
sat数学考试试题
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) 212. If 4(t + u) + 3 = 19, then t + u = ?(A) 3 (B) 4 (C) 5 (D) 6 (E) 73. 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 = -2x4. 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 + 455. 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) 1,7006. 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 = 07. The least integer of a set of consecutive integers (连续整数) is –126. if the sum of these integers is 127, how many integers are in this set?(A) 126 (B) 127 (C) 252 (D) 253 (E) 2548. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 200 seniors, 300 juniors, and 400 sophomores who applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2 time; and each sophomore’s name, 1 times. If a student’s name is chosen at random from the names in the lottery, what is the probability that a senior’s name will be chosen?（A）1/8 (B) 2/9 (C) 2/7 (D) 3/8 (E) 1/2Question #1: 50% of US college students live on campus. Out of all students living on campus, 40% are graduate students. What percentage of US students are graduate students living on campus?(A) 90% (B) 5% (C) 40% (D) 20% (E) 25% Question #2: In the figure below, MN is parallel with BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC?(A) 5/9 (B) 2/3 (C) 4/9 (D) 1/2 (E) 2/9Question #3: If a2 + 3 is divisible by 7, which of the following values can be a?(A)7 (B)8 (C)9 (D)11 (E)4Question #4: What is the value of b, if x = 2 is a solution of equation x2 - b · x + 1 = 0?(A)1/2 (B)-1/2 (C)5/2 (D)-5/2 (E)2Question #5: Which value of x satisfies the inequality | 2x | < x + 1 ?(A)-1/2 (B)1/2 (C)1 (D)-1 (E)2Question #6: If integers m > 2 and n > 2, how many (m, n) pairs satisfy the inequality m n < 100?(A)2 (B)3 (C)4 (D)5 (E)7Question #7: The US deer population increase is 50% every 20 years. How may times larger will the deer population be in 60 years ?(A)2.275 (B)3.250 (C)2.250 (D)3.375 (E)2.500 Question #8: Find the value of x if x + y = 13 and x - y = 5.(A)2 (B)3 (C)6 (D)9 (E)4Question #9:The number of medals won at a track and field championship is shown in the table above. What is the percentage of bronze medals won by UK out of all medals won by the 2 teams?(A)20% (B)6.66% (C)26.6% (D)33.3% (E)10%Question #10: The edges of a cube are each 4 inches long. What is the surface area, in square inches, of this cube?(A)66 (B)60 (C)76 (D)96 (E)65Question #1: The sum of the two solutions of the quadratic equation f(x) = 0 is equal to 1 and the product of the solutions is equal to -20. What are the solutions of the equation f(x) = 16 - x ?(a) x1 = 3 and x2 = -3 (b) x1 = 6 and x2 = -6(c) x1 = 5 and x2 = -4 (d) x1 = -5 and x2 = 4(e) x1 = 6 and x2 = 0Question #2: In the (x, y) coordinate plane, three lines have the equations:l1: y = ax + 1l2: y = bx + 2l3: y = cx + 3Which of the following may be values of a, b and c, if line l3 is perpendicular to both lines l1 and l2?(a) a = -2, b = -2, c = .5 (b) a = -2, b = -2, c = 2(c) a = -2, b = -2, c = -2 (d) a = -2, b = 2, c = .5(e) a = 2, b = -2, c = 2Question #3: The management team of a company has 250 men and 125 women. If 200 of the managers have a master degree, and 100 of the managers with the master degree are women, how many of the managers are men without a master degree? (a) 125 (b) 150 (c) 175 (d) 200 (e) 225 Question #4: In the figure below, the area of square ABCD is equal to the sum of the areas of triangles ABE and DCE. If AB = 6, then CE =(a) 5 (b) 6 (c) 2 (d) 3 (e) 4Question #5:If α and β are the angles of the right triangle shown in the figure above, then sin2α + sin2β is equal to:(a) cos(β)(b) sin(β)(c) 1 (d) cos2(β)(e) -1 Question #6: The average of numbers (a + 9) and (a - 1) is equal to b, where a and b are integers. The product of the same two integers is equal to (b - 1)2. What is the value of a?(a) a = 9 (b) a = 1 (c) a = 0 (d) a = 5 (e) a = 11Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)? (A) x = 1 (B)x1 = 1, x2 = -1(C)x1 = 1, x2 = 0 (D)x = 0(E)x = -1Question #2: What is the length of the arc AB in the figure below, if O is the center of the circle and triangle OAB is equilateral? The radius of the circle is 9(a) π(b) 2 ·π(c) 3 ·π(d) 4 ·π(e) π/2 Question #3: What is the probability that someone that throws 2 dice gets a 5 and a 6? Each dice has sides numbered from 1 to 6.(a)1/2 (b)1/6 (c)1/12 (d)1/18 (e)1/36 Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He bikes from A to B at a speed of 15 miles/hour while his return speed is 10 miles/hour. What is the distance between the 2 towns?(a)11 miles (b)18 miles (c)15 miles (d)12 miles (e)10 miles Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1. What is the height of C2?(a)2·a /π(b)a / π(c)a / (2·π) (d)a / π(e)a + πQuestion #6: How many integers x are there such that 2x < 100, and at the same time the number 2x + 2 is an integer divisible by both 3 and 2?(a)1 (b)2 (c) 3 (d) 4 (e)5Question #7: sin(x)cos(x)(1 + tan2(x)) =(a)tan(x) + 1 (b)cos(x)(c)sin(x) (d)tan(x)(e)sin(x) + cos(x)Question #8: If 5xy = 210, and x and y are positive integers, each of the following could be the value of x + y except:(a)13 (b) 17 (c) 23 (d)15 (e)43Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y?(a)11 (b)17 (c)13 (d)15 (e) 9Question #10: The inequality |2x - 1| > 5 must be true in which one of the following cases?I. x < -5 II. x > 7 III. x > 01.Three unit circles are arranged so that each touches the other two. Find the radii ofthe two circles which touch all three.2.Find all real numbers x such that x + 1 = |x + 3| - |x - 1|.3.(1) Given x = (1 + 1/n)n, y = (1 + 1/n)n+1, show that x y = y x.(2) Show that 12 - 22 + 32 - 42 + ... + (-1)n+1n2 = (-1)n+1(1 + 2 + ... + n).4.All coefficients of the polynomial p(x) are non-negative and none exceed p(0). Ifp(x) has degree n, show that the coefficient of x n+1 in p(x)2 is at most p(1)2/2.5.What is the maximum possible value for the sum of the absolute values of thedifferences between each pair of n non-negative real numbers which do not exceed 1?6.AB is a diameter of a circle. X is a point on the circle other than the midpoint of thearc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show that the line PQ, the tangent at X and the line AB are concurrent.7.Four points on a circle divide it into four arcs. The four midpoints form aquadrilateral. Show that its diagonals are perpendicular.8.Find the smallest positive integer b for which 7 + 7b + 7b2 is a fourth power.9.Show that there are no positive integers m, n such that 4m(m+1) = n(n+1).10.ABCD is a convex quadrilateral with area 1. The lines AD, BC meet at X. Themidpoints of the diagonals AC and BD are Y and Z. Find the area of the triangle XYZ..11.A square has tens digit 7. What is the units digit?12.Find all ordered triples (x, y, z) of real numbers which satisfy the following systemof equations:xy = z - x - yxz = y - x - zyz = x - y - z.。
sat数学考试试题
s a t数学考试试题 TTA standardization office【TTA 5AB- TTAK 08- TTA 2C】S A T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) 212. If 4(t + u) + 3 = 19, then t + u =(A) 3 (B) 4(C) 5(D) 6? (E) 73. 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 = -2x4. 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 + 455. 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) 1,7006. 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 = 07. The least integer of a set of consecutive integers (连续整数) is –126. if the sum of these integers is 127, how many integers are in this set(A) 126? (B) 127? (C) 252? (D) 253(E) 2548. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 200 seniors, 300 juniors, and 400 sophomores who applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2 time; and each sophomore’s name, 1 times. If a student’s name is chosen at random from the names in the lottery, what is the probability that a senior’s name will be chosen（A）1/8? (B) 2/9(C) 2/7? (D) 3/8? (E) 1/2Question #1: 50% of US college students live on campus. Out of all students living on campus, 40% are graduate students. What percentage of US students are graduate students living on campus?(A) 90% (B) 5% (C) 40% (D) 20% (E) 25%Question #2: In the figure below, MN is parallel with BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC?(A) 5/9 (B) 2/3 (C) 4/9 (D) 1/2 (E) 2/9Question #3: If a2 + 3 is divisible by 7, which of the following values can be a?(A)7 (B)8 (C)9 (D)11 (E)4Question #4: What is the value of b, if x = 2 is a solution of equation x2 - b · x + 1 = 0?(A)1/2 (B)-1/2 (C)5/2 (D)-5/2 (E)2Question #5: Which value of x satisfies the inequality | 2x | < x + 1(A)-1/2 (B)1/2 (C)1 (D)-1 (E)2Question #6: If integers m > 2 and n > 2, how many (m, n) pairs satisfy the inequality m n < 100?(A)2 (B)3 (C)4 (D)5 (E)7Question #7: The US deer population increase is 50% every 20 years. How may times larger will the deer population be in 60 years(A) (B) (C) (D) (E)Question #8: Find the value of x if x + y = 13 and x - y = 5.(A)2 (B)3 (C)6 (D)9 (E)4Question #9:The number of medals won at a track and field championship is shown in the table above. What is the percentage of bronze medals won by UK out of all medals won by the 2 teams?(A)20% (B)% (C)% (D)% (E)10%Question #10: The edges of a cube are each 4 inches long. What is the surface area, in square inches, of this cube(A)66 (B)60 (C)76 (D)96 (E)65Question #1: The sum of the two solutions of the quadratic equation f(x) = 0 is equal to 1 and the product of the solutions is equal to -20. What are the solutions of the equation f(x) = 16 - x(a) x1 = 3 and x2 = -3 (b) x1 = 6 and x2 = -6(c) x1 = 5 and x2 = -4 (d) x1 = -5 and x2 = 4(e) x1 = 6 and x2 = 0Question #2: In the (x, y) coordinate plane, three lines have the equations: l1: y = ax + 1l2: y = bx + 2l3: y = cx + 3Which of the following may be values of a, b and c, if line l3 is perpendicular to both lines l1 and l2(a) a = -2, b = -2, c = .5 (b) a = -2, b = -2, c = 2(c) a = -2, b = -2, c = -2 (d) a = -2, b = 2, c = .5(e) a = 2, b = -2, c = 2Question #3: The management team of a company has 250 men and 125 women. If 200 of the managers have a master degree, and 100 of the managers with the master degree are women, how many of the managers are men without a master degree(a) 125 (b) 150 (c) 175 (d) 200 (e) 225Question #4: In the figure below, the area of square ABCD is equal to the sum of the areas of triangles ABE and DCE. If AB = 6, then CE =(a) 5 (b) 6 (c) 2 (d) 3 (e) 4Question #5:If α and β are the angles of the right triangle shown in the figure above, then sin2α + sin2β is equal to:(a) cos(β)(b) sin(β) (c) 1 (d) cos2(β) (e) -1Question #6: The average of numbers (a + 9) and (a - 1) is equal to b, where a and b are integers. The product of the same two integers is equal to (b - 1)2. What is the value of a(a) a = 9 (b) a = 1 (c) a = 0 (d) a = 5 (e) a = 11 Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x) (A) x = 1 (B)x1 = 1, x2 = -1(C)x1 = 1, x2 = 0 (D)x = 0(E)x = -1Question #2: What is the length of the arc AB in the figure below, if O is the center of the circle and triangle OAB is equilateralThe radius of the circle is 9(a) π(b) 2 ·π(c) 3 ·π(d) 4 ·π (e) π/2Question #3: What is the probability that someone that throws 2 dice gets a 5 and a6 Each dice has sides numbered from 1 to 6.(a)1/2 (b)1/6 (c)1/12 (d)1/18 (e)1/36Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He bikes from A to B at a speed of 15 miles/hour while his return speed is 10miles/hour. What is the distance between the 2 towns?(a)11 miles (b)18 miles (c)15 miles (d)12 miles (e)10 miles Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1. What is the height of C2?(a)2·a /π (b)a / π (c)a / (2·π) (d)a / π (e)a + πQuestion #6: How many integers x are there such that 2x < 100, and at the same time the number 2x + 2 is an integer divisible by both 3 and 2?(a)1 (b)2 (c) 3 (d) 4 (e)5Question #7: sin(x)cos(x)(1 + tan2(x)) =(a)tan(x) + 1 (b)cos(x)(c)sin(x) (d)tan(x)(e)sin(x) + cos(x)Question #8: If 5xy = 210, and x and y are positive integers, each of the following could be the value of x + y except:(a)13 (b) 17 (c) 23 (d)15 (e)43Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y(a)11 (b)17 (c)13 (d)15 (e) 9Question #10: The inequality |2x - 1| > 5 must be true in which one of the following casesI. x < -5 II. x > 7 III. x > 01.Three unit circles are arranged so that each touches the other two. Findthe radii of the two circles which touch all three.2.Find all real numbers x such that x + 1 = |x + 3| - |x - 1|.3.(1) Given x = (1 + 1/n)n, y = (1 + 1/n)n+1, show that x y = y x.(2) Show that 12 - 22 + 32 - 42 + ... + (-1)n+1n2 = (-1)n+1(1 + 2 + ... + n).4.All coefficients of the polynomial p(x) are non-negative and noneexceed p(0). If p(x) has degree n, show that the coefficient of x n+1 in p(x)2 is at most p(1)2/2.5.What is the maximum possible value for the sum of the absolutevalues of the differences between each pair of n non-negative realnumbers which do not exceed 1?6.AB is a diameter of a circle. X is a point on the circle other than themidpoint of the arc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show that the line PQ, the tangent at X and the line AB are concurrent.7.Four points on a circle divide it into four arcs. The four midpoints forma quadrilateral. Show that its diagonals are perpendicular.8.Find the smallest positive integer b for which 7 + 7b + 7b2 is a fourthpower.9.Show that there are no positive integers m, n such that 4m(m+1) =n(n+1).10.ABCD is a convex quadrilateral with area 1. The lines AD, BC meet atX. The midpoints of the diagonals AC and BD are Y and Z. Find the area of the triangle XYZ.11. A square has tens digit 7. What is the units digit?12.Find all ordered triples (x, y, z) of real numbers which satisfy thefollowing system of equations:xy = z - x - yxz = y - x - zyz = x - y - z。
美国“高考”SAT考试地数学题
美国“高考〞SAT考试的数学题数学第一局部时间〔25分钟〕16个问题说明：这局部包含有两种类型的问题。
你将有25分钟时间来完成他们。
对于1—8，在所给选项中选出一个最正确答案，然后再答题卡上填上相应的圆圈，你可以使用任何可用的草稿纸空间。
注释：1、可以使用计算器。
2、所有使用的数字均为实数。
3、在测试中，问题中所提供的数字或图表都包含一定的信息，这对于解题很有帮助。
所有图表都是比拟准确的，除非在某些具体问题中，图表没有按比例绘制。
所有数字都呈现于平面上，除非另有说明。
4、除非另有规定，对于任何函数f的值域都是所有实数x的集合，并使得f(x)是实数。
可能用到的公式：1、If4(t+u)+3=19,thent+u=如果4(t+u)+3=19,那么t+u=A3B4C5D6E72、如图，三条直线相交于一点。
如果f=85,e=25,那么a的值是多少？A60B65C70D75E853、如果玛丽开车行驶n英里用了t小时，那么以下哪个可以表示她行驶的平均速度，英里/小时？An/tBt/nC1/ntDntEn2t4、如果a是一个奇数，b是一个偶数，那么选项中哪一个是奇数？A3bBa+3C2(a+b)Da+2bE2a+b5、在平面坐标内，F(-2,1),G(1,4),H(4,1)在以P为圆心的圆上，那么点P的坐标是什么？A〔0,0〕B〔1,1〕C〔1,2〕D〔1，-2〕E〔2.5,2.5〕6、如图，如果-3≤x≤，6那么x有几个值，使得f(x)=2?A零B一个C两个D三个E三个以上7、如果t和t+2的算术平均值是x,t和t-2的算术平均值是y，那么x和y的算术平均值是多少？A1B1/2CtDt+1/2E2t8、对于任何数x和y,假设x△y=x2+xy+y2,那么〔3△1〕△1等于多少？A5B13C27D170E1839、摩根的植物在一年之内从42厘米长到57厘米。
而琳达的植物年前是59厘米，一年之内她的植物生长的高度是摩根植物长高的两倍，那么，在年底琳达植物的高度是多少？10、从1990年开场，一个树木繁茂区的松鼠的数量以每三年三倍的速度在增长。
THUSSAT2021年3月诊断性测试理科数学答案
2 1 3nn n n n -1 n n n - n -1 ⎝ ⎭中学生标准学术能力诊断性测试 2021 年 3 月测试理科数学试卷（一卷）参考答案一、选择题：本题共 12 小题，每小题 5 分，共 60 分．在每小题给出的四个选项中，只有一项是符合题目要求的．1 2 3 4 5 6 7 8 9 10 11 12 CDDBBBCBAAAB二、填空题：本题共 4 小题，每题 5 分，共 20 分．13． - + i5 514． ⎡0,π ⎤ , ⎡5π , π⎤⎢ 3 ⎥⎦ ⎢⎣ 6⎥⎦15． 221716．a ∈(0,1) (3, +∞) 三、解答题：共 70 分．解答应写出文字说明、证明过程或演算步骤．第 17~21 题为必考题， 每个试题考生都必须作答．第 22、23 题为选考题，考生根据要求作答． （一）必考题：共 60 分．17．解：（1） a = S - S (n ≥ 2) ,∴ S - a = S ，则S =(n -1)2(n ≥ 2)， 即S = n 2 (n ∈ N *) ……………3 分 ∴ a = n 2 - (n -1)2 = 2n -1(n ≥ 2)……………5 分经检验a 1 = 1适合，∴ a n = 2n -1……………6 分（2）易知b n > 0 , b n = 22n -1 n 4, b n +1 = 22n +1(n +1)4 ，b 22 n 4⎛ 2n ⎫4∴ n +1 = b n (n +1) 4 = n +1 ⎪ ……………8 分当2n> 1时， n > +1，n +13 所以当1 ≤ n < 3 时， b n > b n +1，当n ≥ 3 时， b n < b n +1……………10 分又b = 1 , b =32，所以当n = 3 时， b 有最小值32……………12 分22381 n8118．解：（1）证明：设平面 PAD 平面 PBC = l ,AD //BC , BC ⊄ 平面 PAD , AD ⊂ 平面 PAD ,∴ B C // 平面 PAD ，又 BC ⊂ 平面 PBC ,∴ BC //l ……………2 分∠PBC = π,∴ PB ⊥ BC ,∴ PB ⊥ l ……………4 分2又因为平面 PAD ⊥ 平面 PBC ,∴ PB ⊥ 平面 PAD ，可得 PB ⊥ PA ，得证．……………6 分（2）解：连结 BD ，在△ BCD 中，易得 BD = ,∴ BD ⊥ BC ，又 PB ⊥ BC ,∴∠PBD 为二面角 P - BC - A 的平面角……………8 分以 D 为原点，分别以 DA , DB 的方向为 x 轴， y 轴正方向，建立空间直角坐标系，∴ A (2, 0, 0) , B (0, 3, 0) , C (-1, 3, 0) ，BC ⊥ BD , BC ⊥ PD , BD PD = D ,∴ BC ⊥ 平面 PBD ，所以平面 PBD ⊥ 平面 ABCD ……………9 分 可设 P (0, y , z ) ．由 PA = 2PC 可得：(0 - 2)2 + y 2 + z 2 = 4(0 +1)2 + 4( y - 3)2 + 4z 2 ，化简可得： 3y 2 - 8 3y + 3z 2 +12 = 0 …①由（1）知 PB ⊥ PA ,∴(-2, y , z ) ⋅ (0, y - 3, z ) = 0 ，化简得 y 2 - 3y + z 2 = 0 …②解方程①②可得y = 4 3 , z =2 3 ……………11 分55∴sin ∠PBD =19．解：z= 2 5 ，则cos ∠PBD = PB 55 ……………12 分5（1）甲是无放回地抽取，甲至多抽到一个黑球：基本事件{没有抽到黑球，抽到一个黑球}，4 10 ⎪10 10 C 4 35 1∴ P { 没有抽到黑球} = 7 = = ……………1 分4 210 6C 3C 1 105 1 P { 抽到一个黑球} = 7 3 = = ……………2 分 4 210 2所以甲至多抽到一个黑球的概率为： 1 + 1 = 2……………5 分6 2 3（2）解法一：乙是有放回地抽取，抽到白球得 10 分，抽到黑球得 20 分，所以抽取 4 次{4 个白球，3 个白球 1 个黑球，2 个白球 2 个黑球，1 个白球 3 个黑球，4 个黑球}，7 对应的 X 取值有{40, 50, 60, 70,80}；而每次抽到白球、黑球的概率分别为10, 3，10设 4 次取球取得黑球次数为r ，则r 的可能取值0,1, 2, 3, 4 ……………6 分⎛ 7 ⎫4-r ⎛ 3 ⎫r∴ P ( X = 40 +10r ) = C r⎝ ⎭ ⎝ ⎭ ，即可得分布列如下：……………10 分∴ E ( X ) = 40 ⨯ 2401 + 50 ⨯ 4116 + 60 ⨯ 2646 + 70 ⨯ 756 + 80 ⨯ 81= 5210000 10000 10000 10000 10000……………12 分解法二：设 4 次取球取得黑球数为Y ，则 X = 40 +10Y ，且Y B ⎛ 4,3 ⎫……………8 分10 ⎪EX = 40 +10EY = 40 +10 ⨯ 4 ⨯ 3 10⎝ ⎭= 52 ……………12 分20．解：C C1+ 1 k 252 1+ k 2 2 k AB ⋅ FM FN5 k 2 +1 2 k5 5k 2 + 2 ⎪x x 20k （1）椭圆的右焦点 F (2, 0) ，设 AB 所在的直线的方程为y = k (x - 2) （ k ≠ 0 ），且 A (x 1, y 1), B (x 2 , y 2 ) ,⎧ y = k (x - 2),……………1 分⎪ 联立方程组⎨ x 2 + y 2 = 1, 可得： (5k 2 +1)x 2 - 20k 2 x + (20k 2- 5) = 0⎪⎩ 5……………3 分2则 x 1 + x 2 = 5k 2 +1 , x 1x 2 = 20k 2- 5 5k 2+1 ⎛ 10k 2-2k ⎫ ，点 N 的坐标为 , ， ⎝ 1 5k +1 ⎭ ∴ON 所在的直线的方程为 y = - 1 5kx ……………5 分椭圆C 在 A , B 处的切线方程分别为 x 1x + y y = 1, x 2 x+ y y = 1 ，⎧ x 1x+ y y = 1, 5 1 52⎪ 5 1联立方程组⎨ ⎪ 2 + y y = 1,⎛⎪ 5 2解得点M 的坐标为⎛ 5( y 2 - y 1) ,x 1 - x 2⎫ , M ⎛ 5 , - 1 ⎫，x y - x y x y - x y ⎪ 2 2k ⎪⎝ 1 2 2 1 1 2 2 1 ⎭ ⎝ ⎭ 所以点M 的坐标满足直线ON 的方程 y = - 1 5kx ，故O , M , N 三点共线……………7 分（2）由（1）可知， AB = x 1 - x 2 = 5k 2+1……………8 分FM = - 2 = ……………9 分FN = - 2 = 5k 2 +1……………10 分∴= ≥ ，当且仅当 k = 1 时，等号成立……………12 分1+ k 22 5(1+ k 2 ) 1+ k 210k 2 5k 2 +1 2 1+ k 22 21．解：（1）f (x ) = ln(x +1) - ax , f '(x ) =1x +1- a ……………1 分①当a ≤ 0 时， f '(x ) =1x +1- a ≥ 0 在 x ∈(0, +∞) 时恒成立，∴ f (x ) = ln(x +1) - ax 在(0, +∞) 上递增，∴ f (x ) > f (0) = 0 ，不符合题意，……………2 分②当0 < a < 1时， f '(x ) =1 x +1 - a ≥ 0 ⇔ 0 < x ≤ 1 -1 ，a∴ f (x ) = ln(x +1) - ax 在⎛ 0, 1 -1⎫ 上递增，在⎛ 1 -1, +∞⎫上递减，a ⎪ a ⎪ ⎝ ⎭ ⎝ ⎭f ⎛ 1 -1⎫>f (0) = 0 ，当 x → +∞ 时， f (x ) → -∞ ，满足题意……………4 分a ⎪ ⎝ ⎭③当a ≥ 1 时， f '(x ) =1 x +1- a < 0 在 x ∈(0, +∞) 时恒成立，∴ f (x ) = ln(x +1) - ax 在(0, +∞) 上递减，∴ f (x ) <综上所述， a 的取值范围是(0,1) ．（2）由（1）知0 < a < 1,∴ a =ln(x 0 +1) ，x 0f (0) = 0 ，不符合题意．……………6 分要证明 x> 2 ⎛ 1 -1⎫ ，只要证明ln(x+1) > 2x 0 ……………7 分 0 a ⎪ 0x + 2⎝ ⎭ 0设 g (x ) = ln(x +1) -2xx + 2 , x > 0 ，'=1-4 =x≥g (x )x +1 (x + 2)2(x +1)(x + 2)20 ，g (x ) = ln(x +1) - 2x > g (0) = 0 ，即 x > 2 ⎛ 1 -1⎫……………9 分x + 20 a ⎪ ⎝ ⎭x 0 x 2 xϕ ϕ 11 另一方面：证法一：要证明x 0 < e a-1，只要证明ln(x 0 +1) < ，a即证明ln(x 0 +1) <x 0 ln(x 0 +1)……………10 分l n ( x 0 +1) > 0 ，即证ln ( x 0 + 1) < ，设h (x ) = ln(x +1) - , x > 0 ，则h '(x ) =1 - 1x +1< 0 ，1所以当 x > 0 时， h (x ) < h (0) = 0 ，即 x 0 < e a -1……………12 分f (x ) ⎛ 1 -1, +∞ ⎫1- > 1 -> 1 -证法二：因为在 在 a ⎪ 上递减，且e a 11, x 0 1 ， ⎝ ⎭a a 1⎛ 1 ⎫ 1 1要证明 x 0 < e a -1，只要证明 f (x 0 ) > f e a-1⎪ ，即证 ⎝ ⎭a - a e a + a < 0……………10 分x 2 +1 -(x -1)2设ϕ(x ) =, x > 1 ,ϕ'(x ) =< 0 ，exexx 2 +1 2∴ (x ) =< (1) = < 1 ，e x e所以当 x > 1 时， e x > x 2 +1， 11 即当0 < a < 1时， e a>+1，a21∴ x 0 < e a -1……………12 分（二）选考题：共 10 分．请考生在第 22、23 题中任选一题．作答如果多做，则按所做的第一题计分． 22．解：C2y 2（1）曲线 2 的普通方程为 x += 1……………2 分43 + cos 2θ - sin 2θ2 3 6 a 2 + ab + b 2 2 2 ⎩max ⎝ ⎭ ⎝ ⎭⎧x = 2 + ⎪4k ,1+ k 2 （2）由曲线C 1 的参数方程为⎨ ⎪ y = ⎩ 2 (1- k 2) 1+ k 2（ k 为参数）， ,得曲线C 1 的普通方程为（x - 2）2+ y 2 = 4 ， 它是一个以C （2, 0）为圆心，半径等于2 的圆，曲线C 的极坐标方程为ρ = 2．……………4 分∴ ρ 2 (3 + cos 2θ - sin 2 θ ) = 4 ，可得4x 2 + y 2 = 4 ……………6 分⎧x = cos β ,则曲线C 2 的参数方程为： ⎨y = 2 s in β ,（ β 为参数），A 是曲线C 1 上的点，B 是曲线C 2 上的点，∴ AB max = BC + 2设 B （cos β , 2 s in β），则 BC = （cos β - 2）2+ 4 s in 2 β =……………8 分=当cos β = - 2时， BC 3，max28 = 2 21 ,∴ AB 3 3max= 2 21 + 2 ……………10 分323．解：（1）f (x ) = x - a + x + b + c ≥x - a - x - b + c = a + b + c = a + b + c = 1……………2 分∴⎛ 1 + 1 + 1 ⎫(2a 2 + 3b 2 + 6c 2 )≥ ⎛ 1 ⨯ 2a + 1 ⨯ 3b + 1 ⨯ 6c ⎫ =1， 2 3 6 ⎪ ⎪∴2a 2 + 3b 2 + 6c 2 ≥ 1，即2a 2 + 3b 2 + 6c 2 的最小值为 1……………5 分⎛ b 3b ⎫ （2） = ≥ a + + ⎪ ……………7 分 2 ⎝ 2 2 ⎭ -3cos 2β - 4cos β + 8-3 cos β + 3 ⎪ + 3 ⎛2 ⎫228 ⎝⎭ ⎛ b ⎫2a + ⎪ + 3 ⎝ 2 ⎭ 4b 2 = 2b 2 + bc + c 22 c 2 + ca + a 2 2 a 2 + ab + b 2 b 2 + bc + c 2 2 2 ∴ ≥ ⎛b +c + 3c ⎫ , ≥ ⎛ c + a + 3a ⎫ ， 2 2 2 ⎪ 2 2 2 ⎪ ⎝ ⎭ ⎝ ⎭因此 + +≥ ⎛ a + b + c + a + b + c + a + b + c ⨯ 3 ⎫2 2 2 ⎪ ⎝ ⎭= ⎛ 3 + 3 ⎫ > 3 ……………10 分 2 2 2 ⎪ 2 ⎝ ⎭c 2 + ca + a 2。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
SAT数学真题精选编辑整理：尊敬的读者朋友们：这里是精品文档编辑中心，本文档内容是由我和我的同事精心编辑整理后发布的，发布之前我们对文中内容进行仔细校对，但是难免会有疏漏的地方，但是任然希望（SAT数学真题精选）的内容能够给您的工作和学习带来便利。
同时也真诚的希望收到您的建议和反馈，这将是我们进步的源泉，前进的动力。
本文可编辑可修改，如果觉得对您有帮助请收藏以便随时查阅，最后祝您生活愉快业绩进步，以下为SAT数学真题精选的全部内容。
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) 212。
If 4(t + u) + 3 = 19, then t + u = ？（A) 3 (B） 4 (C) 5 (D) 6 (E） 73。
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 = -2x4. 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 + 455. 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(A) 800 (B) 1,000 （C) 1，100 （D) 1，300 （E） 1,7006. 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 = 07。
The least integer of a set of consecutive integers （连续整数） is –126. if the sum of these integers is 127， how many integers are in this set？(A） 126 （B) 127 （C) 252 （D） 253 (E) 2548。
A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 200 seniors， 300 juniors, and 400 sophomores who applied。
Each senior’s name is placed in the lottery 3 times； each junior's name， 2 time; and each sophomore’s name，1 times. If a student’s name is chosen at random from the names in the lottery, what is the probability that a senior’s name will be chosen？（A）1/8 （B) 2/9 (C） 2/7 （D） 3/8 (E） 1/2SAT考试数学练习题(一）1。
If f(x） = x²– 3, where x is an integer， which of the following could be a value of f （x）？I 6II 0III —6A. I onlyB. I and II onlyC. II and III onlyD. I and III onlyE. I， II and IIICorrect Answer： A解析:Choice I is correct because f（x) = 6 when x=3。
Choice II is incorrect because to make f （x) = 0， x² would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f（x） = 0, x²would have to be –3 but squares cannot be negative. （The minimum value for x2 is zero； hence， the minimum value for f（x) = -3）2。
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200？A. 48B。
49C。
50D。
51E。
52Correct Answer: C解析：1 〈 4n + 7 < 200. n can be 0， or —1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1. The largest value for n will be an integer < (200 - 7) /4. 193/4 = 48.25， hence 48。
The number of integers between -1 and 48 inclusive is 503. In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different。
What is the sum of A，B，C and D?A. 23B。
22C。
18D。
16E。
14Correct Answer： B解析:First you must realize that the sum of two 2-digit numbers cannot be more that 198 （99 + 99）。
Therefore in the given problem D must be 1. Now use trial and error to satisfy the sum 5A + BC = 143。
A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13. With one to carry over into the tens column， 1 +4. 12 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth, and 40 cm height. How high （in cm) will the water rise?(1 litre = 1000cm³)A. 6B。
8C。
10D。
20E. 40Correct Answer： B解析:Total volume of water = 12 liters = 12 x 1000 cm3。
The base of the aquarium is 50 x 30 = 1500cm3. Base of tank x height of water = volume of water. 1500 x height = 12000; height = 12000 / 1500 = 85. Six years ago Anita was P times as old as Ben was。
If Anita is now 17 years old, how old is Ben now in terms of P ?A。
11/P + 6B. P/11 +6C。
17 - P/6D。
17/PE。
11.5PCorrect Answer: A解析:Let Ben’s age now be B。
Anita’s age now is A. (A — 6) = P（B — 6)But A is 17 and therefore 11 = P（B — 6)。
11/P = B-6（11/P) + 6 = BSAT考试数学练习题（二)1. The distance from town A to town B is five miles。
C is six miles from B。
Which of the following could be the distance from A to C？I 11II 1III 7A。
I onlyB. II onlyC。
I and II onlyD。
II and III onlyE. I, II， or III。
Correct Answer: E解析：Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6。