SAT数学历年真题整理

SAT数学历年真题精选1

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?17. 在上面这个直角三角形中，直线EF ││ (平行于)直线AC。

SAT考试2024数学历年题目全解

SAT考试2024数学历年题目全解SAT考试是一项全球性的标准化考试，旨在评估学生在阅读、写作和数学方面的能力。

数学部分是SAT考试的一个重要组成部分，涵盖了各种数学概念和技巧。

本文将为您提供2024年SAT数学部分的历年题目全解，帮助您更好地应对这一考试。

第一题：题目：求解以下方程：3x + 5 = 20解析：要求解方程3x + 5 = 20，我们首先将5从等式两边减去，得到3x = 15。

然后，我们将方程两边都除以3，即x = 5。

因此，方程的解为x = 5。

第二题：题目：计算以下比例的值：5:8 = x:40解析：要计算比例5:8与x:40的值，我们可以采取交叉乘法的方法。

将5乘以40，并将结果除以8，即可求得x的值。

计算过程如下：5 * 40 / 8 = 200 / 8 = 25因此，比例5:8与x:40的值为25。

第三题：题目：已知一个等边三角形的边长为12，计算其面积。

解析：一个等边三角形的边长为12，则其高可以通过勾股定理求得。

根据勾股定理，我们有：高的平方= 边长的平方- 底边的一半的平方。

设高为h，则有 h^2 = 12^2 - (12/2)^2= 144 - 36= 108因此，高h = √108 = 6√3由于等边三角形的高等于边长的一半乘以根号3，所以面积S可以计算为：S = 1/2 * 12 * 6√3= 6 * 6√3= 36√3因此，该等边三角形的面积为36√3。

第四题：题目：在一个长方形花坛中，长度是宽度的3倍，已知宽度为2米，计算花坛的面积。

解析：我们知道长方形花坛的面积可以通过长度乘以宽度来计算。

已知宽度为2米，则长度为3 * 2 = 6米。

因此，花坛的面积为2 * 6 =12平方米。

通过以上题目的解析，我们可以看到SAT数学部分考察了各种数学概念和技巧，包括方程的求解、比例的计算、勾股定理的应用以及长方形面积的计算等。

熟练掌握这些数学知识，并能够灵活运用于实际问题的解决中，将有助于您在SAT考试中取得更好的成绩。

2024年SAT考试数学历年真题精选辑

2024年SAT考试数学历年真题精选辑一、选择题1. 已知方程 ax^2 + bx + c = 0 中，a ≠ 0，若该方程存在两个相等实数根，则下列哪个条件必然成立？A) a = bB) a = cC) b = cD) a + b = cE) b + c = a2. 投掷一枚均匀硬币，连续抛掷若干次，每次结果独立。

设已知前两次投掷结果都是正面朝上，下一次投掷的正面朝上的概率为多少？A) 1/2B) 1/4C) 1/3D) 2/3E) 2/93. 若函数 f(x) = 2x^2 + kx + 1，对于所有实数 x，f(x) > 0 成立。

则 k 的取值范围是？A) -1 < k < 1B) k > 1C) k < -1D) k ≠ 0E) k = 1二、解答题1. 设正整数 n 满足 n(n+1)(n+2) 可以被 3 和 8 同时整除，求 n 的最小值。

解：根据题意，n(n+1)(n+2) 是 3 和 8 的公倍数。

由于 3 和 8 互质，所以n(n+1)(n+2) 的最小公倍数为 24（3*8）。

因此，n 的最小值为 2。

2. 一辆长为 5 米的火车以恒定速度行驶通过测速点，测速点距离火车的前端 9 米，测得该火车的速度为 72 km/h。

若按该测速点测得的速度计算，火车的长度应为多少米？解：由于测得的速度为火车通过测速点的平均速度，根据平均速度公式v = d/t，我们可以得到火车通过测速点所用的时间 t = 9 米 / 72 km/h = (9/1000) / (72/3600) 小时。

由此，我们可以计算火车通过测速点所用的时间 t = 0.15 秒。

根据速度公式 v = d/t，可以得到火车通过测速点所用的距离 d = v * t = 72 km/h * 0.15 秒 = (72/3600) km * 0.15 秒 = 0.00375 km = 3.75 米。

2024 SAT考试必备数学历年真题练习

2024 SAT考试必备数学历年真题练习近年来，SAT考试已成为全球高中生都渴望通过的重要考试之一。

在数学部分，历年真题练习是提高成绩的重要途径之一。

本文将为大家提供2024 SAT考试必备的数学历年真题练习，帮助考生熟悉考试内容和题型，提高解题能力。

第一部分：选择题1. 题目：下列哪个数是无理数？A. 2B. -1C. πD. 0.5解析：正确答案是C。

无理数是指不能表示为两个整数的比的数，如π（圆周率）。

2. 题目：已知平面上AB为直线段，C为直线l上一点，且AC=2BC。

若直线l与x轴的交点为D，则AB与CD的交点为：A. EB. FC. GD. H解析：正确答案是A。

根据题目条件，由比例关系可得出交点E。

3. 题目：已知函数f(x) = 2x + 3, g(x) = x^2 - 1，求f(g(2))的值。

A. 9B. 10C. 11D. 12解析：首先计算g(2)的值，将x替换为2，得到g(2) = 4 - 1 = 3。

然后将g(2)的值代入f(x)的表达式中，得到f(3) = 2(3) + 3 = 9，因此正确答案是A。

第二部分：填空题4. 题目：已知函数f(x) = √(2x - 7)，求f(5)的值。

解析：将x替换为5，得到f(5) = √(2(5) - 7) = √(10 - 7) = √3。

因此，f(5)的值为√3。

5. 题目：若a + b = 7，a - b = 1，则a的值为（）。

解析：将两个方程相加，得到2a = 8，计算可得a = 4。

因此，a的值为4。

6. 题目：已知三角形ABC，∠ACB = 90°，AB = 5 cm，BC = 12 cm，求∠CAB的正弦值。

解析：根据勾股定理，AC^2 = AB^2 + BC^2，代入数值计算可得AC = 13 cm。

正弦值可由对边与斜边之比得出，即sin(∠CAB) = BC / AC = 12 / 13。

第三部分：解答题7. 题目：已知三角形ABC的周长为24 cm，AB = 8 cm，BC = 10 cm，求AC的长度。

2024 SAT考试数学历年题目大盘点

2024 SAT考试数学历年题目大盘点2024年即将迎来 SAT 考试，作为一项重要的学术考试，数学部分一直是考生们关注的焦点。

为了帮助考生更好地备考，本文将对近年的 SAT 数学试题进行盘点，并分析其中的一些常见考点。

一、代数与函数（Algebra and Functions）1. 方程与不等式（Equations and Inequalities）近年的 SAT 数学试题中，涉及到方程与不等式的题目较为常见。

考生需要熟练掌握一元一次方程、二元一次方程、一元二次方程以及绝对值不等式等的解法。

此外，还需要注意对于方程和不等式解集的理解和应用。

2. 函数（Functions）函数是 SAT 考试中的重点内容之一。

考生需要了解各类常见函数的性质，如线性函数、二次函数、指数函数、对数函数等，并能够灵活运用函数的性质解决问题。

此外，函数的符号表示、定义域、值域以及函数图像的理解也是考点之一。

二、几何（Geometry）1. 平面几何（Plane Geometry）几何部分涉及到平面几何和空间几何的知识。

在平面几何方面，考生需要掌握直线与角、三角形、四边形、圆等图形的性质，能够灵活运用相关定理解决几何问题。

2. 空间几何（Solid Geometry）空间几何侧重于三维几何图形的性质和计算。

考生需要了解球体、圆柱体、锥体、棱柱等立体图形的特征和计算方法，并能够运用相关定理解决与空间几何有关的问题。

三、数据分析（Data Analysis）1. 统计与概率（Statistics and Probability）数据分析部分主要考察考生对统计与概率的理解和运用能力。

考生需要了解统计数据的收集、整理和分析方法，包括频率分布、平均数、中位数、标准差等；同时还需要对概率的计算和应用有一定的掌握。

2. 数据表示与解释（Data Representation and Interpretation）数据表示与解释主要考察考生对数据图表的理解和分析能力。

SAT考试2024数学历年题目精讲

SAT考试2024数学历年题目精讲在本篇文章中，我们将重点讲解SAT考试2024年数学部分的历年题目。

我们将按照题目类型进行分类，并为每个题型提供详细的解答和解题技巧，帮助考生更好地应对这些题目。

一、单选题1. 题目描述：某汽车展厅共展出了150辆汽车，其中的三分之一是SUV车型，四分之一是轿车车型，其余的是其他车型。

问展厅中轿车车型的数量是多少？解答与技巧：首先，计算出SUV车型的数量：150 * (1/3) = 50辆。

然后，计算出其他车型的数量：150 - 50 - 150 * (1/4) = 50辆。

所以，轿车车型的数量是50辆。

2. 题目描述：某商场举办了一次打折活动，原价100元的商品现在只需80元购买。

如果小明购买了3件该商品，他需要支付多少钱？解答与技巧：首先，计算出每件商品的折扣金额：100 - 80 = 20元。

然后，计算出小明需要支付的金额：3 * 20 = 60元。

所以，小明需要支付60元。

二、多选题1. 题目描述：以下哪些数是正整数？（A）-1（B）0（C）1（D）2解答与技巧：在SAT考试中，如果题目要求选择多个选项，我们需要仔细审题。

在这个题目中，需要选择正整数，所以选项B和A都不是正整数。

所以正确答案是（C）和（D）。

2. 题目描述：以下哪些图形具有对称性？（A）正方形（B）长方形（C）圆形（D）三角形解答与技巧：我们需要判断每个选项是否具有对称性。

在这个题目中，正方形和圆形都具有对称轴，所以正确答案是（A）和（C）。

三、填空题1. 题目描述：若a + a^-1 = 5，求a^2 + a^-2的值。

解答与技巧：首先，我们可以对等式两边进行平方操作，得到a^2+ 2 + a^(-2) = 25。

然后，我们需要解方程，将等式左边与右边的常数项进行抵消，得到a^2 + a^(-2) = 23。

2. 题目描述：某比赛共有10个选手参加，其中3个选手退出比赛，剩余的选手中将决出第一名、第二名和第三名。

sat数学试题及答案

sat数学试题及答案SAT数学试题及答案一、选择题1. 一个圆的半径是5，求这个圆的面积。

A. 25πB. 50πC. 75πD. 100π答案：B2. 如果一个数列的前三项是2, 4, 6，那么第10项是多少？A. 18B. 20C. 22D. 24答案：B3. 一个三角形的三边长分别为3, 4, 5，这个三角形是：A. 等边三角形B. 等腰三角形C. 直角三角形D. 钝角三角形答案：C二、填空题4. 一个数的平方根等于它本身，这个数是________。

答案：0或15. 如果一个函数f(x) = 3x + 5，求f(-2)的值。

答案：-16. 一个长方形的长是10厘米，宽是5厘米，求它的周长。

答案：30厘米三、简答题7. 一个圆的周长是31.4厘米，求这个圆的直径。

解：根据圆的周长公式C = πd，我们有31.4 = πd。

解得d = 31.4 / π ≈ 10厘米。

8. 一个等差数列的首项是5，公差是3，求第20项的值。

解：等差数列的通项公式为an = a1 + (n - 1)d。

将首项a1 = 5和公差d = 3代入公式，得到a20 = 5 + (20 - 1) * 3 = 5 + 57 = 62。

9. 一个直角三角形的两条直角边分别是6和8，求斜边的长度。

解：根据勾股定理，斜边c的长度等于两直角边的平方和的平方根，即c = √(6² + 8²) = √(36 + 64) = √100 = 10。

四、解答题10. 一个工厂生产了1000个零件，其中5%是次品。

如果工厂决定只出售合格的零件，那么工厂将出售多少个零件？解：首先计算次品的数量，1000 * 5% = 50个。

然后从总数中减去次品的数量，得到出售的合格零件数量：1000 - 50 = 950个。

11. 一个投资项目预计在第一年结束时产生$10,000的利润，如果每年的增长率为5%，那么第三年结束时的利润是多少？解：使用复合利息公式计算，P = P0 * (1 + r)^n，其中P0是初始利润，r是增长率，n是年数。

SAT数学试题及答案

SAT数学试题及答案本文收集了SAT数学部分的一些题目及其答案，旨在帮助考生更好地备考。

选择题1. 如果$0 \leq x \leq 3$，则不等式$|x-2| \leq 1$的解集为A) $0 \leq x \leq 3$B) $1 \leq x \leq 3$C) $1 \leq x \leq 4$D) $0 \leq x \leq 4$答案：B解析：不等式 $|x-2| \leq 1$ 表示 $x$ 到 $2$ 的距离小于等于$1$。

当 $x$ 在区间 $[1,3]$ 时，$x$ 到 $2$ 的距离都不超过 $1$，因此解集为 $1 \leq x \leq 3$。

2. 抛物线 $y=x^2-2x-3$ 的顶点坐标为A) $(0,-3)$B) $(1,-4)$C) $(2,-3)$D) $(3,0)$答案：C解析：抛物线的顶点坐标为$(\frac{-b}{2a},c-\frac{b^2}{4a})$，其中 $a$、$b$、$c$ 分别是二次项系数、一次项系数和常数项。

将$y=x^2-2x-3$ 化为标准形式，即 $y=(x-1)^2-4$，可知该抛物线的顶点坐标为 $(1,-4)$。

填空题3. 矩阵 $\begin{matrix}3 & 2 \\1 & 4\end{matrix}$ 的逆矩阵是$$\begin{pmatrix}\text{______} & \text{______} \\ \text{______} & \text{______} \end{pmatrix}$$**答案：$\begin{pmatrix}\frac{4}{5} & -\frac{2}{5} \\-\frac{1}{5} & \frac{3}{5}\end{pmatrix}$**解析：设 $\begin{pmatrix}a &b \\c & d\end{pmatrix}$ 表示该矩阵的逆矩阵，则有 $ \begin{pmatrix}3 & 2 \\1 & 4\end{pmatrix}\begin{pmatrix}a &b \\c & d\end{pmatrix}= \begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}，$ 即 $\begin{cases}3a+2c=1, \\3b+2d=0, \\a+4c=0, \\b+4d=1. \\\end{cases}$ 解得逆矩阵为 $\begin{pmatrix}\frac{4}{5} & -\frac{2}{5} \\-\frac{1}{5} & \frac{3}{5}\end{pmatrix}$。

SAT数学真题

SAT数学真题1. How long will Lucy have to wait before for her $2,500 invested at 6% earns $600 in simple interest?A. 2 yearsB. 3 yearsC. 4 yearsD. 5 yearsE. 6 years2. 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. 4B. 8C. 12D. 13E. 163. If r = 5 z then 15 z = 3 y, then r =A. yB. 2 yC. 5 yD. 10 yE. 15 y4. What is 35% of a number if 12 is 15% of a number?A. 5B. 12C. 28D. 33E. 625. A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price?A. $1800B. $1900C. $2000D. $2100E. $22006. 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. $29,250C. $32,500D. $33,800E. $33,9997. After having to pay increased income taxes this year, Edmond has to sell his BMW. Edmond bought the car for $49,000, but he sold it for a 20% loss. What did Edmond sell the car for?A. $24,200B. $28,900C. $35,600D. $37,300E. $39,2008. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?A. 0.8 daysB. 1.09 daysC. 1.23 daysD. 1.65 daysE. 1.97 days9. Find 0.12 ÷12A. 100B. 10C. 1D. 0.01E. 0.00110. Divide x5 by x2A. x25B. x10C. x7D. x3E. x2.511. Which of the following numbers could be described in the following way: an integer that is a natural, rational and whole number?A. 0B. 1C. 2.33D. -312. Find the mode of the following list of numbers: 2, 4, 6, 4, 8, 2, 9, 4, 3, 8A. 2B. 3C. 4D. 5E. 613. In the fraction 3/x, x may not be substituted by which of the following sets?A. {1, 2, 4}B. {-2,-3,-4}C. {1, 3, 7}D. {0, 10, 20}E. {1.8, 4.3}14. Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need?A. She has enough sugar.B. She needs 1/8 of a cup of sugar.C. She needs 3/80 of a cup of sugar.D. She needs 4/19 of a cup of sugar.E. She needs 1/9 of a cup of sugar.15. At a company fish fry, 1/2 in attendance are employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses?A. 10.5%B. 16.7%C. 25%D. 32.3%E. 38%16. In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; History is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a “C” in Trigonometry, a “B” in American History, an “A” in Botany, and a “B” in Microbiology?A. 2.59B. 2.86C. 3.08D. 3.3317. There are 8 ounces in a ? pound. How many ounces are in 7 3/4 lbs?A. 12 ouncesB. 86 ouncesC. 119 ouncesD. 124 ouncesE. 138 ounces18. If the value of x and y in the fraction XZ/Y are both tripled, how does the value of the fraction change?A. increases by halfB. decreases by halfC. triplesD. doublesE. remains the same19. What is the next number in the following pattern? 1, 1/2, 1/4, 1/8, ___A. 1/10B. 1/12C. 1/14D. 1/15E. 1/1620. Of the following units which would be more likely used to measure the amount of water in a bathtub?A. kilogramsB. litersC. millilitersD. centigramsE. volts21. If a match box is 0.17 feet long, what is its length in inchesthe most closely comparable to the following?A. 5 1/16 inch highlighterB. 3 1/8 inch jewelry boxC. 2 3/4 inch lipstickD. 2 3/16 inch staple removerE. 4 1/2 inch calculator22. Which of the following fractions is the equivalent of 0.5%?A. 1/20D. 1/5E. 1/50023. In the graph below, no axes or origin is shown. If point B's coordinates are (10,3), which of the following coordinates would most likely be A's?A. (17, -2)B. (10, 6)C. (6, 8)D. (-10, 3)E. (-2, -17)24. Over the course of a week, Fred spent $28.49 on lunch. What was the average cost per day?A. $4.07B. $3.57C. $6.51D. $2.93E. $5.4125. Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookies?A. degrees CelsiusB. millilitersC. quartsD. kilogramsE. cups26. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best?A. 3 4/5 feetB. 3 2/3 feetC. 3 3/8 feetD. 3 1/4 feetE. 2 1/2 feet27. After purchasing a flat screen television for $750, John realizes that he got a great deal on it and wishes to sell it for a 15% profit. What should his asking price be for the television?B. $833.60C. $842.35D. $862.50E. $970.2528. If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?A. 150/xB. 150xC. 6xD. x/6E. 1500x29. If 6 is 24% of a number, what is 40% of the same number?A. 8B. 10C. 15D. 20E. 2530. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?A. $57B. $90C. $104D. $112E. $12231. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?A. 58%B. 119%C. 158%D. 175%E. 200%32. If 8x + 5x + 2x + 4x = 114, the 5x + 3 =A. 12B. 25D. 47E. 8633. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directlynorth at 150 mph and the other travels directly west at 200 mph?A. 50 milesB. 100 milesC. 500 milesD. 700 milesE. 1,000 miles34. What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot?A. 0.9WLB. 0.3WLC. 0.1WLD. 9WLE. 3WL35. Find 8.23 x 109A. 0.00000000823B. 0.000000823C. 8.23D. 8230000000E. 82300000000036. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday?A. 345B. 1,035C. 1,725D. 3,105E. 9,31537. Which of the following has the least value?A. 0.27B. 1/4C. 3/8D. 2/11E. 11%38. How many boys attended the 1995 convention?A. 358B. 390C. 407D. 540E. 71639. Which year did the same number of boys and girls attend the conference?A. 1995B. 1996C. 1997D. 1998E. None40. Which two years did the least number of boys attend the convention?A. 1995 and 1996B. 1995 and 1998C. 1996 and 1997D. 1997 and 1994E. 1997 and 1998答案:Answer Key1. C2. D3. A4. C5. C6. B7. E8. B9. D10. D11. B12. C13. D14. C15. B16. C17. D18. E19. E20. B21. D22. B23. C24. A25. E26. C27. D28. A29. B30. B31. A32. C33. C34. A35. D36. E37. E38. A39. A40. A。

2024 SAT考试数学历年题目精粹

2024 SAT考试数学历年题目精粹SAT考试是许多学生考入大学的重要考试之一，其中数学部分是考生需要面对的一项挑战。

为了帮助考生更好地备考SAT数学，本文将精选并解析2024年SAT考试数学部分的历年题目，以供参考。

第一部分：选择题题目1：一个矩形的宽度是它的长度的一半，若该矩形的面积为12，求其周长是多少？A. 12B. 14C. 16D. 18解析：设矩形的长度为l，则宽度为l/2。

根据面积的定义，我们可以列出方程l*(l/2)=12。

解方程得到l=4。

根据周长的计算公式，周长为2*l+2*(l/2)=14，选项B为正确答案。

题目2：若函数f(x)定义为f(x)=3x+1，求f(f(2))的值。

A. 9B. 10C. 11D. 12解析：由题意可知，f(2)=3*2+1=7。

将7代入函数f(x)，得到f(f(2))=f(7)=3*7+1=22。

选项D为正确答案。

题目3：已知一个等差数列的公差为3，前两个数的和为10，求这个等差数列的第n个数。

A. 3n-1B. 3n-2C. 3n-3D. 3n-4解析：设等差数列的首项为a，第n个数为an。

根据题意可得到方程a+(a+3)=10，解得a=3。

利用等差数列的通项公式an=a+(n-1)d，代入公差d=3和首项a=3，得到an=3+3(n-1)=3n。

选项A为正确答案。

第二部分：填空题题目1：若a为正整数，满足2a+5=11，则a的值为____________。

解析：将已知条件代入方程，得到2a+5=11，解得a=3。

填入空格中为3。

题目2：一个矩形的面积为25，其中宽度为5，长度为_________。

解析：设矩形的长度为l，则根据面积的定义可得到方程5l=25，解得l=5。

填入空格中为5。

第三部分：解答题题目：一辆汽车以40 mph的速度行驶了3小时，另一辆汽车以50 mph的速度行驶了t小时。

若两辆汽车行驶的距离相同，求t的值。

解析：汽车行驶的距离等于速度乘以时间，可以列出方程40*3=50*t，解得t=2.4。

美国高考sat数学试题及答案

美国高考sat数学试题及答案美国高考SAT数学试题及答案1. 某商店进行促销活动，所有商品打8折。

如果一件商品原价为$50，那么打折后的价格是多少？A. $40B. $45C. $35D. $20答案：B2. 一个长方形的长是宽的两倍，如果宽为$x$，那么长方形的周长是多少？A. $6x$B. $4x$C. $2x$D. $8x$答案：A3. 如果一个数的平方等于36，那么这个数是多少？A. 6B. -6C. 6 或 -6D. 0答案：C4. 在一次数学测试中，平均分是75分。

如果一个学生得了80分，那么他的分数比平均分高了多少？A. 5分B. 10分C. 15分D. 20分答案：A5. 一个圆的半径是5厘米，那么这个圆的面积是多少平方厘米？A. 25πB. 50πC. 75πD. 100π答案：B6. 如果一个函数$f(x) = 2x + 3$，那么$f(-1)$的值是多少？A. -1B. 1C. 5D. 7答案：B7. 一个等差数列的首项是3，公差是2，那么这个数列的第10项是多少？A. 23B. 21C. 19D. 17答案：A8. 如果一个三角形的两边长分别是5和7，且这两边夹角是90度，那么这个三角形的面积是多少？A. 12.5B. 15C. 17.5D. 20答案：A9. 如果一个函数$g(x) = x^2 - 4x + 3$，那么这个函数的最小值是多少？A. -1B. 0C. 1D. 3答案：A10. 在一个装有红球和蓝球的袋子里，红球和蓝球的比例是2:3。

如果随机抽取一个球，抽到红球的概率是多少？A. 2/5B. 3/5C. 4/5D. 1/2答案：A结束语：以上是美国高考SAT数学部分的试题及答案，希望对准备参加SAT考试的学生有所帮助。

2023年SAT数学复习题集及参考答案

2023年SAT数学复习题集及参考答案一、选择题1. 下列哪个数是2的幂次方？A) 5B) 8C) 12D) 15答案：B2. 以点(2, 3)为圆心，边长为4的正方形的一个顶点是点(6, 7)，求该正方形的面积是多少。

A) 6B) 8C) 12D) 16答案：C3. 若a + b = 7，且a - b = 3，则a的值是多少？A) 2B) 3C) 4D) 5答案：D4. 若x² + 4x + 3 = 0，则x的解是什么？A) -1, -3B) -1, 3C) 1, -3D) 1, 3答案：A5. 已知三角形的两条边长分别为5和8，夹角为60°，求第三条边的长是多少？A) 7B) 9C) 10D) 12答案：C二、填空题1. 若f(x) = 2x² - 5x + 3，求f(-1)的值为多少？答案：102. 一辆汽车以每小时60英里的速度行驶，行驶4小时后，总共行驶的路程是多少英里？答案：2403. 若sin²θ + cos²θ = 1，求sin60°的值。

答案：√3/24. 若a:b = 3:4，且b:c = 5:6，求a:c的比值。

答案：9:105. 设直线y = 2x + 3与y = -x + 5交于点P，求点P的坐标。

答案：(1, 5)三、解答题1. 计算下列方程的解：2x + 5 = 3x - 4解答：将方程两边的x合并，得：2x - 3x = -4 - 5化简得：-x = -9将方程两边的x系数变为1，得：x = 9因此，方程的解为x = 9。

2. 已知正方形的面积是64平方单位，求其周长。

解答：设正方形的边长为x，则由已知面积可得：x² = 64解方程得：x = √64 = 8正方形的周长等于4倍边长，故周长为4 * 8 = 32。

因此，正方形的周长为32单位。

3. 某商店原价出售一件衣服，后来进行7折的打折活动，最终售价为315元。

(完整版)sat数学考试试题(可编辑修改word版)

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 radiiof 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 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 ofthe 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 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第11 页共11 页。

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学真题精选

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 adormitory. There are 200 seniors, 300 juniors, a nd 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, 1times. 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, x²would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x) = 0, x² would 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 than1 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?C. 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 + 5 + B = 14, and B = 8. A + C + B + D = 13 + 8 + 1 = 224. 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 1B. 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. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11, but anywhere in between is possible.2. √5 percent of 5√5 =A. 0.05B. 0.25C. 0.5D. 2.5E. 25Correct Answer: B解析:We can write the state ment mathematically, using x to mean ‘of’ and /100 for ‘per cent’. So ( √5/100) x 5√5 = 5 x 5 /100 = 0.253. If pqr = 1 , rst = 0 , and spr = 0, which of the following must be zero?A. PB. QC. RD. SE. TCorrect Answer: D解析:If pqr = 1, none of these variable can be zero. Since spr = 0 , and since p and r are not zero, s must be zero. (Note that although rst = 0, and so either s or t must be zero, this is not sufficient to state which must be zero)4.A. 1/5B. 6/5C. 6³D. 64 / 5E. 64Correct Answer: E解析:65 = 64x 6(64 x 6) - 64 = 64(6 - 1) = 64 x 5 Now, dividing by 5 will give us 645. -20 , -16 , -12 , -8 ....In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence?A. 0B. 200C. 440D. 668E. 762Correct Answer: E解析:All terms in the sequence will be multiples of 4. 762 is not a multiple of 4SAT考试数学练习题㈢1. Which of the following could be a value of x, in the diagram above?A. 10B. 20C. 40D. 50E. any of the above2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?A. 10B. 15C. 20D. 25E. 303. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?A. 5 : 1B. 10 : 5C. 15 : 2D. 20 : 24. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?A. 2.5πB. 3πC. 5πD. 4πE. 10π5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?A. 4B. 7C. 8D. 12E. it cannot be determined from the information given.SAT考试数学练习题㈣1. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?A. f(-1)B. f(0)C. f(1)D. f(3)E. f(4)2. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?A. 2.25B. 3C. 4D. 4.5E. 63. If n ≠ 0, which of the following must be greater than n?II n²III 2 - nA. I onlyB. II onlyC. I and II onlyD. II and III onlyE. None4. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?A. 20B. 15C. 8D. 5E. 3.25. n and p are integers greater than 15n is the square of a number75np is the cube of a number.The smallest value for n + p isA. 14B. 18C. 20D. 30E. 50SAT考试数学练习题㈤1. If a² = 12, then a4 =A. 144B. 72C. 36D. 24E. 16Correct Answer: A解析:a4 = a2 x a2 = 12 x 12 = 1442. If n is even, which of the following cannot be odd?I n + 3II 3nIII n² - 1A. I onlyB. II onlyD. I and II onlyE. I, II and IIICorrect Answer: B解析:In case I , even plus odd will give odd. In case II, odd times even will give even. In case III even squared is even, and even minus odd is odd. (You can check this by using an easy even number like 2 in place of n). Only case II cannot be odd.3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?I 24II 20III 5A. I onlyB. II onlyC. III onlyD. II and III onlyE. I, II and IIICorrect Answer: D解析:The maximum area of the triangle will come when the given sides are placed at right angles. If we take 8 as the base and 5 as the height the area = ½ x 8 x 5 = 20. We can alter the angle between the sides to make it less or more than 90, but this will only reduce the area. (Draw it out for yourself). Hence the area can be anything less than or equal to 20.4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?A. 12B. 11C. 10D. 9E. 8Correct Answer: E解析:Food consumed per day = 39/6. In the remaining days it will consume 91 - 39 pounds = 52 pounds. Now divide the food by the daily consumption to find the number of days. 52 / (39/6) = 52 x (6 / 39) = 85. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?A. 8pB. pqC. pq + 27D. -pE. (p - q)6Correct Answer: C解析:A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5. Consider the answer choices in turn. 8 is the cube of 2, and p is a cube, and so the product will also be a cube. pq will also be a cube as shown above.pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube. -p will be a cube. Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).SAT考试数学练习题㈥1. What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)?A. 3B. √31C. √41D. 7E. 9Correct Answer: C解析:Sketch a diagram and calculate the distance (hypotenuse of a right triangle) using Pythagoras theorem.Vertical hei ght of triangle = 5 ; horizontal side = 4 ; hypotenuse = √(25 + 16) = √412. n is an integer chosen at random from the set{5, 7, 9, 11 }p is chosen at random from the set{2, 6, 10, 14, 18}What is the probability that n + p = 23 ?A. 0.1B. 0.2C. 0.25D. 0.3Correct Answer: A解析:Each of the integers in the first set could be combined with any from the second set, giving a total of 4 x 5 = 20 possible pairs. Of these the combinations that could give a sum of 23 are (5 + 18), and (9 + 14). This means that the probability of getting a sum of 23 is 2/20 = 1/103. A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?A. 0.75DB. 0.76DC. 0.765DD. 0.775DE. 0.805DCorrect Answer: C解析:If the price is reduced by 15 %, then the new price will be 0.85D. If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D4. All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?A. 2B. 2√2C. 3D. √10E. √20Correct Answer: E解析:The longest line segment that can be drawn without passing through any dots other than those at the beginning and end of the segment, such a line could go from the middle dot in the top row to either the bottom left or right dot. In any case the segment will be the hypotenuse of a right triangle with sides 2 and 4. Using Pythagoras theorem the hypotenuse will be √(2 ² + 4 ² ) = √205. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?A. 9B. 10C. 11D. 12E. 13Correct Answer: D解析:If the radius is 7, the circumference = 14π. The length of the arc is 100/360 of the circumference. Taking π as 22/7 we get. (100 x 14 x 22) / (360 x 7) which reduces to 440/ 36 = 12.22 (i.e. approx. 12)SAT数学重要公式14个SAT数学考试并不需要考生记忆数学公式，对于一些常用的简单公式都会列在试卷的前面。

sat数学试题及答案

sat数学试题及答案1. 题目：解下列方程求x的值：$2x - 5 = 3x + 1$。

答案：首先将方程中的x项移到同一边，得到$2x - 3x = 1 + 5$，简化后得到$-x = 6$。

然后将系数化为1，得到$x = -6$。

2. 题目：计算下列表达式的值：$\frac{3}{4} \times\frac{8}{9}$。

答案：将分子相乘得到$3 \times 8 = 24$，分母相乘得到$4\times 9 = 36$，所以表达式的值为$\frac{24}{36}$。

化简分数得到$\frac{2}{3}$。

3. 题目：一个矩形的长是宽的两倍，如果宽是5单位，那么矩形的周长是多少？答案：矩形的长是宽的两倍，所以长为$5 \times 2 = 10$单位。

矩形的周长是$2 \times (\text{长} + \text{宽}) = 2 \times (10 + 5) = 2 \times 15 = 30$单位。

4. 题目：如果一个数的平方是25，那么这个数是多少？答案：设这个数为$x$，则有$x^2 = 25$。

解这个方程，我们得到$x = \pm 5$。

所以这个数可以是5或者-5。

5. 题目：计算下列多项式的乘积：$(x + 3)(x - 2)$。

答案：使用分配律，我们得到$x(x - 2) + 3(x - 2) = x^2 - 2x +3x - 6$。

合并同类项，得到$x^2 + x - 6$。

6. 题目：一个圆的半径是4厘米，求这个圆的面积。

答案：圆的面积公式是$A = \pi r^2$，其中$r$是半径。

将半径4厘米代入公式，得到$A = \pi \times 4^2 = 16\pi$平方厘米。

7. 题目：如果一个函数$f(x) = 2x + 3$，求$f(-1)$的值。

答案：将$x = -1$代入函数$f(x)$，得到$f(-1) = 2(-1) + 3 = -2 + 3 = 1$。

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。