SAT数学历年真题精选1

美国“高考”SAT考试的数学题

美国“高考”SAT考试的数学题数学第一部分时间（25分钟）16个问题说明：这部分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佳答案，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。

所有图表都是比较准确的，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、If 4(t+u) + 3 =19, then t+u=如果4(t+u) + 3 =19, 那么t+u=A 3B 4C 5D 6E 72、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？A 60B 65C 70D 75E 853、如果玛丽开车行驶n 英里用了t 小时，那么下列哪个可以表示她行驶的平均速度，英里/小时？A n/tB t/nC 1/ntD ntE n²t4、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？A 3bB a+3C 2(a+b)D a+2bE 2a+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？A 1B 1/2C tD t+1/2E 2t8、对于任何数x 和y,假设x△y=x²+xy+y²,那么（3△1）△1等于多少？A 5B 13C 27D 170E 1839、摩根的植物在一年之内从42厘米长到57厘米。

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。

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。

SAT数学真题精选

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 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 bea value of f(x)? I 6 II 0 III -6 A. I only B. I and II only C. II and III only D. I and III only E. I, II and III Correct 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, 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 than 1 and less than 200? A. 48 B. 49 C. 50 D. 51 E. 52 Correct 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 50 3. 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. 23 B. 22 C. 18 D. 16 E. 14 Correct 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 = 22 4. 12 litres of water a poured into an aquarium of dimensions50cm length , 30cm breadth, and 40 cm height. How high (in cm) will the water rise? (1 litre = 1000cm³) A. 6 B. 8 C. 10 D. 20 E. 40 Correct 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 = 8 5. 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 + 6 B. P/11 +6 C. 17 - P/6 D. 17/P E. 11.5P Correct 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 fromB. Which of the following could be the distance from A to C? I 11 II 1 III 7 A. I only B. II only C. I and II only D. II and III only E. 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. 0.05 B. 0.25 C. 0.5 D. 2.5 E. 25 Correct Answer: B 解析: We can write the statement mathematically, using x to mean ‘of’and /100 for ‘per cent’. So ( √5/100) x 5√5 = 5 x 5 /100 = 0.25 3. If pqr = 1 , rst = 0 , and spr = 0, which of the following must be zero? A. P B. Q C. R D. S E. T Correct 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. 1/5 B. 6/5 C. 6³ D. 64 / 5 E. 64 Correct Answer: E 解析: 65 = 64x 6 (64 x 6) - 64 = 64(6 - 1) = 64 x 5 Now, dividing by 5 will give us 64 5. -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. 0 B. 200 C. 440 D. 668 E. 762 Correct 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. 10 B. 20 C. 40 D. 50 E. any of the above 2. 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 areneeded. How many helpers are required? A. 10 B. 15 C. 20 D. 25 E. 30 3. 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 : 1 B. 10 : 5 C. 15 : 2 D. 20 : 2 E. 25 : 2 4. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle? A. 2.5π B. 3π C. 5π D. 4π E. 10π 5. 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. 4 B. 7 C. 8 D. 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) 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. 2.25 B. 3 C. 4 D. 4.5 E. 6 3. If n ≠ 0, which of the following must be greater than n? I 2n II n² III 2 - n A. I only B. II only C. I and II only D. II and III only E. None 4. 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. 20 B. 15 C. 8 D. 5 5. n and p are integers greater than 1 5n is the square of a number 75np is the cube of a number. The smallest value for n + p is A. 14 B. 18 C. 20 D. 30 E. 50SAT考试数学练习题㈤　1. If a² = 12, then a4 = A. 144 B. 72 C. 36 D. 24 E. 16 Correct Answer: A 解析: a4 = a2 x a2 = 12 x 12 = 144 2. If n is even, which of the following cannot be odd? I n + 3 II 3n III n² - 1 A. I only B. II only C. III only D. I and II only E. I, II and III Correct 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 haslength 5. Which of the following could be the area of the triangle? I 24 II 20 III 5 A. I only B. II only C. III only D. II and III only E. I, II and III Correct 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. 12 B. 11 C. 10 D. 9 E. 8 Correct 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) = 8 5. 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. 8p B. pq C. pq + 27 D. -p E. (p - q)6 Correct Answer: C 解析:A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 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. 3 B. √31 C. √41 D. 7 E. 9 Correct Answer: C 解析: Sketch a diagram and calculate the distance (hypotenuse of a right triangle) using Pythagoras theorem. Vertical height of triangle = 5 ; horizontal side = 4 ; hypotenuse =√(25 + 16) = √41 2. 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. 0.1 B. 0.2 C. 0.25 D. 0.3 E. 0.4 Correct 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 = 1/10 3. 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. 0.75D B. 0.76D C. 0.765D D. 0.775D E. 0.805D Correct 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 = 0.765D 4. 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. 2 B. 2√2 C. 3 D. √10 E. √20 Correct 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 ) = √20 5. 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. 9 B. 10 C. 11 D. 12 E. 13 Correct 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数学测验试题

8. 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)1/2(B)-1/2(C)5/2(D)-5/2(E)2
Question #5: Which value of x satisfies the inequality | 2x | < x + 1 ?
(A)-1/2(B)1/2(C)1(D)-1(E)2
Question #6: If in2, how many (m, n) pairs satisfy the inequality mn< 100?
(A) y = -1/2 x
(B) y = -1/2 x + 1
(C) y = - x
(D) y = - x + 2
(E) y = -2x
4. If K is divisible by 2,3, and 15, which of the following is also divisible by these numbers?

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。

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; andeach 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) 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) -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)1/36Question #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 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 couldbe 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). 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 absolute values of the differencesbetween 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 a quadrilateral.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. The midpointsof 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。

SAT数学卷子

SAT数学卷⼦1、If 5252+=+x x ,then x can equal which of the following? ( ) (A) 51(B) 54(C) 1(D) 25(E) 5 2、,962-=+x x If what is the value of 34-x ?( )(A)-5(B)-9(C) -15(D) -18(E) -213、,1455==tk and t If what is the value of k ?( ) (A)451(B)91(C) 51(D) 5(E) 9 4、The average of x and y is 5 and the average of y x ,,and z is 8.What is the value of z ?( )(A) 19(B) 14(C) 13(D) 11(E) 35、If ,8212-=x xwhat is the value of x ?( )(A) 2(B) 3(C) 4(D) 5(E) 66、In the xy -plane,the equation of line l is 52+=x y .If line m is the reflection of line l in the axis x -,what is the equation of line m ?( )(A) 52--=x y (B) 52+-=x y (C)52-=x y (D)521--=x y (E)521+-=x y 7、If ()s x a =++12,what is 1+x ,in terms of s and a ? ( ) (A) a s 2(B) 2a s -(C) 2a s +(D) a s -2(E) a s +28、If ,12325+==+y x and x y what is the value of y ?9、Let the operation *and ? be defined for all real numbers a and b as follows: b a b a b a b a 4*,3+=+=? ?,4*)5()5(4y of value the is what y y IF =?1、If 32=y x ,what is the value of y x 23?( ) (A) 31 (B) 32 (C) 1 (D) 23 (E) 492、If1624=x ,then =x ( ) (A) 1 (B) 2 (C) 4 (D) 8 (E) 123、 How much greater than 2-r is 5+r ? ( )(A) 2 (B) 3 (C) 5 (D) 6 (E) 74、?75,4273n of is what is n of IF ( ) (A)70 (B) 45 (C) 30 (D) 185、If and y x 7322=+24=xy ,what is the value of ()2y x +? ( ) (A) 73 (B) 97 (C) 100 (D) 121 (E) 1446、If ,1,52+-x x and 83-x are all integers and 1+x is the median of these integers, which of the following could be a value for x ( )(A) 5 (B) 7 (C) 9 (D) 10 (E) 117、If 02<<y x="" ,which="" of="" the="" following="" is="" greatest="" ?="" (="" )<="" p="" bdsfid="89">。