sat数学试题.doc

SAT数学题分成了选择题和计算题，相对于SAT数学选择题，答案还有一些提示的作用，SAT数学计算题就需要大家自己进行解答了。下面为大家推荐的这道SAT数学计算题是非常典型的代数方程类的题目，大家一起来看看吧。What value ofsatisfies both of the equations above?The correct answer is1/2 or .5ExplanationDifficulty: MediumSince, the value ofis eitheror.ORThe two values ofthat satisfy the first equation areand.Since, the value ofis eitheror.ORThe two values ofthat satisfy the second equation areand.You are asked to find the value ofthat satisfies both equations. That value is. The answer can be entered in the grid asor.下面是两道SAT数学练习题，都是选择题，后面附有答案及其解析。SAT数学练习题可以让大家更快更好的了解SAT数学考试的出题方式以及应对方式。下面是详细内容，我们一起来看一下这些SAT数学练习题的吧。1、 Cone A has volume 24. When its radius and height are multiplied by the same factor, the cones surface area doubles. What is Cone As new volume?(A)(B)48(C)(D)96(E)Not enough information to tell2、 Arectangle stands so that its 6 inch side lies flat against the ground. If the rectangle is rotated around the axis of one of its two 4 inch sides, what is the volume of the resulting cylinder?(A)24(B)36(C)64(D)96(D)144Answers1、 CThe formula for a cones surface area is r2 + rl. A cones volume is 1/ 3r2h. So if the dimensions of a cone are multiplied by the same factor, a,then its surface area multiplies by the square of that factor. If the dimensions of a cone are multiplied by the same factor, the volume becomes multiplied by the cube of that factor:In general, for solids, if each dimension of a cone is multiplied by the same factor, the solids surface area is multiplied by the square of that factor, and its volume increases by the cube of that factor. If the surface area of Cone A doubles, its dimensions are multiplied by a factor ofThus, the cones volume is multiplied by a factor ofCone As new volume is2、 EIf the rectangle is rotated about a side of length 4, then the height of the cylinder will be 4 and the radius will be 6.Once you visualize the cylinder, you can plug in the values for the volume of a cylinder:一道SAT数学题(抛物线)天道留学时间：2011-08-26点击：26次下面是一道关于抛物线的SAT数学题及其解法的内容，非常详细。SAT题中，抛物线是必考的一类，虽然中学课程都有所涉及，还是相对比较抽象，尤其是在理解SAT数学题的表达方式上。下面我们来看看这道关于抛物线的SAT数学题吧。 Read the following SAT test question and then click on a button to select your answer.The quadratic functionis graphed in the-plane above. Iffor all values of, which of the following could be the coordinates of point?Answer Choices(A)(B)(C)(D)(E)The correct answer is CExplanationThe fact thatfor all values ofmeans that the pointis the maximum of the quadratic function, somust be the vertex of the parabola. The parabola intersects the-axis at the pointsand, somust be halfway betweenand. Therefore,. Of the choices, the only one with-coordinate equal tois. Therefore,could be the coordinates of point.1. 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 height of triangle = 5 ; horizontal side = 4 ; hypotenuse = (25 + 16) = 412. n is an integer chosen at random from the set5, 7, 9, 11 p is chosen at random from the set2, 6, 10, 14, 18What is the probability that n + p = 23 ?A. 0.1B. 0.2C. 0.25D. 0.3E. 0.4Correct 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. 22C. 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 + 4 ) = 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 = 14. The length of the arc is 100/360 of the circumference. Taking as 22/7 we get. (100 x 14 x 22) / (360 x 7) which reduces to 440/ 36 = 12.22 (i.e. approx. 12)1、At Central High School, the math club hasmembers and the chess club hasmembers. If a total ofstudents belong to only one of the two clubs, how many students belong to both clubs?Answer Choices(A)(B)(C) (D)(E)The correct answer is CExplanationLetstand for the number of students who belong to both clubs. Themembers of the math club can be broken down into two groups: those who are in both clubs (there arestudents in this category) and those who are in the math club only (there arestudents in this category).Themembers of the chess club can also be broken down into two groups:students who are in both clubs andstudents who are in the chess club only.Since a total ofstudents belong to only one of the two clubs, you know that. Solving this equation gives, sostudents belong to both clubs。2、Ifis divisible by, and, which of the following is also divisible by these numbers?Answer Choices(A)(B)(C)(D)(E)The correct answer is DExplanationSinceis divisible by, and,must be a multiple of, asis the least common multiple of, and. Some multiples ofare, and.If you add two multiples of, the sum will also be a multiple of. For example,andare multiples ofand their sum, is also a multiple of.If you add a multiple ofto a number that is not a multiple of, the sum will not be a multiple of. For example,is a multiple ofandis not. Their sum, is not a multiple of.The question asks which answer choice is divisible by, and; that is, which answer choice is a multiple of. All the answer choices are in the form of plus a number. Only choice (D), hasadded to a multiple of. The sum ofandis also a multiple of, so the correct answer is choice (D).3、In ansolution of water and alcohol, the ratio by mass of water to alcohol isto. Ifgrams of a solution consisting ofgrams water for each gram of alcohol is added to thesolution, what fraction by mass of the new solution is alcohol?Answer Choices(A)(B)(C)(D)(E)The correct answer is BExplanationTo find what fraction by mass of the new solution is alcohol, you can find how many grams of alcohol are in the final solution ofgrams. Since thesolution ispart alcohol toparts water, it isalcohol. So it containsgrams of alcohol. Similarly, thesolution isalcohol by mass, so it containsgrams of alcohol. Thus, the final 20-gram solution containsgrams of alcohol, so, or, of it is alcohol.1. Of the following, which is greater than ?A. 2/5B. 4/7C. 4/9D. 5/11E. 6/132. If an object travels at five feet per second, how many feet does it travel in one hour?A. 30B. 300C. 720D. 1800E. 180003. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?A. 90B. 95C. 100D. 105E. 1104. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?A. 48B. 32C. 24D. 18E. 125. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both French and German. How many students are not enrolled in either course?A. 6B. 15C. 24D. 33E. 541.Correct Answer: BExplanation:One way to deal with fractions is to convert them all to decimals. (Using your calculator, divide the numerator by the denominator).In this case all you would need to do is to see which is greater than 0.5.Otherwise to see which is greater than ?, double the numerator and see if the result is greater than the denominator. In B, the correct answer, doubling the numerator gives us 8, which is bigger than 7.2.Correct Answer: EExplanation:If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour. Answer = 18000 (E)3.Correct Answer: CExplanation:You could add up all the multiples of 10 (10 + 20 + 30 .+190), and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers is equal to the value of the middle term (or the average of the two middle terms if there are an even number of terms). The middle term out of 19 is the tenth term in the series = 100.4.Correct Answer: AExplanation:If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.5.Correct Answer: CExplanation:You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither78 = (41-9) + (22-9) + 9 + neither.Not enrolled students = 24练习一下吧，不是很难。1. What is the sum of all the positive integer factors of 12 ?2. The average IQ of 4 people is 110. If three people each have an IQ of 105, what is the IQ of the fourth person ?3. Of 60 students in a class 2/3 are girls, and 2/5 of the class are taking music lessons. What is the maximum number of girls that are not taking music lessons?4. If 2 n + 1 = 8, what is the value of n ?5. In a certain game of 50 questions, the final score is calculated by subtracting twice the number of wrong answers from the total number of correct answers. If a player attempted all questions and received a final score of 35, how many wrong answers did he give?6. Family 1 comprising mother, father and son are to be seated at a table with family 2 comprising mother, father and daughter. The layout of the table is shown in the diagram. F represents one of the fathers and M represents one of the mothers. X represents any family member but with the condition that a male family member must sit opposite a female of the other family. How many different seating plans are possible?1. 145 300 610 1230In the above sequence every term after the first is formed by multiplying by x and then adding y, where x and y are positive integers. What is the value of x + y?2. A confectioner has 500 mint, 500 orange and 500 strawberry flavored sweets. He wishes to make packets containing 10 mint, 5 orange and 5 strawberry sweets. What is the maximum number of packets of this type he can make?3. If S is the sum of 8,6,4,2 and x, what must be the value of x for x to equal 1/5 S ?4. 25 per cent of 600 is equal to 15 per cent of what number?5. What is the maximum number of points of intersection of four distinct lines in a plane?6. If one edge of a 6-inch ruler is to be marked in 1/10 inch units, how many marks will there be on the edge including the 0 and 6 inch marks?7. If the area of the right triangle above is 72, what is the value of x?8. Given that the sum of the odd integers from 1 to 99 inclusive is 2500, what is the sum of the even integers from 2 to 100 inclusive?The projected sales volume of a video game cartridge is given by the functionwhereis the number of cartridges sold, in thousands;is the price per cartridge, in dollars; andis a constant. If according to the projections,cartridges are sold atper cartridge, how many cartridges will be sold atper cartridge?Answer Choices(A)(B)(C)(D)(E)The correct answer is CExplanationDifficulty: MediumForcartridges sold atper cartridge,(sinceis the number of cartridges sold, in thousands) and. Substituting into the equation yields.Solving this equation foryields.Sinceis a constant, the function can be written as. To determine how many cartridges will be sold atper cartridge, you need to evaluate. Sinceis given in thousands, there will becartridges sold atper cartridge.A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There areseniors,juniors, andsophomores who applied. Each seniors name is placed in the lotterytimes; each juniors name,times; and each sophomores name,time. What is the probability that a seniors name will be chosen?Answer Choices(A)(B)(C)(D)(E)The correct answer is DExplanationDifficulty: HardTo determine the probability that a seniors name will be chosen, you must determine the total number of seniors names that are in the lottery and divide this number by the total number of names in the lottery. Since each seniors name is placed in the lotterytimes, there areseniors names. Likewise, there arejuniors names andsophomores names in the lottery. The probability that a seniors name will be chosen is.Which of the following inequalities is graphed below?(A)y 2x 2(B)y 2x 2(C)y x 2(D)y x 2Correct Choice：AExplanation：The slope of the line pictured is 126 = 2. The y-intercept of the line pictured is 2. So the equation of the line pictured is y = 2x 2. This leaves three choices. The line in the picture is dotted; this means that the inequality is either , not or . Now we have two choices left.Because the region to the right and above is shaded, is the correct inequality, but just to make sure, plug in a point or two. In this case, try the origin, (0,0). It is in the shaded region, and must therefore satisfy the inequality. Which inequality does is satisfy? It satisfies y 2x 2, so this is the correct choice.1. The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance from A to C?I 11II 1III 7A. I onlyB. II onlyC. I and II onlyD. II and III onlyE. I, II, or III.Correct Answer: E解析:Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. 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 55 =A. 0.05B. 0.25C. 0.5D. 2.5E. 25Correct Answer: B解析:We can write the statement mathematically, using x to mean of and /100 for per cent. So ( 5/100) x 55 = 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:4.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)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 4。Mathematics Standard Multiple ChoiceRead the following SAT test question and then click on a button to select your answer.If the length and width of rectanglearepercent less andpercent less, respectively, than the length and width of rectangle, the area ofis equal to what percent of the area of?Answer Choices(A)(B)(C)(D)(E)The correct answer is AExplanationLetandrepresent the length and width, respectively, of rectangle. Thenandrepresent the length and width, respectively, of rectangle. Simplifyingandgivesandfor the length and width, respectively, of rectangle. The area of rectangleis. The area of rectangleis, or. Therefore, the area of rectangleispercent of the area of rectangle下面为大家提供一些和这些SAT官方每日一题相似的题目，供大家练习： In the xy-coordinate (坐