sat2 math level2

合集下载

SAT 2 数学2 college board官网全部原题加答案讲解 SAT Subject Test Math Level 2

SAT Subject Test Practice - Results Summary Mathematics Level 21Your answer Omitted!What is the distance in space between the points with coordinates and ?(A)(B)(C)(D)(E)ExplanationDifficulty: EasyThe correct answer is D.The distance between the points with coordinates and is given by the distance formula: .Therefore, the distance between the points with coordinates and is:,which simplifies to .2Your answer Omitted!If , what value does approach as gets infinitely larger?(A)(B)(C)(D)(E)ExplanationDifficulty: EasyThe correct answer is E.One way to determine the value that approaches as gets infinitely larger is to rewrite the definition of the function to use only negative powers of and then reason about the behavior of negative powers of as gets infinitely larger. Since the question is only concerned with what happens to as gets infinitely larger, one can assume that is positive. For , theexpression is equivalent to the expression . As gets infinitely larger, the expression approaches the value , so as gets infinitely larger, the expression approaches the value . Thus, as gets infinitely larger, approaches .Alternatively, one can use a graphing calculator to estimate the height of the horizontal asymptote for the function . Graph the function on an interval with “large”, say, from to .By examining the graph, the all seem very close to . Graph the function again, from, say, to .The vary even less from . In fact, to the scale of the coordinate plane shown, the graph of the function is nearly indistinguishable from the asymptotic line . This suggests that as gets infinitely larger, approaches , that is, .Note: The algebraic method is preferable, as it provides a proof that guarantees that the value approaches is . Although the graphical method worked in this case, it does not provide a complete justification; for example, the graphical method does not ensure that the graph resembles a horizontal line for “very large”such as .3Your answer Omitted!If is a factor of , then(A)(B)(C)(D)(E)ExplanationDifficulty: EasyThe correct answer is A.By the Factor Theorem, is a factor of only when is a root ofthat is, , which simplifies to . Therefore, .Alternatively, one can perform the division of by and then find a value for so that the remainder of the division is .Since the remainder is , the value of must satisfy . Therefore, .4Your answer Omitted!Alison deposits into a new savings account that earns percent interest compounded annually. If Alison makes no additional deposits or withdrawals, how many years will it take for the amount in the account to double?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumAfter year, the amount in the account is equal to . After years, the amount isequal to , and so on. After years, the amount is equal to . You needto find the value of for which . There are several ways to solve this equation. You can use logarithms to solve the equation as follows.Since , it will take more than years for the amount in the account to double. Thus, you need to round up to .Another way to find is to use your graphing calculator to graph and . From the answer choices, you know you need to set the viewing window with values from to about and values extending just beyond . The of the point of intersection is approximately . Thus you need to round up to .5Your answer Omitted!In the figure above, when is subtracted from , what is the length of the resultant vector?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe resultant of can be determined by . The length of the resultant is:6Your answer Omitted!In the -plane, what is the area of a triangle whose vertices are , , and ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumIt is helpful to draw a sketch of the triangle:The length of the base of the triangle is and the height of the triangle is . Therefore, the area of the triangle is . The correct answer is B.7Your answer Omitted!A right circular cylinder has radius and height . If and are two points on its surface, what is the maximum possible straight-line distance between and ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe maximum possible distance occurs when and are on the circumference of opposite bases: You can use the Pythagorean Theorem:The correct answer is (B).8Your answer Omitted!Note: Figure not drawn to scale.In the figure above, and the measure of is . What is the value of ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThere are several ways to solve this problem. One way is to use the law of sines. Since ,the measure of is and the measure of is . Thus, and . (Make sure your calculator is in degree mode.)You can also use the law of cosines:Since is isosceles, you can draw the altitude to the triangle.9Your answer Omitted!The function is defined by for .What is the difference between the maximum and minimum values of ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumIt is necessary to use your graphing calculator for this question. First graph the function. It is helpful to resize the viewing window so the -values go fromto . On this interval the maximum value of is and the minimum value of is. The difference between these two values is , which rounds to .10Your answer Omitted!Suppose the graph of is translated units left and unit up. If the resulting graph represents , what is the value of ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumIt may be helpful to draw a graph of and .The equation for is . Therefore,. The correct answer is B.11Your answer Omitted!A sequence is recursively defined by , for . If and , what is the value of ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe values for and are given. is equal to . is equal to. is equal to . is equal to.If your graphing calculator has a sequence mode, you can define the sequence recursively and findthe value of . Let , since the first term is . Define . Let , since we have to define the first two terms and . Then examining a graph or table, you can find .12Your answer Omitted!The diameter and height of a right circular cylinder are equal. If the volume of the cylinder is , what is the height of the cylinder?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe correct answer is A.To determine the height of the cylinder, first express the diameter of the cylinder in terms of theheight, and then express the height in terms of the volume of the cylinder.The volume of a right circular cylinder is given by , where is the radius of the circular base of the cylinder and is the height of the cylinder. Since the diameter and height are equal, . Thus . Substitute the expression for in the volume formula to eliminate :. Solving for gives . Since the volume of the cylinder is , theheight of the cylinder is .13Your answer Omitted!If ,then(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe correct answer is E.One way to determine the value of is to apply the sine of difference of two angles identity: . Since and , the identity gives . Therefore, .Another way to determine the value of is to apply the supplementary angle trigonometric identity for the sine: . Therefore, .14Your answer Omitted!A line has parametric equations and , where is the parameter. The slope of the line is(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe correct answer is B.One way to determine the slope of the line is to compute two points on the line and then use the slope formula. For example, letting gives the point on the line, and letting gives the point on the line. Therefore, the slope of the line is equal to .Alternatively, one can express in terms of . Since and , it follows that . Therefore, the slope of the line is .15Your answer Omitted!What is the range of the function defined by ?(A) All real numbers(B) All real numbers except(C) All real numbers except(D) All real numbers except(E) All real numbers between andExplanationDifficulty: MediumThe correct answer is D.The range of the function defined by is the set of such thatfor some .One way to determine the range of the function defined by is to solve the equation for and then determine which correspond to at least one . To solve for , first subtract from both sides to get and then take the reciprocal of both sides to get . The equation shows that for anyother than , there is an such that , and that there is no such for . Therefore, the range of the function defined by is all real numbers except .Alternatively, one can reason about the possible values of the term . The expression can take on any value except , so the expression can take on any value except . Therefore, the range of the function defined by is all real numbers except .16Your answer Omitted!The table above shows the number of digital cameras that were sold during a three-day sale. The prices of models , , and were , , and , respectively. Which of the following matrix representations gives the total income, in dollars, received from the sale of the cameras for each of the three days?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe correct answer is C.A correct matrix representation must have exactly three entries, each of which represents the total income, in dollars, for one of the three days. The total income for Day is given by the arithmetic expression , which is the single entry of the matrix product; in the same way, the total income for Day is given by, the single entry of ; and the total income for Day is given by , the single entry of. Therefore, the matrix representationgives the total income, in dollars, received from the sale of the cameras for each of the three days. Although it is not necessary to compute the matrix product in order to answer the question correctly, equals .17Your answer Omitted!The right circular cone above is sliced horizontally forming two pieces, each of which has the sameheight. What is the ratio of the volume of the smaller piece to the volume of the larger piece?(A)(B)(C)(D)(E)ExplanationDifficulty: HardIt is helpful to label the figure.The top piece is a cone whose height is one-half the height of the original cone . Using the properties of similar right triangles, you should realize the radii of these two cones must be in the same ratio. So if the top cone has radius , the original cone has radius .The volume of the top piece is equal to . The volume of the bottom piece is equal to the volume of the original cone minus the volume of the top piece.The ratio of the volume of the smaller piece to the volume of the larger piece is .18Your answer Omitted!In the figure above, is a regular pentagon with side of length . What is the -coordinate of ?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe sum of the measures of the interior angles of a regular pentagon is equal to . Each interior angle has a measure of . Using supplementary angles, has a measure of . You can use right triangle trigonometry to find the -coordinate of point .Since , is about . Since the length of each side of the pentagon is , the -coordinate of point is . Putting the information together tells us that the -coordinate of point is . The correct answer is (B).19Your answer Omitted!For a class test, the mean score was , the median score was , and the standard deviation of the scores was . The teacher decided to add points to each score due to a grading error. Which of the following statements must be true for the new scores?I. The new mean score is .II. The new median score is .III. The new standard deviation of the scores is .(A) None(B) only(C) only(D) and only(E) , , andExplanationDifficulty: HardFor this type of question you need to evaluate each statement separately. Statement is true. If you add to each number in a data set, the mean will also increase by . Statement is also true. The relative position of each score will remain the same. Thus, the new median score will be equal to more than the old median score. Statement is false. Since each new score is more than the old score, the spread of the scores and the position of the scores relative to the mean remain the same. Thus, the standard deviation of the new scores is the same as the standard deviation of the old scores.20Your answer Omitted!A game has two spinners. For the first spinner, the probability of landing on blue is . Independently, for the second spinner, the probability of landing on blue is What is the probability that the first spinner lands on blue and the second spinner does not land on blue?(A)(B)(C)(D)(E)ExplanationDifficulty: HardSince the two events are independent, the probability that the first spinner lands on blue and the second spinner does not land on blue is the product of the two probabilities. The first probability is given. Since the probability that the second spinner lands on blue is the probability that thesecond spinner does not land on blue is Therefore, . The correct answer is (E).21Your answer Omitted!In January the world’s population was billion. Assuming a growth rate of percent per year, the world’s population, in billions, for years after can be modeled by theequation . According to the model, the population growth from January to January was(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is C.According to the model, the world’s population in January was and in January was . Therefore, according to the model, the population growth from January to January , in billions, was , or equivalently,.22Your answer Omitted!What is the measure of one of the larger angles of a parallelogram in the that has vertices with coordinates , , and ?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is C.First, note that the angle of the parallelogram with vertex is one of the two larger angles of the parallelogram: Looking at the graph of the parallelogram in the makes this apparent. Alternatively, the sides of the angle of the parallelogram with vertex are a horizontal line segment with endpoints and and a line segment of positive slope with endpoints and that intersects the horizontal line segment at its left endpoint , so the angle must measure more than Since the sum of the measures of the four angles of aparallelogram equals , the angle with vertex must be one of the larger angles.One way to determine the measure of the angle of the parallelogram with vertex is to apply the Law of Cosines to the triangle with vertices , , and . The length of the two sides of the angle with vertex are and; the length of the side opposite the angle is . Let represent the angle with vertex and apply the Law of Cosines: , so. Therefore, the measure of one of the larger angles of the parallelogram is .Another way to determine the measure of the angle of the parallelogram with vertex is to consider the triangle , , and . The measure of the angle of this triangle with vertex is less than the measure of the angle of the parallelogram with vertex . The angle of the triangle has opposite side of length and adjacent side of length , so the measure of this angle is . Therefore, the measure of the angle of the parallelogram withvertex is .Yet another way to determine the measure of the angle of the parallelogram with vertex is to use trigonometric relationships to find the measure of one of the smaller angles, and then use the fact that each pair of a larger and smaller angle is a pair of supplementary angles. Consider the angle of the parallelogram with vertex ; this angle coincides with the angle at vertex of the right triangle with vertices at , , and , with opposite side of lengthand adjacent side of length , so the measure of this angle is . This angle, together with the angle of the parallelogram with vertex , form a pair of interior angles on the same side of a transversal that intersects parallel lines, so the sum of the measures of the pair of angles equals . Therefore, the measure of the angle of the parallelogram with vertex is.23Your answer Omitted!For some real number , the first three terms of an arithmetic sequence are, and . What is the numerical value of the fourth term?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is E.To determine the numerical value of the fourth term, first determine the value of and then apply the common difference.Since , and are the first three terms of an arithmetic sequence, it must be true that, that is, Solving for gives . Substituting for in the expressions of the three first terms of the sequence, one sees that they are , , and , respectively. The common difference between consecutive terms for this arithmetic sequence is , and therefore, the fourth term is .24Your answer Omitted!In a group of people, percent have brown eyes. Two people are to be selected at random from the group. What is the probability that neither person selected will have brown eyes?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is A.One way to determine the probability that neither person selected will have brown eyes is to count both the number of ways to choose two people at random from the people who do not have brown eyes and the number of ways to choose two people at random from all people, and then compute the ratio of those two numbers.Since percent of the people have brown eyes, there are people with brown eyes, and people who do not have brown eyes. The number of ways of choosing two people, neither of whom has brown eyes, is : there are ways to choose a first person and ways to choose a second person, but there are ways in which that same pair of people could be chosen. Similarly, the number of ways of choosing two people at random from the people is . Therefore, the probability that neither of the two people selected has brown eyes is.Another way to determine the probability that neither person selected will have brown eyes is to multiply the probability of choosing one of the people who does not have brown eyes at random from the people times the probability of choosing one of the people who does not have brown eyes at random from the remaining people after one of the people who does not have brown eyes has been chosen.Since percent of the people have brown eyes, the probability of choosing one of the people who does not have brown eyes at random from the people is . If one of the people who does not have brown eyes has been chosen, there remain people who do not have brown eyes out of a total of people; the probability of choosing one of the people who does not have brown eyes at random from the people is . Therefore, if two people are to be selected from the group at random, the probability that neither person selected will have brown eyes is .25Your answer Omitted!If , what is ?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is E.One way to determine the value of is to solve the equation for . Since , start with the equation , and cube both sides to get. Isolate to get , and apply the cube root to both sides of the equation to get .Another way to determine the value of is to find a formula for and then evaluate at Let and solve for : cubing both sides gives , so , and. Therefore, , and .26Your answer Omitted!Which of the following equations best models the data in the table above?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is D.One way to determine which of the equations best models the data in the table is to use a calculator that has a statistics mode to compute an exponential regression for the data.The specific steps to be followed depend on the model of calculator, but can be summarized as follows: Enter the statistics mode, edit the list of ordered pairs to include only the four points givenin the table and perform an exponential regression. The coefficients are, approximately, for the constant and for the base, which indicates that the exponential equation is the result of performing the exponential regression. If the calculator reports a correlation, it should be a number that is very close , to which indicates that the data very closely matches the exponential equation. Therefore, of the given models, best fits the data.Alternatively, without using a calculator that has a statistics mode, one can reason about the data given in the table.The data indicates that as increases, increases; thus, options A and B cannot be candidates for such a relationship. Evaluating options C, D and E at shows that option D is the one that gives a value of that is closest to In the same way, evaluating options C, D and E at each of the other given data points shows that option D is a better model for that one data point than either option C or option E. Therefore, is the best of the given models for the data.27Your answer Omitted!The linear regression model above is based on an analysis of nutritional data from 14 varieties of cereal bars to relate the percent of calories from fat to the percent of calories from carbohydrates . Based on this model, which of the following statements must be true?I. There is a positive correlation between and .II. When percent of calories are from fat, the predicted percent of calories from carbohydrates is approximately .III. The slope indicates that as increases by , decreases by .(A) II only(B) I and II only(C) I and III only(D) II and III only(E) I, II, and IIIExplanationDifficulty: HardThe correct answer is D.Statement I is false: Since , high values of are associated with low values of which indicates that there is a negative correlation between and .Statement II is true: When percent of calories are from fat, and the predicted percent of calories from carbohydrates is .Statement III is true: Since the slope of the regression line is , as increases by , increases by ; that is, decreases by .28Your answer Omitted!The number of hours of daylight, , in Hartsville can be modeled by , where is the number of days after March . The day with the greatest number of hours of daylight has how many more daylight hours than May ? (March and May have days each. April and June have days each.)(A) hr(B) hr(C) hr(D) hr(E) hrExplanationDifficulty: HardThe correct answer is A.To determine how many more daylight hours the day with the greatest number of hours of daylight has than May , find the maximum number of daylight hours possible for any day and then subtract from that the number of daylight hours for May .To find the greatest number of daylight hours possible for any day, notice that the expressionis maximized when , which corresponds to , so. However, for this problem, must be a whole number, as it represents a count of days after March . From the shape of the graph of the sine function, either or corresponds to the day with the greatest number of hours of daylight, and since, the expression is maximized when days after March . (It is not required to find the day on which the greatest number of hours of daylight occurs, but it is days after March ,that is, June .)Since May is days after March , the number of hours of daylight for May is .Therefore, the day with the greatest number of hours of daylight hasmore daylight hours than May .。

SAT-II-Math(美国SAT数学几何题目和答案)

10.Geometry1.In a circle with center at O, arc ST measures 110°. What is the measure of angle STO?2.If the angles of a triangle are in the ratio of 2:3:5, what is the measure of the smallest angle?3.In the figure x.4.The diagonal of a rectangle is 26 cm and its height is 10 cm. Find the area of the rectangle in squarecentimeters.5. A ship travels 60 mi north, 90 mi west, and then 60 mi north again. How many miles is it fromits starting point?6.Find the length in inches of a tangent drawn to a circle with a 10 in. radius from a point 26 in.from the center of the circle.7.If the largest possible circular disc is cut from a rectangular piece of tin 8 in. by 12 in., what isthe area of the waste tin in square inches in terms of π?8. A circle is inscribed in a square. What is the ratio of the area of the square to that of the circle interms of π?9.At 4:20 PM., how many degrees has the hour hand of a clock moved since noon?10.Find the volume of a cube in cubic centimeters if the total surface area of its faces is 150 sq cm.11.A cylindrical can has a circular base with a diameter of 14 in. and a height of 9 in. Approxi-12.What is the volume in cubic inches of an open box made by snipping squares 2 in. by 2 in. fromthe corners of a sheet of metal 8 in. by 11 in. and then folding up the sides?13.Water 6 in. high in a fish tank 15 in. long by 8 in. wide is poured into a tank 20 in. long by 12 in.wide. What height in inches does it reach in the larger tank?14.A 6 ft pole is casting a 5 ft shadow at the same time that a flagpole is casting a 22 ft shadow. Howmany feet high is the flagpole?15.In the figure, PQRST is a regular pentagon inscribed in the circle. andthe pentagon, forming an angle of x° as shown. What does x equal?16.A treasure is buried 10 ft from tree T and 12 ft from a straight fence F. If T is 20 ft from F, in howmany places may the treasure be buried?17.If a given statement is true, which of the following statements must also be true?(A)the converse of the statement(B)the inverse of the statement(C)the contrapositive of the statement(D)the negative of the statement(E)none of these18.Given point P on a line. In a given plane containing the line, what is the total number of pointsthat are at a distance of 4 units from P and also at a distance of 3 units from the given line? 19.Point Q is 20 cm from plane P in space. What is the locus of points 8 cm from P and 12 cm frompoint Q?20.The sum of the measures of the interior angles of a convex polygon is 720°. What is the sum of themeasures of the interior angles of a second convex polygon that has two more sides than the first?10.GEOMETRY1.The correct answer is (35º).Let PT be a diameter of Circle O.2.The correct answer is (36º). Let 2x = smallest angle in degrees, 3x and 5x = other two anglesin degrees.3.The correct answer is (120º).m (alernate interior angles), and mAngle x is an exterior angle of ∆DEF and isequal to the sum of the measures of the two remote interior angles.x= 50º + 70º = 120º5.The correct answer is (150).The tangent is perpendicular to the radiusat the point of tangency.In right triangle OTP7.The correct answer is (96 - 16π).8.The correct answer isLet radius of circle be 1.Side of square is 1 + 1 =2.9.The correct answer is (130º).From noon to 4:00 PM., the hour hand has moved from 12 to 4: of360º = 120º. In the next 20 minutes it moves of the distance from 4:00 to 5:00: of30º = 10º.120º + 10º = 130º10.The correct answer is (125).11.The correct answer is (6).12.The correct answer is (56).13.The correct answer is (3).14.The correct answer isCross-multiply.15.The correct answer is (108°).16.The correct answer is (2).The locus of points 10 ft. from T is acircle of radius 10. The locus of points12 ft from F consists of two parallellines 12 ft from F on each side. Thecircle and one parallel line intersect intwo points.17.The correct answer is (C). The only statement that has the same truth value as the given statement isthe contrapositive of the original statement. This is the converse of the inverse of the original statement.18.The correct answer is (4).The locus of points 4 units from P is a circleof radius 4 with center at P. The locusof points 3 units from the given line consistsof two parallel lines 3 units from theline. The two parallel lines intersect thecircle in 4 points.19.The correct answer is (1).The locus of points 8 cm from P consistsof two planes parallel to P and 8 cm fromit. The locus of points 12 cm from Q is asphere of radius 12 and center at Q. Thesphere intersects one of the parallel planesin one point (point of tangency).20.The correct answer is (1080°). The sum of the interior angles of an n-sided polygon is (n – 2) 180°= 720°. Divide by 180.The second polygon has 6 + 2 = 8 sides.Sum of the measures of its interior angles = 180(8 – 2)= 180(6) = 1080°。

sagemath输出准确值

sagemath输出准确值SageMath是一种开源的数学软件，它基于Python编程语言，并提供了一个交互式环境来进行数学计算和建模。

它可以用于计算代数、几何、概率、统计和数值计算等各种数学问题。

SageMath的输出准确值是指它在进行数学计算时，尽可能地提供精确的数值结果。

与其他计算机软件和计算器不同，SageMath使用高精度的计算方法，可以避免浮点数舍入误差和截断误差。

SageMath支持多种数据类型和数学函数，可以处理整数、有理数、实数和复数等各种数值。

它在进行数学计算时，会自动选择合适精度的计算方法，以保证结果的精确性。

例如，在进行数值计算时，SageMath会自动选择合适的数值精度，并进行必要的舍入处理。

这样可以保证计算结果的准确性，并将误差控制在可接受的范围内。

此外，SageMath还支持符号计算，可以进行代数计算和符号操纵。

它可以处理多项式、方程、函数和向量等符号对象，并对其进行运算和求解。

通过使用符号计算的功能，SageMath可以输出精确的代数表达式和符号解，而不仅仅是数值结果。

这对于数学研究、教学和工程应用来说非常有用。

另外，SageMath还支持精确的符号计算积分和微分。

它可以对各种函数进行积分和微分运算，并输出准确的结果。

这对于解决复杂的积分和微分问题非常有帮助。

除了数学计算，SageMath还具有数据可视化和图形绘制功能。

它可以生成各种类型的图形，如散点图、线图、柱状图和饼图等。

这样，用户可以直观地展示和分析数学数据和结果。

总之，SageMath是一个强大而全面的数学软件，它可以输出准确值，并在数学计算、代数计算和符号计算等方面提供丰富的功能和工具。

它可以满足数学研究、教学和工程应用的需求，并帮助用户处理各种数学问题。

无论是简单的数值计算还是复杂的符号计算，SageMath都可以提供准确的结果，帮助用户更好地理解和解决数学问题。

mathmetical

120第十章附录10.1 Notebook 文件的存取用户在Mathematica 的Notebook 用户区使用完Mathematica 想退出Mathematica 系统或想调用以前的Notebook 文件，就涉及到Notebook 文件的存取操作。

保存一个Notebook 文件用户在Notebook 用户区使用完Mathematica 或因为有事要中途退出Mathematica 系统，退出时想保留调在Notebook 用用户区的内容以便下次调用，这种保存Notebook 文件的操作为：１）用鼠标点击Mathematica 系统集成界面右上角的关闭按钮，屏幕出现一个对话框,询问是否保存用户区的内容, 如图：图10.1 提示保存文件对话框２）如果单击对话框的“否(N)”按钮, 则不保存Notebook 中的文件, 退出Mathematica 系统; 如果单击对话框的“取消”按钮，则返回Mathematica 系统集成界面；如果单击对话框的“是(Y)”按钮, 则在保存Notebook 文件窗口的左上部分的文件名窗口先提示你用一个具有扩展名为 .ma 的文件名来保存用户区内的内容, 如果你想以另一个文件名保存该文件,可以在文件名窗口键入你自己的文件名,并选择好驱动器(Drives)和子目录(Directories)然后单击OK 按钮,既可以达到保存Notebook 文件在相应驱动器的对应目录下的目的,同时退出Mathematica 系统。

Notebook 文件窗口如图：图10.2 保存Notebook文件窗口打开一个Notebook文件用户在Mathematica 的Notebook用户区如果要打开一个Notebook文件，对应的打开Notebook文件的操作为:1)在在Mathematica的工作窗口键入Ctrl+ O,调出如下Open窗口:图10.3 打开Notebook文件窗口2)在打开Notebook文件窗口中的文件名窗口键入想要打开的文件名,并选择好对应的驱动器(Drives)和子目录(Directories), 然后单击OK按钮,既可以把对应的Notebook文件调入Notebook工作区。

软件介绍之Hisat2

软件介绍之Hisat2咱们《生信技能树》的B站有一个lncRNA数据分析实战，缺乏配套笔记，所以我们安排了100个lncRNA组装案例文献分享，以及这个流程会用到的100个软件的实战笔记教程！下面是100个lncRNA组装流程的软件的笔记教程一、Hisat2介绍Hisat是一种高效的RNA-seq实验比对工具。

它使用了基于BWT 和Ferragina-manzini (Fm) index 两种算法的索引框架。

使用了两类索引去比对，一类是全基因组范围的FM索引来锚定每一个比对，另一类是大量的局部索引对这些比对做快速的扩展。

比对原理可阅读文献原文：HISAT: a fast spliced aligner with low memory requirements.二、Hisat2设计原则1.优化了索引建立策略hisat2应用了基于bowtie2的方法去处理很多低水平的用于构建和查询FM索引的操作。

但是与其它比对器不同的是，该软件应用了两类不同的索引类型：代表全基因组的全局FM索引和大量的局部小索引，每个索引代表64000bp的区域。

以人类基因组为例，创建了约48000个局部索引，每一个索引与其相邻索引重叠1024bp，最终可以覆盖这个30亿个碱基的基因组。

这种存在交叉（overlap）的边界可以轻松的比对那些跨区域的read（可变剪切体）。

尽管有很多索引，但是hisat会把他们使用合适方法压缩，最终只占4GB左右的内存。

2.采用了新的比对策略RNA-seq产生的reads可能跨越长度比较大的内含子，在哺乳动物中甚至最长能达到1MB，同时外显子比较短，read也比较短。

当使用100-bp reads时，会有很多read（模拟数据中大概34%）跨两个外显子的情况。

为了更好的比对，将跨外显子的reads分成了三类：1）长锚定read，两个外显子中的每个都至少有16 bp；2）中间锚定read，一个外显子中具有8-15bp；3）短锚定read，仅与其中一个外显子比对上1-7bp。

SAT2数学冷门知识点大起底

SAT2数学冷门知识点大起底任何考试研究OG，也就是官方的考试指南是非常有意义的，SAT2跟SAT1都是College Board官方出的题目，SAT1和SAT2的出题考点会对应的非常明显，但是SAT2的考点范围更大。

而且，他们两个有个共同的点，不会明确说哪些方面不会考。

这样的话，对于我们备考来说，就会带来很大的困难。

但是SAT2里收集到题目的量比较少，所以OG将成为我们一个非常重要的备考资料，我们从大纲看起。

这张考点，Level1和Level2的不同都以斜体标出，这个是复习的重点，所以我们将从几个点展开，看一下SAT2考的并不是很多但是非常重要的点。

graphical properties of complex numbers这个不同我们可以看到，它会考到graphical properties of complex numbers在平面坐标系中的一些性质。

我们来看下在OG中出现的例子。

这道题说白了是考察虚数的乘法，我们假设w=a+bi，a代表的就是它对应的X轴上的坐标，b对应的就是Y轴的坐标。

这样可以看出，a＜0，b＞0，我们把-iw乘起来，这样的话就等于b-ia，实数部分变成了b，所以说只可能是A、B、C三个点。

虚数部分是-a，是个正数，所以这道题应该选A。

这道题在真题的考试中并不是很多见，但既然在OG中出现过类似的例题，我们还是着重去了解一下，以免以后碰到类似的题目不知道如何下手。

三角函数和反三角函数我们继续看大纲，上图中的斜体字trigonometric, inverse trigonometric是三角函数和反三角函数，这个是很多备考的学生比较薄弱的环节，这个点可以考的很难，也可以考的很简单，度不大好掌握。

我们来看一下SAT2中，对于这个点是怎么考察的。

首先，跟SAT1不同的是SAT2对三角函数的难度明显加大了很多，我们首先看到一个函数。

这个是三角函数中非常喜欢考的一个东西，这里一共有四个参数A、B、C、D。

SAT2测试各科允许错多少

SAT2测试各科允许错多少？SAT2相关常识总结SAT2容错率
·每科考试时间一个小时，全部为选择判断题，满分800分。

·不答不给分，答错道扣分。

·由于SAT2是选拔性考试，容错率低，时间紧张，拿高分不容易
·数学level 2共50题，容错率约为5个;
·物理共75题，容错率约为10-15个
·化学共85题，容错率约为4个
·美国历史90道选择题，容错率约为10个
·生物共80道题;
公共部分60题，学生自选20题可选择偏分子生物学方向的Molecular试题或者偏生态学方向的Ecological试题，容错率约为3-4个。

如果考生对生物群落、种群和能量流动等内容更加擅长，建议选择E试题;如果考生对生物化学、细胞结构、细胞中重要反应等内容比较熟悉，建议选择M试题。

·数学考试可以使用计算器，其他科目考试时计算器放在考场座位旁的地上。

推荐使用德州仪器TI-Nspire，AP也可以用
·每一次SAT2考试最多可以同时报考三个科目。

·考试时会发一本试题册，包含考试的所有科目试题，
·如果报考多门考试，试题册编号需要自己涂在每一科考试的答题卡上。

·不能跨区考试
·取消成绩必须取消整场考试所报的所有科目
·可以拼分
·可以加科目和弃考
·使用HB和IB铅笔都可以
·最好带一件长袖外套
·如果决定取消成绩，在考试当天向考官提出，或者在考试之后的周三给大学理事会发取消成绩的信。

赛达2数学考试常见知识点总结

赛达2数学考试常见知识点总结SAT2数学考试常见知识点总结下面为大家总结的是SAT2数学考试的知识点。

SAT2数学考试分成了Level 1和Level 2两个部分。

大家在备考这两个部分的时候，知识点的掌握上稍稍有一些不同。

下面我们就来看看详细内容吧。

（小马过河国际教育）SAT2数学Level 1知识点Math ICAlgebraPlane geometry (lines and angles, triangles, polygons, circles)Solid geometry (cubes, cylinders, cones, spheres, etc.)Coordinate geometry (in two dimensions)Trigonometry (properties and graphs of sine, cosine, and tangent functions, identities) Algebraic functionsStatistics and sets (distributions, probability, permutations and combinations, groups and sets) Miscellaneous topics (logic, series, limits, complex and imaginary numbers) SAT2数学Level 2知识点Math IIC (covers all areas in Math IC with some additional concepts) AlgebraPlane geometrySolid geometryCoordinate geometry (in two and three dimensions, vectors, polar coordinates, parametric equations) Trigonometry (cosecant, secant, cotangent functions, inverse functions, in non-right triangles) Statistics and sets其他：·Question difficulty. Not only does the Math IIC cover additional topics, it also covers the basic topics in more difficult ways than the Math IC does.·College choice. As you choose between the two tests, keep in mind the specific colleges you’re applying to. Colleges with a strong focus on math, such as MIT and Cal Tech, require the Math IIC test. Most other colleges have no such requirement, but some may prefer that you take the IIC.· Battle of the test curves. The Level IIC test is scored on a much more liberal curve: you can miss six or seven questions and still achieve a score of 800. On the IC test, however, you would probably need to answer all the questions correctly to get a perfect score. If you wanted to score a 600 on either test, you would need around 20 correct answers on the IIC test and 33 on the IC test. Some students with strong math backgrounds think that they can get a marvelous score on the less difficult Math IC while their score on the IIC will only be average. But if you gettripped up by just one or two questions on the Math IC, your score will not be as impressive as you might expect.以上就是关于SAT2数学考试知识点的全部内容，包括了Level 1和Level 2两个部分和一些杂项。

【天道世界名校介绍】加州大学欧文分校University of California Irvine

天道留学 /【天道世界名校介绍】加州大学欧文分校 University of California Irvine学校网址：地理位置 UCI 位于加州南部的小城 Irvine 市，位于 Orange county（橘子郡）的中心地带，橘子郡是美国很有名的富人居住区，著名旅游胜地.Irvine 可以说是一个 “订做出来的城市 ”，由著名建筑师威廉姆 · 佩雷拉（ William Pereira ）精心规划设计，整个城市的绿化和街道交通规划都非常完善，城市空间舒适宽敞令人印象深刻，整个城市显得相当安详和谐。

而 UCI 恰恰是设计师设计的城市之中心。

Irvine 是美国最安全的城市之一，学校治安极好，临近太平洋，开车 10 分钟就到沙滩，距离 LA 45 分钟车程左右。

UCI 附近有个著名的新港市 City of Newport Beach ，是世界著名的帆船、游艇集中地，时常举办世界级的大型帆船比赛。

UCI 周边也有不少高新科技公司，包括世界知名的游戏公司暴雪。

学校简介；吉祥物：Peter the Anteater天道教育带您走向成功留学之道！天道留学 /天道教育带您走向成功留学之道！天道留学 /公立大学，创立于 1965 年，是 UC 系统中第二年轻的学校，占地 1526 英亩，本科生 22000 多人，研究生 5600 多人，本科国际学生 6%，UCI 属于 UC 系统第三 tier 的学校，跟 UCSB，UCD 实力相当，成立时间较短，发展比较快，学校亚裔很多，占本科人数 50%以上。

Overlap：UCLA，UCSD，UCSB，UCB，USC 学校优势：综合排名 44，AAU 成员，学校在国内推广预科项目力度比较大，有一定名气，研究生院研究实力比较强，是世界上第一所教职人员在同一年在两个不同领域获得诺贝尔奖的大学，地理位置好，很安全，气候好，周边就业机会还不错，尤其是理工类专业。

SAT1、SAT2最新详解,美国留学必看!

SAT1、SAT2最新详解，美国留学必看！2018年号称最难申请季，即使高分狂魔、活动大神，都是要全力地在申请大军中杀出一条血路。

都说高分优势不在，然而事实并非如此，申请藤校还是要注重全面发展。

所以，成绩依旧是第一关卡，三高仍然是申藤利器（GPA,SAT,TOEFL）。

时值8月，SAT即将考试之际，小编就给大家详细介绍一下SAT考试的相关内容。

包括考试时间，内容科目，各大学2018年最新对SAT1、2的成绩要求等，方方面面为你解密SAT考试。

基本知识S A T与SAT2S A T是由美国大学委员会（C o l l e g e B o a rd）主办的一场考试，它和A CT（Am e r i c a n Co l l e ge Te s t）都被称为美国高考。

通常，我们所说的S A T2是指S A T科目测试，S A T（S A T1）主要考察英语语言能力，S A T2注重考察某一方面的专业知识。

备考攻略S A T下半年考试时间SAT考试内容及SAT2考试科目2016年改革后新SAT总分共1600分，分为阅读、文法和数学三部分，写作改为选考。

SAT2考试科目包括：数学Level1，数学Level2，化学，物理，生物。

美国历史，世界历史。

英语文学、德语、德语（带听力）、法语、法语（带听力）、西班牙语、西班牙语（带听力）、日语（带听力）、韩语（带听力）、中文（带听力）、拉丁语、意大利语、希伯来语。

一般情况下，多数学校不用必须提交SAT2成绩，但是，良好的SAT2分数是申请时有力的buff加持。

需要此成绩的大学一般要求至少有2门成绩，考生一般参加3门。

我国学生主要选择数学2，物理和化学。

生物难度较大，文科由于语言障碍选择的同学相对较少。

难度上，SAT数学<数学1<数学2。

有些理工科学校要求申请者提供数学1或数学2的成绩SAT与SAT2考试报名须知：报名地址：报名日期：考场有限，需提前报名报名费用：SAT152.5美元，国际考生94.5美元；SAT2基本费用$26 加$42 的亚太国际考场费用，每考一科不包含听力的考试加$16，每考一科包含听力的考试加$26。

SAT2化学容错率是多少

SAT2化学容错率是多少关于sat2考试，你需要知道SAT2化学容错率，三立在线SAT频道为大家带来SAT2化学容错率是多少一文，希望对大家SAT备考有所帮助。

更多精彩尽请关注三立在线SAT频道!化学部分答题时间1h，涵盖85道问题，不可以使用计算器，考点涵盖整本Princeton教材的知识点，不含超过国内高中化学的知识点，melody老师就不一一例举了。

在考试过程中会提供给大家一张化学元素周期表，一份涉及计算题中所需的基本数据比如比热容的值等，不用刻意背，非常仁慈哦!SAT2化学容错率化学考试相对于数学来说容错率较小，只有三四个，而化学备考中要记忆很多专业词汇，但是中国考生如此青睐化学还是由于化学考试更加简单一些。

因为考生只要学完了高中前两本必修教材，基本上就掌握了化学的基础知识，帮助也是不小，所以备考起来不会太难。

备考建议：1. 做完Part A和Part B两部分之后先填涂这两部分的答题卡，之后再开始Part C部分，这样可以避免一下子填涂85道题的答题卡，手会发酸的;2. 题目中给的数字也都非常规整，一定是整数倍或好除开的倍数关系，不会出现除不尽的情况，这也是大家检查错误的小技巧;3. SAT2化学由于题量大，所以出题特点具有题目短，思路直，概念题型多，因此基础知识非常重要。

基础知识扎实的学生一般在45min内就能够完成一套题目，且Part A和Part C部分全部正确，同学们可做参考哦;4. 建议同学们把充裕的时间留给检Part B，因为Part B部分属于逻辑判断题，左右两句话是否构成CE关系需要反复斟酌，同一道题的3个空中(T，T，CE)填错一个，整道题就都没有分数了;网友解答：SAT2化学，传说中化学容错率很小，这里解释一下，容错率指的就是错多少道题仍然是满分。

没有人能说出准确的容错率，但是level2大概只有三四个。

而且有很多专业词汇要去记忆，很头疼。

其实SAT2化学还是比较不错的。

SAT2计算器使用攻略

三立教育
SAT2计算器使用攻略
旧SAT考试中对计算器的使用没有限制，但是，新SAT数学存在着需要大量计算的题目，虽都是基础的运算，但数据之多、之杂是旧SAT无法比拟的。

所以，选择正确的计算器对我们来说非常重要。

SAT2数学部分可以全程使用计算器，需要的操作除了基本的加减乘除外，还有次方、对数、三角函数和反三角函数等的运算，建议准备一个能做函数图像的计算器。

主流官方建议的是TI-84和TI-Nspire。

TI-Nispire分彩色版和黑白版，对SAT2来说，黑白款已经能满足所有需要。

使用计算器的注意事项：
1. 不论什么计算器，不要考试的时候才用，不要舍不得用你昂贵的计算器，一定要对它相当熟悉才行，平时有复杂问题用得到它解决获取很耗时间的计算，熟能生巧;
2. 使用时，不要使用计算器的记忆功能，否则很可能出现程序错误导致的结果错误;
3. 注意同时需要计算加减乘除的时候输入的式子需要打括号，否则结果会出错;
4. 记得算完一次要清除结果，以免下次的计算结果出错;
5. 弄清你的计算器的电池型号，在考试前几天准备双份(一份给计算器换上;一份带到考场，如果需要使用起子等工具才能开启更换电池的计算器，把起子也带上。

Level2-S-function

Level2-S-function level2的S函数可以允许多个输⼊和输出，且其可以包含任何的数据类型。

1、⾸先要更改msfuntmpl为⾃⼰需要的函数名 2、修改初始化函数setup，该函数传⼊了⼀个block对象作为参数修改输⼊输出的端⼝数⽬ block.NumInputPorts、block.NumOutputPorts确定输⼊输出端⼝的数据类型block.InputPort(1).DatatypeID、block.InputPort(1).Complexity 、 block.OutputPort(1).DatatypeID、block.OutputPort(1).Complexity确定参数个数及block.NumDialogPrms（模块GUI参数个数）、block.DialogPrmsTunable（指定哪些 S-Function 的对话框参数是可调的）确定连续状态变量数⽬NumContStates确定采样时间block.SampleTimesblock.SetAccelRunOnTLC(指定是否使⽤此模块的 TLC ⽂件为使⽤它的模型⽣成仿真⽬标）后⾯就是注册⼀系列需要调⽤的函数了。

　3、CheckPrms⽤于检查输⼊的参数是否正确 4、DoPostPropSetup⽤于初始化Dwork⼯作向量，规定其个数及每个向量的维数，数据类型、离散状态变量名称和虚实性（当不同的S 函数模块之间需要通过全局变量或静态变量进⾏数据交互时，必须使⽤Dwork向量来进⾏存储） 5、InitializeConditions⽤于初始化状态变量的值或者Dwork的值 6、start函数与InitializeConditions功能⼀致，但是其仅在仿真开始的时候初始化⼀次，InitializeConditions是在每次⼦系统使能时都能被调⽤。

7、output函数⽤于计算S函数的输出 8、update⽤于计算离散状态变量的值 9、Derivatives⽅法⽤于计算连续状态的值 10、Terminate⽤于终⽌function msfuntmpl(block)%MSFUNTMPL A Template for a MATLAB S-Function% The MATLAB S-function is written as a MATLAB function with the% same name as the S-function. Replace 'msfuntmpl' with the name% of your S-function.% Copyright 2003-2018 The MathWorks, Inc.%% The setup method is used to setup the basic attributes of the% S-function such as ports, parameters, etc. Do not add any other% calls to the main body of the function.%setup(block);%endfunction% Function: setup ===================================================% Abstract:% Set up the S-function block's basic characteristics such as:% - Input ports% - Output ports% - Dialog parameters% - Options%% Required : Yes% C MEX counterpart: mdlInitializeSizes%function setup(block)% Register the number of ports.block.NumInputPorts = 1;block.NumOutputPorts = 1;% Set up the port properties to be inherited or dynamic.block.SetPreCompInpPortInfoToDynamic;block.SetPreCompOutPortInfoToDynamic;% Override the input port properties.block.InputPort(1).DatatypeID = 0; % doubleblock.InputPort(1).Complexity = 'Real';% Override the output port properties.block.OutputPort(1).DatatypeID = 0; % doubleblock.OutputPort(1).Complexity = 'Real';% Register the parameters.block.NumDialogPrms = 3;block.DialogPrmsTunable = {'Tunable','Nontunable','SimOnlyTunable'};% Set up the continuous states.block.NumContStates = 1;% Register the sample times.% [0 offset] : Continuous sample time% [positive_num offset] : Discrete sample time%% [-1, 0] : Inherited sample time% [-2, 0] : Variable sample timeblock.SampleTimes = [0 0];% -----------------------------------------------------------------% Options% -----------------------------------------------------------------% Specify if Accelerator should use TLC or call back to the% MATLAB fileblock.SetAccelRunOnTLC(false);% Specify the block's operating point compliance. The block operating% point is used during the containing model's operating point save/restore)% The allowed values are:% 'Default' : Same the block's operating point as of a built-in block% 'UseEmpty': No data to save/restore in the block operating point% 'Custom' : Has custom methods for operating point save/restore% (see GetOperatingPoint/SetOperatingPoint below)% 'Disallow': Error out when saving or restoring the block operating point.block.OperatingPointCompliance = 'Default';% -----------------------------------------------------------------% The MATLAB S-function uses an internal registry for all% block methods. You should register all relevant methods% (optional and required) as illustrated below. You may choose% any suitable name for the methods and implement these methods% as local functions within the same file.% -----------------------------------------------------------------% -----------------------------------------------------------------% Register the methods called during update diagram/compilation.% -----------------------------------------------------------------%% CheckParameters:% Functionality : Called in order to allow validation of the% block dialog parameters. You are% responsible for calling this method% explicitly at the start of the setup method.% C MEX counterpart: mdlCheckParameters%block.RegBlockMethod('CheckParameters', @CheckPrms);%% SetInputPortSamplingMode:% Functionality : Check and set input and output port% attributes and specify whether the port is operating% in sample-based or frame-based mode% C MEX counterpart: mdlSetInputPortFrameData.% (The DSP System Toolbox is required to set a port as frame-based)%block.RegBlockMethod('SetInputPortSamplingMode', @SetInpPortFrameData); %% SetInputPortDimensions:% Functionality : Check and set the input and optionally the output% port dimensions.% C MEX counterpart: mdlSetInputPortDimensionInfo%block.RegBlockMethod('SetInputPortDimensions', @SetInpPortDims);%% SetOutputPortDimensions:% Functionality : Check and set the output and optionally the input% port dimensions.% C MEX counterpart: mdlSetOutputPortDimensionInfo%block.RegBlockMethod('SetOutputPortDimensions', @SetOutPortDims);%% SetInputPortDatatype:% Functionality : Check and set the input and optionally the output% port datatypes.% C MEX counterpart: mdlSetInputPortDataType%block.RegBlockMethod('SetInputPortDataType', @SetInpPortDataType);%% SetOutputPortDatatype:% Functionality : Check and set the output and optionally the input% port datatypes.% C MEX counterpart: mdlSetOutputPortDataType%block.RegBlockMethod('SetOutputPortDataType', @SetOutPortDataType);%% SetInputPortComplexSignal:% Functionality : Check and set the input and optionally the output% port complexity attributes.% C MEX counterpart: mdlSetInputPortComplexSignal%block.RegBlockMethod('SetInputPortComplexSignal', @SetInpPortComplexSig); %% SetOutputPortComplexSignal:% Functionality : Check and set the output and optionally the input% port complexity attributes.% C MEX counterpart: mdlSetOutputPortComplexSignal%block.RegBlockMethod('SetOutputPortComplexSignal', @SetOutPortComplexSig); %% PostPropagationSetup:% Functionality : Set up the work areas and the state variables. You can% also register run-time methods here.% C MEX counterpart: mdlSetWorkWidths%block.RegBlockMethod('PostPropagationSetup', @DoPostPropSetup);% -----------------------------------------------------------------% Register methods called at run-time% -----------------------------------------------------------------%% ProcessParameters:% Functionality : Call to allow an update of run-time parameters.% C MEX counterpart: mdlProcessParameters%block.RegBlockMethod('ProcessParameters', @ProcessPrms);%% InitializeConditions:% Functionality : Call to initialize the state and the work% area values.% C MEX counterpart: mdlInitializeConditions%block.RegBlockMethod('InitializeConditions', @InitializeConditions);%% Start:% Functionality : Call to initialize the state and the work% area values.% C MEX counterpart: mdlStart%block.RegBlockMethod('Start', @Start);%% Outputs:% Functionality : Call to generate the block outputs during a% simulation step.% C MEX counterpart: mdlOutputs%block.RegBlockMethod('Outputs', @Outputs);%% Update:% Functionality : Call to update the discrete states% during a simulation step.% C MEX counterpart: mdlUpdate%block.RegBlockMethod('Update', @Update);% Derivatives:% Functionality : Call to update the derivatives of the% continuous states during a simulation step.% C MEX counterpart: mdlDerivatives%block.RegBlockMethod('Derivatives', @Derivatives);%% Projection:% Functionality : Call to update the projections during a% simulation step.% C MEX counterpart: mdlProjections%block.RegBlockMethod('Projection', @Projection);%% SimStatusChange:% Functionality : Call when simulation enters pause mode% or leaves pause mode.% C MEX counterpart: mdlSimStatusChange%block.RegBlockMethod('SimStatusChange', @SimStatusChange);%% Terminate:% Functionality : Call at the end of a simulation for cleanup.% C MEX counterpart: mdlTerminate%block.RegBlockMethod('Terminate', @Terminate);%% GetOperatingPoint:% Functionality : Return the operating point of the block.% C MEX counterpart: mdlGetOperatingPoint%block.RegBlockMethod('GetOperatingPoint', @GetOperatingPoint);%% SetOperatingPoint:% Functionality : Set the operating point data of the block using% from the given value.% C MEX counterpart: mdlSetOperatingPoint%block.RegBlockMethod('SetOperatingPoint', @SetOperatingPoint);% -----------------------------------------------------------------% Register the methods called during code generation.% -----------------------------------------------------------------%% WriteRTW:% Functionality : Write specific information to model.rtw file.% C MEX counterpart: mdlRTW%block.RegBlockMethod('WriteRTW', @WriteRTW);%endfunction% -------------------------------------------------------------------% The local functions below are provided to illustrate how you may implement% the various block methods listed above.% -------------------------------------------------------------------function CheckPrms(block)a = block.DialogPrm(1).Data;if ~isa(a, 'double')me = MSLException(block.BlockHandle, message('Simulink:blocks:invalidParameter')); throw(me);end%endfunctionfunction ProcessPrms(block)block.AutoUpdateRuntimePrms;%endfunctionfunction SetInpPortFrameData(block, idx, fd)block.InputPort(idx).SamplingMode = fd;block.OutputPort(1).SamplingMode = fd;function SetInpPortDims(block, idx, di)block.InputPort(idx).Dimensions = di;block.OutputPort(1).Dimensions = di;%endfunctionfunction SetOutPortDims(block, idx, di)block.OutputPort(idx).Dimensions = di;block.InputPort(1).Dimensions = di;%endfunctionfunction SetInpPortDataType(block, idx, dt)block.InputPort(idx).DataTypeID = dt;block.OutputPort(1).DataTypeID = dt;%endfunctionfunction SetOutPortDataType(block, idx, dt)block.OutputPort(idx).DataTypeID = dt;block.InputPort(1).DataTypeID = dt;%endfunctionfunction SetInpPortComplexSig(block, idx, c)block.InputPort(idx).Complexity = c;block.OutputPort(1).Complexity = c;%endfunctionfunction SetOutPortComplexSig(block, idx, c)block.OutputPort(idx).Complexity = c;block.InputPort(1).Complexity = c;%endfunctionfunction DoPostPropSetup(block)block.NumDworks = 2;block.Dwork(1).Name = 'x1';block.Dwork(1).Dimensions = 1;block.Dwork(1).DatatypeID = 0; % doubleblock.Dwork(1).Complexity = 'Real'; % realblock.Dwork(1).UsedAsDiscState = true;block.Dwork(2).Name = 'numPause';block.Dwork(2).Dimensions = 1;block.Dwork(2).DatatypeID = 7; % uint32block.Dwork(2).Complexity = 'Real'; % realblock.Dwork(2).UsedAsDiscState = true;% Register all tunable parameters as runtime parameters. block.AutoRegRuntimePrms;%endfunctionfunction InitializeConditions(block)block.ContStates.Data = 1;%endfunctionfunction Start(block)block.Dwork(1).Data = 0;block.Dwork(2).Data = uint32(1);%endfunctionfunction WriteRTW(block)block.WriteRTWParam('matrix', 'M', [1 2; 3 4]);block.WriteRTWParam('string', 'Mode', 'Auto');%endfunctionblock.OutputPort(1).Data = block.Dwork(1).Data + block.InputPort(1).Data; %endfunctionfunction Update(block)block.Dwork(1).Data = block.InputPort(1).Data;%endfunctionfunction Derivatives(block)block.Derivatives.Data = 2*block.ContStates.Data;%endfunctionfunction Projection(block)states = block.ContStates.Data;block.ContStates.Data = states+eps;%endfunctionfunction SimStatusChange(block, s)block.Dwork(2).Data = block.Dwork(2).Data+1;if s == 0disp('Pause in simulation.');elseif s == 1disp('Resume simulation.');end%endfunctionfunction Terminate(block)disp(['Terminating the block with handle ' num2str(block.BlockHandle) '.']); %endfunctionfunction operPointData = GetOperatingPoint(block)% package the Dwork data as the entire operating point of this block operPointData = block.Dwork(1).Data;%endfunctionfunction SetOperatingPoint(block, operPointData)% the operating point of this block is the Dwork data (this method% typically performs the inverse actions of the method GetOperatingPoint) block.Dwork(1).Data = operPointData;%endfunction。

爱德思s2数学内容

爱德思s2数学内容
爱德思S2数学内容：
爱德思S2数学课程是一门旨在帮助学生建立扎实的数学基础的课程。

在这门课程中，学生将学习多个数学概念和技巧，以帮助他们发展数学思维和解决实际问题的能力。

在爱德思S2数学课程中，学生将学习以下内容：
1. 代数：学生将学习如何解方程、化简表达式、理解函数和图像以及解决实际问题。

2. 几何：学生将学习几何概念，包括平面几何和立体几何。

他们将学习如何计算面积、周长、体积等，并能够应用这些知识解决实际问题。

3. 统计学和概率论：学生将学习如何收集和处理数据，分析统计图表，并了解基本的概率概念和计算方法。

4. 数学推理和证明：学生将学习如何进行数学推理和证明，培养逻辑思维和分析问题的能力。

通过爱德思S2数学课程，学生将不仅掌握数学知识和技巧，还能培养他们的问题解决能力和数学思维。

这门课程旨在帮助学生在数学领域取得成功，并为他们将来的学习和职业发展打下扎实的数学基础。

二阶牛顿迭代法python代码实现

二阶牛顿迭代法python代码实现二阶牛顿迭代法是一种用于求解非线性方程的数值方法，它通过利用函数的二阶导数信息来逼近方程的根。

在Python中，我们可以使用以下代码实现二阶牛顿迭代法。

```pythonimport mathdef newton_method(f, f_prime, f_double_prime, x0, epsilon, max_iter): """二阶牛顿迭代法求解非线性方程的根:param f: 方程的函数:param f_prime: 方程的一阶导数函数:param f_double_prime: 方程的二阶导数函数:param x0: 初始迭代值:param epsilon: 精度要求:param max_iter: 最大迭代次数:return: 方程的根"""x = x0iter_count = 0while abs(f(x)) > epsilon and iter_count < max_iter:x = x - f_prime(x) / f_double_prime(x)iter_count += 1if abs(f(x)) <= epsilon:return xelse:return None# 示例：求解方程x^2 - 2 = 0的根def f(x):return x**2 - 2def f_prime(x):return 2 * xdef f_double_prime(x):return 2x0 = 1.5 # 初始迭代值epsilon = 1e-6 # 精度要求max_iter = 100 # 最大迭代次数root = newton_method(f, f_prime, f_double_prime, x0, epsilon, max_iter)if root is not None:print("方程的根为：", root)else:print("未找到方程的根")```在上述代码中，我们首先定义了一个`newton_method`函数，该函数接受方程的函数、一阶导数函数、二阶导数函数、初始迭代值、精度要求和最大迭代次数作为参数。

mathematica 第二类贝塞尔函数

mathematica 第二类贝塞尔函数Mathematica中计算第二类贝塞尔函数的函数名为BesselY[n,x]，其中n为阶数，x为自变量。

第二类贝塞尔函数是一种与第一类贝塞尔函数相关的特殊函数，它在物理学、工程学和应用数学中有着广泛的应用，常用于描述电磁波、声波等波动现象。

BesselY[n,x]函数的调用方式为：
```
BesselY[n,x]
```
其中，n和x分别为函数的两个参数，可以是实数或复数。

例如，计算第二类贝塞尔函数在n=2，x=3时的值，可以使用以下代码：
```
BesselY[2, 3]
```
该代码的输出结果为：
```
-0.0195634
```
Mathematica中还提供了其他一些计算第二类贝塞尔函
数的函数，如BesselYZero[n, k]可以计算第n个零点处的函数值，BesselYPrime[n, x]可以计算第二类贝塞尔函数的导数等。

这些函数可以根据具体需求来选择和使用。