sat2 math level2

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 .。

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。

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！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。