新SAT数学全解
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 .。
2024 SAT考试历年真题数学专题全解
2024 SAT考试历年真题数学专题全解2024年SAT考试数学部分依然是考生们最为担心和重视的科目之一。
为了帮助广大考生更好地应对考试，本文将为大家提供全面的2024 SAT考试历年真题数学专题全解。
通过对历年真题的详细解析，希望能够帮助考生们更好地掌握数学知识和解题技巧。
一、整数与小数整数与小数是SAT数学中一个重要的基础知识点。
在解题过程中，考生需要灵活运用整数与小数之间的转换以及四则运算等概念。
在解题过程中，考生应注意以下几点：1.了解整数与小数之间的转换关系。
2.掌握四则运算的基本规则。
3.注意小数位数计算和精确度问题。
二、代数与方程代数与方程是SAT数学中的核心内容之一。
考生需要熟练掌握代数运算的基本规则，灵活运用代数方程知识解题。
在解题过程中，考生应注意以下几点：1.理解代数方程的含义和定义。
2.熟悉代数运算的基本规则。
3.运用代数方程的性质和解题技巧。
三、几何与三角学几何与三角学是SAT数学中的另一个重要内容。
考生需要掌握几何图形的性质和运算规则，灵活运用三角学知识解题。
在解题过程中，考生应注意以下几点：1.掌握几何图形的基本性质和定义。
2.熟练运用三角学的相关概念和运算规则。
3.注意几何图形的变换和投影等问题。
四、数据与统计数据与统计是SAT数学中的重要内容之一。
考生需要了解数据分析和统计学的基本概念，掌握数据处理和统计方法。
在解题过程中，考生应注意以下几点：1.熟悉数据分析和统计学的基本概念。
2.掌握数据处理和统计方法。
3.灵活运用数据与统计知识解题。
五、概率与排列组合概率与排列组合是SAT数学中的难点之一。
考生需要掌握概率和排列组合的基本概念，灵活运用相关知识解题。
在解题过程中，考生应注意以下几点：1.理解概率和排列组合的基本概念。
2.熟悉概率和排列组合的运算规则。
3.注意概率和排列组合在实际问题中的应用。
通过对以上五个数学专题的全面解析与讲解，相信考生们已经对2024 SAT考试数学部分有了更深入的理解与掌握。
新SAT数学OG题目解读 注重考察解决实际问题的能力
新SAT数学OG题目解读注重考察解决实际问题的能力
新SAT数学考试的内容会涉及四个方面，主要是前三部分，第一部分是代数核心，第二个是实际生活中的问题解决以及统计问题，这个部分因为会涉及到实际生活中比较复杂的代数运算，所以不会让大家在非计算器使用部分去作答，而都会出现在第四个section部分。
然后第三部分是高级数学入门，第四部分是一些数学的额外话题。
小编今天为大家讲解的是下面这道新SATOG数学题目：
材料：The Official SAT Study Guide
试卷：4
页数：717
题号：14
答案: C
答案解析：这道题问的是additional money 5%比3%多的，compound monthly，第二个月的principal要加上第一个月的interest，每个月都累加算，一年一共12 months, 一个月的interest rate 就是annual interest rate/ 12，一共算12months的。
代入5%，3%，算difference.
新SATOG上的题目希望考生们能够认真对待，考试指南上的资料是非常有参考价值的内容。
新SAT数学考试题目的长度变长以及考察更多的是解决日常生活中实际问题的数学题。
所以，在考试备考中一方面应该增加数学词汇量，另一方面提升数学解决实际问题的能力，能将实际问题转换成数学公式等解决问题。
新SAT数学OG题目解读注重考察解决实际问题的能力
/forum.php?mod=viewthread&tid=373&fromuid=1
(出处: 明志论坛)。
SAT考试2024数学历年题目全解
SAT考试2024数学历年题目全解SAT考试是一项全球性的标准化考试，旨在评估学生在阅读、写作和数学方面的能力。
数学部分是SAT考试的一个重要组成部分，涵盖了各种数学概念和技巧。
本文将为您提供2024年SAT数学部分的历年题目全解，帮助您更好地应对这一考试。
第一题：题目：求解以下方程：3x + 5 = 20解析：要求解方程3x + 5 = 20，我们首先将5从等式两边减去，得到3x = 15。
然后，我们将方程两边都除以3，即x = 5。
因此，方程的解为x = 5。
第二题：题目：计算以下比例的值：5:8 = x:40解析：要计算比例5:8与x:40的值，我们可以采取交叉乘法的方法。
将5乘以40，并将结果除以8，即可求得x的值。
计算过程如下：5 * 40 / 8 = 200 / 8 = 25因此，比例5:8与x:40的值为25。
第三题：题目：已知一个等边三角形的边长为12，计算其面积。
解析：一个等边三角形的边长为12，则其高可以通过勾股定理求得。
根据勾股定理，我们有：高的平方= 边长的平方- 底边的一半的平方。
设高为h，则有 h^2 = 12^2 - (12/2)^2= 144 - 36= 108因此，高h = √108 = 6√3由于等边三角形的高等于边长的一半乘以根号3，所以面积S可以计算为：S = 1/2 * 12 * 6√3= 6 * 6√3= 36√3因此，该等边三角形的面积为36√3。
第四题：题目：在一个长方形花坛中，长度是宽度的3倍，已知宽度为2米，计算花坛的面积。
解析：我们知道长方形花坛的面积可以通过长度乘以宽度来计算。
已知宽度为2米，则长度为3 * 2 = 6米。
因此，花坛的面积为2 * 6 =12平方米。
通过以上题目的解析，我们可以看到SAT数学部分考察了各种数学概念和技巧，包括方程的求解、比例的计算、勾股定理的应用以及长方形面积的计算等。
熟练掌握这些数学知识，并能够灵活运用于实际问题的解决中，将有助于您在SAT考试中取得更好的成绩。
SAT数学真题解析
SAT数学真题解析SAT数学部分是考试中最具挑战性的部分之一，要求考生具备扎实的数学基础和解题能力。
本文将对SAT数学真题进行详细解析，帮助考生更好地应对这一部分的考试。
一、概述SAT数学部分涵盖的知识点包括代数、几何、数据分析和数学问题解决等。
题型主要包括选择题和解答题，其中选择题又分为单选和多选题。
考生在备考过程中，除了要系统学习相关知识点，还要注重解题技巧和策略的培养。
二、代数题解析代数是SAT数学部分的重点考察内容之一，下面将以一道典型的代数题为例进行解析。
Example 1:If 2x + 5 = 13, what is the value of x?解析：根据题目中的等式，我们可以求解出变量x的值。
首先，将等式中的5移到等号的另一边，得到2x = 13 - 5，即2x = 8。
接下来，我们将等式两边都除以2，得到x = 8 / 2，即x = 4。
所以，x的值为4。
三、几何题解析几何是SAT数学部分另一个重要的考察内容，下面以一道几何题进行解析。
Example 2:In triangle ABC, angle BAC = 60°, and BC = AB. What is the measureof angle BCA?解析：根据题目中给出的信息，我们需要求解角BCA的度数。
根据三角形内角和定理，三角形ABC的三个内角之和等于180度，即角BAC + 角ABC + 角BCA = 180°。
已知角BAC = 60°，并且BC = AB。
由于BC = AB，我们可以得出角ABC = 角ACB。
将以上信息代入角和的等式中，得到60° + 2角ABC = 180°。
进一步化简，得到2角ABC = 120°。
再继续化简，得到角ABC = 60°。
因为角ABC = 角ACB，所以角BCA的度数也为60°。
四、数据分析题解析数据分析是SAT数学部分的重要题型之一，要求考生对给定的数据进行分析和解读。
最新SAT数学知识讲解：三角形
最新SAT数学知识讲解：三角形这篇关于最新SAT数学知识讲解：三角形，是笔者特地为大家整理的，希望对大家有所帮助！30-60-90 TrianglesThe guy who named 30-60-90 triangles didn’t have much of an imagination. These triangles have angles of ,, and. What’s so special about that? This: The side lengths of 30-60-90 triangles always follow a specific pattern. Suppose the short leg, opposite the 30° angle, has length x. Then the hypotenuse has length 2x, and the long leg, opposite the 60° angle, has length x . The sides of every 30-60-90 triangle will follow this ratio of 1:: 2 . This constant ratio means that if you know the length of just one side in the triangle, you’ll immediately be able to calculate the lengths of all the sides. If, for example, you know that the side oppositethe 30º angle is 2 meters long, then by using the 1:: 2 ratio, you can work out that the hypotenuse is 4 meters long, and the leg opposite the 60º angle is 2meters.And there’s another amazing thing about 30-60-90 triangles. Two of these triangles joined at the side opposite the 60º angle will form an equilateral triangle. Here’s why you need to pay attention to this extra-special feature of 30-60-90 triangles. If you know the side length of an equilateral triangle, you can figure out the triangle’s height: Divide the side length by two and multiply it by. Similarly, if you drop a “perpendicular bisector” (this is the term the SAT uses) from any vertex of an equilateral triangle to the base on the far side, you’ll have cut that triangle into two30-60-90 triangles.Knowing how equilateral and 30-60-90 triangles relate is incredibly helpful on triangle, polygon, and even solids questions on the SAT. Quite often, you’ll be able to break down these large shapes into a number of special triangles, and then you can use the side ratios to figure out whatever you need to know.45-45-90 TrianglesA 45-45-90 triangle is a triangle with two angles of 45° and one right angle. It’s sometimes called an isosceles right triangle, since it’s both isosceles and right. Like the 30-60-90 triangle, the lengths of the sides of a 45-45-90 triangle also follow a specific pattern. If the legs are of length x (the legs will always be equal), then the hypotenuse has length x : Know this 1: 1:ratio for 45-45-90 triangles. It will save you time and may even save your butt.Also, just as two 30-60-90 triangles form an equilateral triangles, two 45-45-90 triangles form a square. We explain the colossal importance of this fact when we cover polygons a little later in this chapter.Similar TrianglesSimilar triangles have the same shape but not necessarily the same size. Or, if you prefer more math-geek jargon, two triangles are “similar” if theratio of the lengths of their corresponding sides is constant (which you now know means that their corresponding angles must be congruent). Take a look at a few similar triangles: As you may have assumed from the figure above, the symbol for “is similar to” is ~. So, if triangle ABC is similar to triangle DEF, we write ABC ~ DEF.There are two crucial facts about similar triangles.Corresponding angles of similar triangles are identical.Corresponding sides of similar triangles are proportional.For ABC ~ DEF, the corresponding angles areThe corresponding sides are AB/DE = BC/EF =CA/FD.The SAT usually tests similarity by presenting you with a single triangle that contains a line segment parallel to one base. This line segment creates a second, smaller, similar triangle. In the figure below, for example, line segment DE is parallel to CB, and triangle ABC is similar to triangle AE. After presenting youwith a diagram like the one above, the SAT will ask a question like this:If= 6 and=, what is?。
SAT考试数学历年真题全解2024年版
SAT考试数学历年真题全解2024年版在备考SAT考试过程中，熟悉并掌握历年真题是一项重要的任务。
通过解析历年真题，考生可以了解考试的出题风格、难度以及考察的知识点，有助于提高备考效果。
本文将为您提供2024年版本的SAT考试数学部分历年真题全解，帮助您更好地备考。
下面将根据考试的各个部分，逐一解析2024年版SAT数学部分的历年真题。
第一部分：选择题解析选择题是SAT数学部分最主要的题型，考生需要在给定的选项中选择正确答案。
以下是2024年版SAT数学选择题的解析：1. 题目描述2. 解析3. 答案解释4. 解题思路通过对每个选择题的详细解析，考生可以了解题目的解题思路、关键步骤以及答案的解释。
在解析选择题过程中，本文将注重解题思路的讲解，帮助考生更好地理解解题的方法和技巧。
第二部分：填空题解析填空题是SAT数学部分的另一种题型，与选择题不同的是，填空题要求考生填写一个具体的数值或表达式。
以下是2024年版SAT数学填空题的解析：1. 题目描述2. 解析3. 答案解释4. 解题思路通过对每个填空题的详细解析，考生可以了解填空题的解题方法和技巧。
在解析填空题过程中，本文将注重解题思路的讲解，帮助考生更好地理解解题的方法和技巧。
第三部分：解答题解析解答题是SAT数学部分的较难题型，要求考生根据题目给出的条件和要求，用数学方法进行解答。
以下是2024年版SAT数学解答题的解析：1. 题目描述2. 解答步骤3. 解答思路4. 结论通过对每个解答题的分步解析，考生可以了解解答题的解题方法和技巧。
在解析解答题过程中，本文将注重解答步骤和思路的讲解，帮助考生更好地理解解题的方法和技巧。
结语通过对2024年版SAT数学部分历年真题的全面解析，考生可以更加深入地了解考试的出题方式和要求，提高备考效果。
同时，解析中的解题思路和技巧也可以帮助考生更好地掌握数学知识和解题方法。
在备考过程中，考生可以结合解析内容进行针对性的练习和复习，提高数学部分的得分。
SAT考试2024数学历年真题全视角
SAT考试2024数学历年真题全视角SAT考试是全球范围内备受关注的一项重要考试，对于申请美国高校的学生来说具有重要的意义。
而数学部分一直是考生们普遍关注的焦点。
本文将全面深入地探讨SAT考试2024年数学部分的历年真题，带您以全视角认识这一难点。
通过对历年真题的分析，希望能够为考生们提供一些有益的建议和解题思路，提高大家的数学水平。
1. Algebra（代数）代数部分是SAT数学部分的重头戏之一，其中包含了一系列高中数学的基本知识和概念。
历年真题中常涉及到的内容包括方程、不等式、函数以及图形等。
这些题目往往要求考生熟练掌握求解方程、图像分析和函数变化等技巧。
例题：给定一个二次方程 y = ax^2 + bx + c，已知该二次方程的图像经过点 P(1, 4) 和 Q(3, 16)，求 a、b 和 c 的值。
解析：根据已知条件，我们可以列出两个方程：4 = a + b + c （代入点P的坐标）16 = 9a + 3b + c （代入点Q的坐标）通过联立这两个方程进行求解，我们可以得到 a、b 和 c 的值。
这类题目常涉及二次方程的性质和应用，需要考生熟练掌握解二次方程、理解二次函数图像等知识点。
2. Geometry（几何）几何部分是SAT数学部分的另一个重要内容，主要考察学生对几何概念、图形性质和几何推理的理解。
历年真题中的几何题目大多数是多步解题，需要考生利用几何知识进行推理和分析。
例题：在一个平面直角坐标系中，点 A(-3, 2) 和点 B(4, -1) 分别为线段 AB 的两个端点。
如果点 C(-1, -5) 在线段 AB 上，求点 C 的坐标。
解析：通过计算 AB 的斜率和 AC 的斜率可以判断点 C 是否在线段AB 上。
然后可以通过线段的中点公式来计算点 C 的坐标。
此类题目要求考生掌握直线和线段的性质、坐标点的计算等知识，能够熟练运用它们来解答几何问题。
3. Data Analysis（数据分析）数据分析部分是近年来SAT数学部分中新增的一部分内容，主要考察考生对数据收集、理解和分析的能力。
2024年SAT考试数学真题深度解读
2024年SAT考试数学真题深度解读在2024年的SAT考试数学部分中，出现了一系列挑战性的问题，涵盖了几个重要的数学概念和技巧。
本文将对这些问题进行深度解读，帮助同学们更好地理解题目，并为他们提供解题思路和解题技巧。
问题1：在一个三角形ABC中，角A的度数是50。
已知边AB与BC的长度分别为5和8，求边AC的长度。
解析：首先，我们可以利用三角形的角度之和为180度的性质，求得角B为130度。
然后，我们可以使用余弦定理来求解边AC的长度。
根据余弦定理，我们有：AC^2 = AB^2 + BC^2 - 2 * AB * BC * cosA代入已知值，我们可以得到：AC^2 = 5^2 + 8^2 - 2 * 5 * 8 * cos50通过计算，我们可以得到AC的长度为约9.18。
问题2：已知函数f(x) = 2x^3 + 3x^2 - 4x + 1，求f'(2)的值。
解析：我们需要求函数f(x)在x = 2处的导数值，即f'(2)。
首先，我们对函数f(x)进行求导，得到f'(x) = 6x^2 + 6x - 4。
然后，将x = 2代入f'(x)中，我们可以计算得到f'(2)的值为28。
问题3：已知一个等差数列的第一个项为a，公差为d。
如果这个数列的第100项是200，求a和d的值。
解析：由于等差数列的通项公式为an = a + (n - 1)d，我们可以得到第100项的表达式a + 99d = 200。
而且，我们还知道该数列的第1项即为a，因此可以得到第1项的表达式a + 0d = a。
由题意可知，第100项与第1项的差值为99d，即200 - a = 99d。
将这两个方程组合起来，我们可以得到一个二元一次方程组：a + 99d = 200200 - a = 99d通过求解这个方程组，我们可以得到a的值为101，d的值为1。
问题4：某公司的销售额在过去的几年呈现如下的增长趋势：2019年为100万，2020年为120万，2021年为140万。
SAT数学考点讲解之如何求解多项函数
SAT数学考点讲解之如何求解多项函数今天三立在线教育SAT网为大家带来的是SAT数学考点讲解之如何求解多项函数的相关资讯，备考的烤鸭们，赶紧来看看吧！SAT数学多项式函数考点实例A polynomial function P has zeros -3,3/2,and 8. Which of the following polynomial functions could define P?多项式函数P存在-3,3/2,8三个零点，则P的多项式函数是以下哪一个?A. P(x)=-3(x-3/2)(x-8)B.P(x)=-(x-3)(x+3/2)(x+8)C. P(x)=(x+3)(3x-2)(x-8)D.P(x)=(x+3)(2x-3)(x-8)答案：D解析：Recall that if K is a zero of a polynomial function defined as y=f(x), then x-k is a factor of f.要牢记，如果K是函数y=f(x)的零点，则x-k是函数f的一个因式Since the polynomial function P has the zeros -3,3/2,and 8,it follows that(x-(-3)),(x-3/2),and (x-8) must be factors of P.既然该多项式函数P有-3,3/2,8三个零点，则可得到(x-(-3)),(x-3/2), (x-8)都是P的因式。
Therefore, we can define P as P(x)=a(x+3)(x-3/2)(x-8), where a is a nonzero constant.所以，我们可以定义函数P为P(x)=a(x+3)(x-3/2)(x-8), 其中a是非零常量。
A constant factor, such as a, does not affect the zeros of the polynomial function. In order to rewrite the equation with integral coeffecients, let a=2.最后一步，用整数系数改写一下该方程。
SAT考试2024数学历年题目精讲
SAT考试2024数学历年题目精讲在本篇文章中，我们将重点讲解SAT考试2024年数学部分的历年题目。
我们将按照题目类型进行分类，并为每个题型提供详细的解答和解题技巧，帮助考生更好地应对这些题目。
一、单选题1. 题目描述：某汽车展厅共展出了150辆汽车，其中的三分之一是SUV车型，四分之一是轿车车型，其余的是其他车型。
问展厅中轿车车型的数量是多少？解答与技巧：首先，计算出SUV车型的数量：150 * (1/3) = 50辆。
然后，计算出其他车型的数量：150 - 50 - 150 * (1/4) = 50辆。
所以，轿车车型的数量是50辆。
2. 题目描述：某商场举办了一次打折活动，原价100元的商品现在只需80元购买。
如果小明购买了3件该商品，他需要支付多少钱？解答与技巧：首先，计算出每件商品的折扣金额：100 - 80 = 20元。
然后，计算出小明需要支付的金额：3 * 20 = 60元。
所以，小明需要支付60元。
二、多选题1. 题目描述：以下哪些数是正整数？（A）-1（B）0（C）1（D）2解答与技巧：在SAT考试中，如果题目要求选择多个选项，我们需要仔细审题。
在这个题目中，需要选择正整数，所以选项B和A都不是正整数。
所以正确答案是（C）和（D）。
2. 题目描述：以下哪些图形具有对称性？（A）正方形（B）长方形（C）圆形（D）三角形解答与技巧：我们需要判断每个选项是否具有对称性。
在这个题目中，正方形和圆形都具有对称轴，所以正确答案是（A）和（C）。
三、填空题1. 题目描述：若a + a^-1 = 5，求a^2 + a^-2的值。
解答与技巧：首先，我们可以对等式两边进行平方操作，得到a^2+ 2 + a^(-2) = 25。
然后，我们需要解方程，将等式左边与右边的常数项进行抵消，得到a^2 + a^(-2) = 23。
2. 题目描述：某比赛共有10个选手参加，其中3个选手退出比赛，剩余的选手中将决出第一名、第二名和第三名。
SAT考试专题2024数学历年题目解析
SAT考试专题2024数学历年题目解析2024年的SAT考试将继续囊括数学科目，下面将对该年度的数学部分历年题目进行解析，帮助考生更好地准备SAT数学考试。
1. 第一题解析该题目是一道代数题，要求求解方程：3x + 5 = 20。
解题思路：将方程中的变量与常数项分离，得到：3x = 20 - 5。
计算得：3x = 15，再将等式两边同时除以3，得到：x = 5。
因此，方程的解为x = 5。
2. 第二题解析该题目是一道几何题，要求计算三角形的面积。
解题思路：已知三角形的底边长度为6，高为8。
直接使用三角形面积公式：面积 = 底边长度 ×高 ÷ 2。
代入已知的数值进行计算：面积 = 6 × 8 ÷ 2 = 24。
因此，该三角形的面积为24平方单位。
3. 第三题解析该题目是一道概率题，要求计算从一副标准扑克牌中随机抽取一张牌，该牌为红桃的概率。
解题思路：一副标准扑克牌中共有52张牌，其中有13张红桃牌。
因此，红桃牌的概率为：概率 = 红桃牌数目 ÷总牌数目。
代入已知数值进行计算：概率 = 13 ÷ 52 = 1 ÷ 4 = 0.25。
因此，从一副标准扑克牌中随机抽取一张牌，该牌为红桃的概率为0.25。
4. 第四题解析该题目是一道函数题，要求计算函数的值。
解题思路：已知函数 f(x) = 2x^2 + 3x + 1，需要计算当 x = 2 时的函数值。
将 x = 2 代入函数表达式中，得到：f(2) = 2 × 2^2 + 3 × 2 + 1。
计算得：f(2) = 8 + 6 + 1 = 15。
因此，当 x = 2 时，函数 f(x) 的值为15。
5. 第五题解析该题目是一道统计题，要求根据给定的数据计算平均数。
解题思路：已知一组数据为：10, 12, 15, 18, 20。
需要计算这组数据的平均数。
平均数的计算公式为：平均数 = 总和 ÷数据个数。
SAT数学题型全解析
SAT数学题型全解析SAT（Scholastic Assessment Test）是美国大学入学考试，其中数学部分是SAT数学考试。
SAT数学考试主要测试学生在数学领域的基本知识和解决问题的能力。
本文将全面解析SAT数学考试的各种题型，并给出相应解题策略和技巧。
一、选择题SAT数学考试中的选择题分为两种：无计算器部分和有计算器部分。
无计算器部分包括多项式、代数、几何和数据分析等题型，而有计算器部分包括数据分析和统计、概率和二次方程等题型。
1. 多项式题型多项式题型主要考察学生对多项式的理解和运算能力。
解题技巧包括：- 将多项式展开，化简，合并同类项；- 利用因式分解；- 利用韦达定理求根等。
2. 代数题型代数题型主要考察学生的代数运算和方程组的解题能力。
解题技巧包括：- 利用等式的性质进行等式推导；- 运用代数运算规则，如消元法、合并同类项等；- 运用代数方程的求解方法，如变量替换、联立方程等。
3. 几何题型几何题型主要考察学生对几何形状和关系的理解和分析能力。
解题技巧包括：- 运用几何形状的性质和定理，如角度的性质、平行线的性质等；- 利用图形的特点进行推理和证明；- 运用三角形的性质和相似三角形的判定等。
4. 数据分析题型数据分析题型主要考察学生对数据的理解和分析能力。
解题技巧包括：- 对数据进行图表分析，如线图、柱状图、饼图等；- 运用统计学的相关概念和方法，如平均值、中位数、标准差等；- 运用概率的知识进行问题求解。
二、解答题解答题在SAT数学考试中占比较小，主要考察学生的解决实际问题的能力和应用数学知识的能力。
解答题的解题步骤和策略如下：- 仔细阅读问题，理解问题的要求和条件；- 找到解题思路，确定解题方法和公式；- 进行计算或推导，得到解答并进行合理的估算；- 检查答案是否符合问题的要求，并对解题过程进行合理的陈述。
总之，SAT数学考试是对学生数学知识和解决问题能力的综合考察，掌握相应的解题技巧和策略对于考试的成功至关重要。
SAT 数学(2020) 附答案和解析
SAT 数学（2020）附答案和解析MathematicsA polynomial function f has x+8 as a factor. Which of the followingbe true about the function f?I.f(0)=8II.f(8)=0III.f(-8)=0A.I onlyB.II onlyC.III onlyD.II and III only答案：C解析：Choice C is correct. Recall that if x-k is a factor of a polynomial P, then P(k)=0.It is given that x+8 or x-(-8) is a factor of f.Therefore, it follows that f(-8)=0.It is not known whether or not x-8 is a factor of f and so we cannot say w hether or not f(8)=0.Additionally, no other information about function f is given, and so we d o not know whether or not f(0)=8.Therefore, I and II may or may not be true, but III must be true.MathematicsA taxi ride cost a customer a total of $13.48, which included 4% sales tax and a $1 surcharge after the tax. What was the subtotal before the surch arge and sales tax?A.$0.48B.$12.00C.$12.96D.$312.00答案：B解析：Option B is correct. The total minus the surcharge is 13.48-1, or 12.48 d ollars. The subtotal before tax and surcharge is then 12.48 divided by the decimal equivalent of the sales tax percentage,0.04, plus 1, or 12.48/1.04.MathematicsIn a recent study to determine how often people in different parts of the United States check the weather, a random sample of residents in New England and a random sample of residents on the West Coast were surve yed. The study found over 90% of people surveyed in New England chec ked the weather daily, while 70% of people surveyed on the West Coast d id so. If the margin of error of both samples were the same, which of the following statements is best supported by the study's findings?A.People in New England check the weather more often because the clim ate is colder than on the West Coast.B.People in New England check the weather more often because there is more weather coverage on television than there is on the West Coast.C.There is evidence that people in New England check the weather more often than people on the West Coast.D.There is evidence that people in New England check the weather on th eir smartphones more than do people on the West Coast.答案：C解析：Choice C is correct. A sample survey is a study that obtains data from a s ubset of a population, usually through a questionnaire or interview, in o rder to estimate population attributes.Since the margin of error is the same for each sample, the only reasonab le conclusion based on the data from the observational study is that there is evidence (although not a guarantee) that people in New England chec k the weather more often than people do on the West Coast.Mathematics>Standard Multiple ChoiceRead the following SAT test question and then click on a button to select your answer.A consumer-monitoring service wants to determine television viewing h abits among 18- to 29-year-olds in a particular city. Which of the follow ing survey methods is most likely to produce valid results?A.Select a random sample of 1000 18- to 29-year-olds in that city.B.Select a random sample of 100018- to 29-year-olds in that city who attended a computer camp when they were in high school.C.Select a random sample of 100018- to 29-year-olds in that city who played a varsity sport in high school.D.Select a random sample of 100018- to 29-year-olds in that city who played chess in high school.答案：A解析：Choice A is correct. In order to produce unbiased, valid data, the sampl e should berandomly selected and be representative of the entire population of int erest. In this case, an appropriately conducted survey should give each co nsumer aged 18 to 29years in the city an equal chance of being surveyed.The choices that involve a particular high school, the chess team, and co mputer campers would not be representative of the entire population of 18- to 29-year-olds inthe city.Mathematics>Standard Multiple ChoiceRead the following SAT test question and then click on a button to select your answer.(a+3)(2a^2-5a+7)Which of the following is equivalent to the expression above?A.2a^3-5a+21B.2a^3+a^2-8a+21C.2a^3+6a^2-5a+7D.2a^3+11a^2+22a+21答案：B解析：Choice B is correct. When multiplying polynomials, be sure to multiply e ach term in the first polynomial by each term in the second polynomial. This can be done as follows:(a+3)(2a^2-5a+7)=2a^3-5a^2+7a+6a^2-15a+21Combine like terms to get:2a^3+a^2-8a+21The equivalent expression is 2a^3+a^2-8a+21.Mathematics>Standard Multiple ChoiceRead the following SAT test question and then click on a button to select your answer.Karim has a $35 gift card to his favorite restaurant. The tax on his meal is 14.3%. Karim would also like to leave a $5 tip. If c represents Karim's pretax bill, in dollars, and he wants to pay the entire meal amount, including tip and tax, using the gift card, which of the following inequalities best m odels the situation described above?A.1.143c-5≥35B.1.143c+5≤35C.0.143c-5≤35D.0.143c+5≥35答案：B解析：Choice B is correct. Karim's total meal cost consists of three parts: Karim' s pretax bill, the tax, and the tip, all added together. That amount will nee d to be less than or equal to Karim's gift card amount.Since c represents the cost, in dollars, of the pretax bill, it should be multi plied 0.143(the tax in decimal form). Since Karim has decided to tip $5, the total me al cost can be represented by the expression space c+0.143c+5.Next, combine like c terms to get 1.143c. So, the final inequality for Kar im's situation is 1.143c+5≤35.Mathematics>Standard Multiple ChoiceRead the following SAT test question and then click on a button to select your answer.y^2-y-3(1-x)y=2xIf (x1,y1) and (x2,y2) are two distinct solutions to the system of equation s shown above, what is the sum of x1 and x2?A.-1/4B.1/4C.1D.-1答案：A解析：Choice A is .。
新SAT评分详解及样题
* Combined score of two raters, each scoring on a 1– 4 scale 1-4
SAT 1. Composite Score 2 2. SAT raw score 3 3. SAT Test Score Evidence-Based Reading and Writing raw score 4. SAT Studies OG 1—15 5. SAT Subscore 7 Cross-section Score 3 Section Score 400—1600
3.
)
25+15min 49
:35min 44
2-12 25min
2-8 50min
History Questions 1-5 are based on the following passage.
This passage is adapted from a speech delivered by Congresswoman Barbara Jordan of Texas on July 25, 1974, as a member of the Judiciary Committee of the United States House of Representatives. In the passage, Jordan discusses how and when a United States president may be impeached, or charged with serious offenses, while in office. Jordan’s speech was delivered in the context of impeachment hearings against then president Richard M. Nixon.
新SAT数学符号解析 新SAT数学符号对应的中英文表示
新SAT数学考试中符号是同学们理解题目的关键，如果对不上号，那么一切都是白搭了，下面分享SAT数学中所有可能考到的符号及其中英文表示，还记不住的小伙伴们每天拿出来看几眼吧！符号+ plus加号；正号- minus减号；负号± plus or minus正负号× is multiplied by乘号÷ is divided by除号＝is equal to等于号≠ is not equal to不等于号≡ is equivalent to全等于号≌ is equal to orapproximately equalto等于或约等于号≈ is approximately equal to约等于号＜is less than小于号＞is greater than大于号≮ is not less than不小于号≯ is not more than不大于号≤ is less than or equal to小于或等于号≥ is more than or equal to大于或等于号% per cent百分之…‰ per mill千分之…∞ infinity无限大号∝ varies as与…成比例√ (square) root平方根∵ since; because因为∴ hence所以∷ equals, as(proportion)等于，成比例∠ angle角≲ semicircle半圆≰ circle圆○ circumference圆周π pi 圆周率△ triangle三角形≱ perpendicular to垂直于∪ union of并，合集∩ intersection of 交，通集∫ the integral/differentialof …的积/微分∑ (sigma) summation of总和° degree度′ minute分″ second秒℃ Celsius system摄氏度{ open brace, open curly左花括号} close brace, close curly右花括号( open parenthesis, open paren左圆括号) close parenthesis, close paren右圆括号() brackets/ parentheses括号[ open bracket 左方括号] close bracket 右方括号[] square brackets方括号| vertical bar, vertical virgule竖线& ampersand, and, reference, ref和，引用* asterisk, multiply, star, pointer星号，乘号，星，指针/ slash, divide, oblique 斜线，斜杠，除号// slash-slash, comment 双斜线，注释符# pound井号\ backslash, sometimes escape反斜线转义符，有时表示转义符或续行符~ tilde波浪符. period, dot, full stop句号, comma逗号: colon冒号; semicolon分号? question mark问号! exclamation mark (英式英语)exclamation point (美式英语)' apostrophe撇号- hyphen连字号-- dash 破折号... dots/ ellipsis省略号" single quotation marks 单引号"" doublequotation marks 双引号‖ parallel 双线号& ampersand = and～swung dash 代字号§ section; division 分节号→ arrow 箭号；参见号上海托福培训多少钱?这个问题是学生和家长在考虑培训学校时主要考虑的问题。
最新SAT数学知识讲解：三角形
这篇关于最新SAT数学知识讲解：三⾓形，是⽆忧考特地为⼤家整理的，希望对⼤家有所帮助！30-60-90 Triangles The guy who named 30-60-90 triangles didn’t have much of an imagination. These triangles have angles of,, and. What’s so special about that? This: The side lengths of 30-60-90 triangles always follow a specific pattern. Suppose the short leg, opposite the 30° angle, has length x. Then the hypotenuse has length 2x, and the long leg, opposite the 60° angle, has length x. The sides of every 30-60-90 triangle will follow this ratio of 1:: 2 . This constant ratio means that if you know the length of just one side in the triangle, you’ll immediately be able to calculate the lengths of all the sides. If, for example, you know that the side opposite the 30º angle is 2 meters long, then by using the 1:: 2 ratio, you can work out that the hypotenuse is 4 meters long, and the leg opposite the 60º angle is 2meters. And there’s another amazing thing about 30-60-90 triangles. Two of these triangles joined at the side opposite the 60ºangle will form an equilateral triangle. Here’s why you need to pay attention to this extra-special feature of 30-60-90 triangles. If you know the side length of an equilateral triangle, you can figure out the triangle’s height: Divide the side length by two and multiply it by. Similarly, if you drop a “perpendicular bisector” (this is the term the SAT uses) from any vertex of an equilateral triangle to the base on the far side, you’ll have cut that triangle into two 30-60-90 triangles. Knowing how equilateral and 30-60-90 triangles relate is incredibly helpful on triangle, polygon, and even solids questions on the SAT. Quite often, you’ll be able to break down these large shapes into a number of special triangles, and then you can use the side ratios to figure out whatever you need to know. 45-45-90 Triangles A 45-45-90 triangle is a triangle with two angles of 45° and one right angle. It’s sometimes called an isosceles right triangle, since it’s both isosceles and right. Like the 30-60-90 triangle, the lengths of the sides of a 45-45-90 triangle also follow a specific pattern. If the legs are of length x (the legs will always be equal), then the hypotenuse has length x: Know this 1: 1:ratio for 45-45-90 triangles. It will save you time and may even save your butt. Also, just as two 30-60-90 triangles form an equilateral triangles, two 45-45-90 triangles form a square. We explain the colossal importance of this fact when we cover polygons a little later in this chapter. Similar Triangles Similar triangles have the same shape but not necessarily the same size. Or, if you prefer more math-geek jargon, two triangles are “similar” if the ratio of the lengths of their corresponding sides is constant (which you now know means that their corresponding angles must be congruent). Take a look at a few similar triangles: As you may have assumed from the figure above, the symbol for “is similar to” is ~. So, if triangle ABC is similar totriangle DEF, we write ABC ~ DEF. There are two crucial facts about similar triangles. Corresponding angles of similar triangles are identical. Corresponding sides of similar triangles are proportional. For ABC ~ DEF, the corresponding angles areThe corresponding sides are AB/DE = BC/EF = CA/FD. The SAT usually tests similarity by presenting you with a single triangle that contains a line segment parallel to one base. This line segment creates a second, smaller, similar triangle. In the figure below, for example, line segment DE is parallel to CB, and triangle ABC is similar to triangle AE. After presenting you with a diagram like the one above, the SAT will ask a question like this: If= 6 and=, what is。
美国高考sat数学试题及答案
美国高考sat数学试题及答案美国高考SAT数学试题及答案1. 某商店进行促销活动，所有商品打8折。
如果一件商品原价为$50，那么打折后的价格是多少？A. $40B. $45C. $35D. $20答案：B2. 一个长方形的长是宽的两倍，如果宽为$x$，那么长方形的周长是多少？A. $6x$B. $4x$C. $2x$D. $8x$答案：A3. 如果一个数的平方等于36，那么这个数是多少？A. 6B. -6C. 6 或 -6D. 0答案：C4. 在一次数学测试中，平均分是75分。
如果一个学生得了80分，那么他的分数比平均分高了多少？A. 5分B. 10分C. 15分D. 20分答案：A5. 一个圆的半径是5厘米，那么这个圆的面积是多少平方厘米？A. 25πB. 50πC. 75πD. 100π答案：B6. 如果一个函数$f(x) = 2x + 3$，那么$f(-1)$的值是多少？A. -1B. 1C. 5D. 7答案：B7. 一个等差数列的首项是3，公差是2，那么这个数列的第10项是多少？A. 23B. 21C. 19D. 17答案：A8. 如果一个三角形的两边长分别是5和7，且这两边夹角是90度，那么这个三角形的面积是多少？A. 12.5B. 15C. 17.5D. 20答案：A9. 如果一个函数$g(x) = x^2 - 4x + 3$，那么这个函数的最小值是多少？A. -1B. 0C. 1D. 3答案：A10. 在一个装有红球和蓝球的袋子里，红球和蓝球的比例是2:3。
如果随机抽取一个球，抽到红球的概率是多少？A. 2/5B. 3/5C. 4/5D. 1/2答案：A结束语：以上是美国高考SAT数学部分的试题及答案，希望对准备参加SAT考试的学生有所帮助。
SAT 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 SummaryMathematics 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 , the expression is equivalent to the expression . As gets infinitelylarger, the expression approaches the value , so as gets infinitely larger, the expressionapproaches 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 find the 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 the height, 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 equationfor 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 same height. 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 tomore 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 Januaryto 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 twosides 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 thelarger 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 angleof 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 with vertex 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 twopeople, neither of whom has brown eyes, is : there are ways to choose a first person andways to choose a second person, but there are ways in which that same pair of people could bechosen. 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 given in 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 hashow 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 expression is 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 orcorresponds 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 Mayis .Therefore, the day with the greatest number of hours of daylight hasmore daylight hours than May .。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
新SAT数学全解
在以往SAT各科考试中，数学一直是中国学生以引为傲的优势科目。
与美国学生相比，中国学生普遍数学知识和计算能力非常扎实，取得800分的成绩并不鲜见。
然而随着2016年1月旧SAT最后一次考试结束，SAT考试将全面改革。
那么新SAT考试登场，中国学生是否还能继续延续以往在数学科目上的优势，首先让我们一起来看看新SAT数学做了哪些改变！考试形式总体上发生了比较大的变化，比较明显的是计分标准、题目长度和考察知识点。
虽然考试时间增加10min，但是总题目数也增加4道，同时易错的填空题增加了3道。
中国学生普遍数字计算能力较强，所以是否使用计算器相信影响并不是很大，但是考场上分秒必争，如何精简做题步骤，提高做题效率则是那么在最重要的考试内容和题型方面，到底新SAT数学做了哪些变化，这些变化对学生备考有什么影响。
考察知识点
1. 新旧SAT知识点变化：
新SAT去掉了对于数字或者公式本身的运算考查以及经常让同学们头疼的排列组合题目。
然而，新增了一些部分同学没有接触过或者很少使用的知识点如：置信区间，抛物线趋势等。
不过大家不用担心，这部分知识点大家只需要知道并理解概念即可，并不需要同学们去实际计算。
2. 知识点全分布
很多同学看到CB给出的新SAT数学知识点分类会感到无从下手，其实CB的分类主要是根据考查学生在数学技能、实际应用以及是否已经具备好进入高等学府学习的知识储备方面来划分的;
第一部分为代数核心，顾名思义是围绕代数相关的知识，主要包括常变量、不等式、一次方程等；
第二部分解决问题和分析数据，主要考查学生在实际生活中运用数学知识和思维解决问题的能力（包括阅读图表），这个部分题目因为会涉及到与实际相关的比较复杂的运算，所以只会出现在可以使用计算器的部分；
第三部分通往高等数学，包括对复杂的函数和方程等的考查，检测学生是否有能力进入STEM（Science, technology,engineering and math）领域进行更深入的学习；
第四部分附加内容，主要涉及一些额外知识点，这个部分内容是不计入Subscore评分的，其中主要包括平面、解析几何以及三角函数和虚数的基础知识内容。
四个部分分别对应考查学生不同方面的能力以及对同一知识点不同层级的掌握。
那么新SAT实际上究竟考查哪些知识点呢？
方程、函数，不等式，代数式变化以及比例等能够与实际问题紧密结合的知识点的考查比重较大。
不过大家并不需要太过担心，这些知识点中国学生在初高中基本已经学过，并且题目难度相比初高中练习题可要简单不少。
只不过在题目阅读量增加的前提下，学生必须非常
熟练的掌握上面提到的每一个知识点的概念以及相关公式，才能在有限的时间内完成所有题目。
题目分析及策略
新SAT数学不仅在知识点考查方面更加贴近实际生活应用，包括题目和题型也变得更加接地气。
最明显的表现是题目长度大大增加，单词难度加大，长句出现频率增加，这对学生的阅读能力和速度提出了更高的要求。
阅读量增加
新SAT数学平均每道题字数增长约10个字左右，最长的题有330字。
与美国学生相比，以往中国学生赢在数学知识和计算能力，但中国学生在专业英语词汇量、与实际生活联系、逻辑思维、批判性思维阅读上与美国学生存在很大差距。
所以，在单词方面，学生首先要对数学专业词汇以及常见表达熟练掌握，同时在平常也需要更多积累其他STEM相关领域词汇和背景知识。
针对题目中的长句，则需要快速理解题意辨识出考查的知识点，然后分析句子结构，迅速剥离出与解题相关的数据信息。
包括题目最后的问题也会经常出现在长句中，如果句子没有读懂，那么很有可能会减缓做题速度甚至会影响解题切入点。
例题：
An online store receives customer satisfaction ratings between 0 –100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings.
题目主要意思为：一家在线商店会收到评分为0-100分之间的顾客满意度评价，收到的前10个评价得分平均为75，如果要保证前20个评价的平均得分为85，商店收到的第11个评价的最少为多少分？
大家可以发现题目非常贴近我们的生活，在网购如此发达的中国，相信大家作为买家都给过店家评价吧。
在这道题中，商店需要计算好评率。
这类题我们都可以看做“应用题”，解答应用题首先需要将题目给出的情境抽象化：
在0-100中先按顺序选择10个数，他们的平均数为75，如果再依次选择10个数，为了保证这20个数的平均数为85，第11个数最少应该是几？
然后再根据我们已经掌握的相关知识点解题即可。
题目的内容和形式更加多样化
与实际生活、工作相结合
要求：积累与留心更多社会常识与经验
例题：
A bank has opend a new branch and ,as part of a promotion, the bank branch is offering $1,000 certificates of deposit at an interst rate of 4% per year, compounded semiannually. The bank is selling certificates with terms of 1,2,3 or 4 years. Which of the following fuctions gives the total amount, A, in dollars, a customer will receive when a certificate with a term of k years is finnally paid.
A) A= 1,000(1+0.04K)
B) A=1,000(1+0.08K)
C) A=1,000(1.04)k
D) A=1,000(1.04)2k
解读：银行几乎与每个人的生活都息息相关，存款利率与收益具体如何计算则是这道题考查的重点。
例题：
The cost of using a telephone in a hotel meeting room is $0.20 per minute. Which of the following equations represents the total cost c, in dollars, for h hours of phone use?
A) c = 0.20(60h)
B) c = 0.20h+60
C) c = 60h/0.20
D) c = 0.20h/60
解读：在实际生活中，在酒店除了房间费用，其他费用包括电话，mini-bar里的食品，甚至网络都是要收取相应费用的。
这道题则是需要我们根据题目提供的信息建立酒店会议室电话费的计算公式。
图表题增加
要求：提高解读和整合数据能力
扫描二维码限时获取免费视频课程。
来源于：时代焦点。