SatMath

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°。

SAT数学模拟练习题及答案SAT考试数学练习题SAT Math Practice Test 21. Which of the following could be a value of x, in the diagram above?A. 10B. 20C. 40D. 50E. any of the above2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?A. 10B. 15C. 20D. 25E. 303. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?A. 5 : 1B. 10 : 5C. 15 : 2D. 20 : 2E. 25 : 24. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?A. 2.5πB. 3πC. 5πD. 4πE. 10π5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?A. 4B. 7C. 8D. 12E. it cannot be determined from the information given.6. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?A. f(-1)B. f(0)C. f(1)D. f(3)E. f(4)7. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?A. 2.25B. 3C. 4D. 4.5E. 68. If n ≠ 0, which of the following must be greater than n?I 2nII n2III 2 - nA. I onlyB. II onlyC. I and II onlyD. II and III onlyE. None9. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?A. 20B. 15C. 8D. 5E. 3.210. n and p are integers greater than 15n is the square of a number75np is the cube of a number.The smallest value for n + p isA. 14B. 18C. 20D. 30E. 50参考答案见下一页1.Correct Answer: BExplanation:The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB.Also ABC is not a straight line and must be less than 180.Therefore 90 < 5x < 180The only value of x which satisfies this relation is 20.2.Correct Answer: AExplanation:20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.3.Correct Answer: EExplanation:Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.Now US : Indian = 25 : 10, and Indian : British = 10 : 2Hence the two ratios can be combined and US : British = 25 : 24.Correct Answer: CExplanation:Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore, 5.Circumference = π.diameter = 5π5.Correct Answer: DExplanation:If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets as n + (n + 1) + (n + 2) + (n + 3 ) and(n + 3) + (n + 4) + (n + 5) + (n + 6)Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 126.Correct Answer: DExplanation:You can solve this by back solving – substitute the answer choices in the expression and see which gives the greatest value.satA (-1 + 2) / (-1-2) = -2 / 2 = -1;B (0 + 2) / (0-2) = 2/ -2 = -1;C (1 + 2) / (1-2) = 3/-1 = -3;D (3 + 2) / (3-2) = 5/1 = 5;E (4+ 2) / (4-2) = 6/2 = 3If you had just chosen the largest value for x you would have been wrong. So although it looks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.7.Correct Answer: DExplanation:(Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral9 - (2 x x 3 x 1.5) = 4.58.Correct Answer: EExplanation:Remember that n could be positive negative or a fraction. Try out a few cases:In case I, if n is -1, then 2n is less than n.In case II, if n is a fraction such as then n2 will be less than n.In case III, if n is 2, then 2-n = 0, which is less than n.Therefore, none of the choices must be greater than n9.Correct Answer: CExplanation:If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 810.Correct Answer: AExplanation:The smallest value for n such that 5n is a square is 5.75np can now be written as 75 x 5 x p.This gives prime factors.... 3 x 5 x 5 x 5 x pTo make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9n + p = 5 + 9 = 14文档内容到此结束，欢迎大家下载、修改、丰富并分享给更多有需要的人。

数学英语词汇数学mathematics, maths(BrE), math(AmE)公理axiom 定理theorem 计算calculation 运算operation 证明prove假设hypothesis, hypotheses(pl.) 命题proposition 算术arithmetic 加plus(prep.), add(v.), addition(n.) 被加数augend, summand 加数addend 和sum 减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend 减数subtrahend 差remainder乘times(prep.), multiply(v.), multiplication(n.) 被乘数multiplicand, faciend 乘数multiplicator 积product 除divided by(prep.), divide(v.), division(n.) 被除数dividend 除数divisor 商quotient等于equals, is equal to, is equivalent to 大于is greater than 小于is lesser than 大于等于is equal or greater than 小于等于is equal or lesser than 运算符operator 数字digit 数number 自然数natural number 整数integer 小数decimal 小数点decimal point 分数fraction 分子numerator 分母denominator 比ratio正positive 负negative 零null, zero, nought, nil 十进制decimal system 二进制binary system 十六进制hexadecimal system 权weight, significance 进位carry 截尾truncation 四舍五入round 下舍入round down 上舍入round up 有效数字significant digit 无效数字insignificant digit 代数algebra 公式formula, formulae(pl.) 单项式monomial 多项式polynomial, multinomial 系数coefficient 未知数unknown, x-factor, y-factor, z-factor 等式，方程式equation 一次方程simple equation 二次方程quadratic equation 三次方程cubic equation 四次方程quartic equation 不等式inequation 阶乘factorial 对数logarithm 指数，幂exponent 乘方power 二次方，平方square 三次方，立方cube 四次方the power of four, the fourth power n 次方the power of n, the nth power 开方evolution, extraction 二次方根，平方根square root 三次方根，立方根cube root 四次方根the root of four, the fourth root n 次方根the root of n, the nth root 集合aggregate 元素element 空集void 子集subset 交集intersection并集union 补集complement 映射mapping 函数function 定义域domain, field of definition 值域range 常量constant 变量variable 单调性monotonicity 奇偶性parity 周期性periodicity 图象image 数列，级数series 微积分calculus 微分differential 导数derivative 极限limit 无穷大infinite(a.) infinity(n.) 无穷小infinitesimal 积分integral定积分definite integral 不定积分indefinite integral 有理数rational number 无理数irrational number 实数real number 虚数imaginary number 复数complex number 矩阵matrix 行列式determinant 几何geometry 点point 线line 面plane 体solid 线段segment 射线radial 平行parallel 相交intersect 角angle 角度degree 弧度radian锐角acute angle 直角right angle 钝角obtuse angle 平角straight angle 周角perigon 底base 边side 高height 三角形triangle 锐角三角形acute triangle 直角三角形right triangle 直角边leg 斜边hypotenuse 勾股定理Pythagorean theorem 钝角三角形obtuse triangle 不等边三角形scalene triangle 等腰三角形isosceles triangle 等边三角形equilateral triangle 四边形quadrilateral 平行四边形parallelogram 矩形rectangle 长length 宽width 菱形rhomb, rhombus, rhombi(pl.), diamond 正方形square 梯形trapezoid 直角梯形right trapezoid 等腰梯形isosceles trapezoid 五边形pentagon 六边形hexagon 七边形heptagon 八边形octagon 九边形enneagon 十边形decagon 十一边形hendecagon 十二边形dodecagon 多边形polygon 正多边形equilateral polygon 圆circle 圆心centre(BrE), center(AmE) 半径radius 直径diameter 圆周率pi 弧arc 半圆semicircle 扇形sector 环ring椭圆ellipse 圆周circumference 周长perimeter 面积area 轨迹locus, loca(pl.) 相似similar 全等congruent四面体tetrahedron 五面体pentahedron 六面体hexahedron 平行六面体parallelepiped 立方体cube 七面体heptahedron 八面体octahedron 九面体enneahedron 十面体decahedron 十一面体hendecahedron 十二面体dodecahedron 二十面体icosahedron 多面体polyhedron 棱锥pyramid 棱柱prism 棱台frustum of a prism 旋转rotation 轴axis 圆锥cone 圆柱cylinder 圆台frustum of a cone 球sphere 半球hemisphere 底面undersurface 表面积surface area 体积volume 空间space 坐标系coordinates 坐标轴x-axis, y-axis, z-axis 横坐标x-coordinate 纵坐标y-coordinate 原点origin 双曲线hyperbola 抛物线parabola 三角trigonometry 正弦sine 余弦cosine 正切tangent 余切cotangent 正割secant 余割cosecant 反正弦arc sine 反余弦arc cosine 反正切arc tangent 反余切arc cotangent 反正割arc secant 反余割arc cosecant 相位phase 周期period 振幅amplitude 内心incentre(BrE), incenter(AmE) 外心excentre(BrE), excenter(AmE) 旁心escentre(BrE), escenter(AmE) 垂心orthocentre(BrE), orthocenter(AmE) 重心barycentre(BrE), barycenter(AmE) 内切圆inscribed circle 外切圆circumcircle 统计statistics 平均数average 加权平均数weighted average 方差variance 标准差root-mean-square deviation, standard deviation 比例propotion 百分比percent 百分点percentage 百分位数percentile 排列permutation 组合combination 概率，或然率probability 分布distribution 正态分布normal distribution 非正态分布abnormal distribution 图表graph 条形统计图bar graph 柱形统计图histogram 折线统计图broken line graph 曲线统计图curve diagram 扇形统计图pie diagram数学专业英语词汇代数部分1. 有关数* 算add ，plus 加? subtract 减? difference 差?? multiply,times 乘?product 积? divide 除? divisible 可被整除的? divided evenly 被整除?dividend 被除数，红利? divisor 因子，除数? quotient 商? remainder 余数?? factorial 阶乘? power 乘方? radical sign, root sign 根号round to 四舍五入?to the nearest 四舍五入2. 有关集合union 并集? proper subset 真子集solution set 解集??3. ?有关代数式、方程和不等式algebraic term 代数项like terms, similar terms 同类项numerical coefficient 数字系数?literal coefficient 字母系数??inequality 不等式?triangle inequality 三角不等式?? range 值域??original equation 原方程equivalent equation 同解方程，等价方程?linear equation 线性方程(e.g. 5?x?+6=22)?4. ? 有关分数和小数proper fraction 真分数improper fractionmixed number假分数? 带分数?vulgar fraction ，common fraction 普通分数?simple fraction complex fraction 简分数?繁分数??numerator 分子? denominator 分母?(least) common denominator (最小)公分母quarter 四分之一?decimal fraction 纯小数?infinite decimal 无穷小数recurring decimal 循环小数tenths unit 十分位??5. 基本数学概念??arithmetic mean 算术平均值weighted average 加权平均值geometric mean 几何平均数?exponent 指数，幂? base 乘幂的底数,底边? cube 立方数，立方体? square root 平方根? cube root 立方根?? common logarithm 常用对数digit 数字? constant 常数? variable 变量??inverse function 反函数? complementary function 余函数? linear 一次的，线性的? factorization 因式分解?absolute value 绝对值，e.g. | -32 | =32?round off 四舍五入?6. ?有关数论?natural number 自然数positive number 正数? negative number 负数odd integer, odd number even integer, even number 奇数?偶数?integer, whole number 整数positive whole number 正整数negative whole number 负整数?? consecutive number 连续整数? real number, rational number 实数,有理数?irrational (number )无理数?? inverse 倒数?composite number 合数e.g. 4,6,8,9,10,12,14,15 ..... ?prime number 质数e.g. 2,3,5,7,11,13,15 •注意：所有的质数(2除外)都是奇数，但奇数不一定是质数reciprocal 倒数??common divisor 公约数?multiple 倍数?(least)common multiple ( 最小)公倍数??(prime) factor ( 质)因子?common factor 公因子??ordinary scale, decimal scale 十进制? nonnegative 非负的??tens 十位?units 个位??mode 众数?median 中数??common ratio 公比??7. ? 数列arithmetic progression(sequence) geometric progression(sequence) 等差数列? 等比数列??8. ? 其它?approximate 近似?(anti)clockwise ( 逆) 顺时针方向cardinal 基数? ordinal 序数direct proportion 正比distinct 不同的?estimation parentheses proportion permutation combination 估计，近似? 括号? 比例?排列?组合?table 表格?trigonometric function unit单位,位?几何部分三角函数?1. 所有的角alternate angle 内错角? corresponding angle 同位角? vertical angle 对顶角? central angle 圆心角?interior angle 内角?exterior angle 外角? supplementary angles 补角? complementary angle 余角? adjacent angle 邻角?acute angle 锐角?obtuse angle 钝角?right angle 直角?round angle 周角?straight angle 平角?included angle 夹角??2. ? 所有的三角形equilateral triangle 等边三角形scalene triangle 不等边三角形? isosceles triangle 等腰三角形? right triangle 直角三角形? oblique 斜三角形?inscribed triangle 内接三角形??3. ?有关收敛的平面图形，除三角形外semicircle 半圆?concentric circles 同心圆? quadrilateral 四边形?pentagonhexagon 五边形? 六边形? heptagonoctagon七边形? 八边形? nonagon 九边形?decagonpolygon 十边形? 多边形? parallelogram 平行四边形equilateral 等边形? plane 平面?square 正方形，平方?rectangle 长方形?regular polygon 正多边形rhombus 菱形?trapezoid 梯形??4. ? 其它平面图形arc 弧?line, straight line 直线?line segment 线段? parallel lines 平行线? segment of a circle 弧形??5. ?有关立体图形cube 立方体，立方数? rectangular solid 长方体? regular solid/regular polyhedron circular正多面体? cylinder 圆柱体? cone 圆锥? sphere球体?solid 立体的??6. ?有关图形上的附属物altitude 高? depth 深度?side 边长?circumference, perimeter 周长radian 弧度?surface area 表面积? volume 体积?arm 直角三角形的股? cross section 横截面? center of a circle 圆心?chord 弦?radius 半径?angle bisector 角平分线? diagonal 对角线? diameter 直径?edge 棱?face of a solid 立体的面hypotenuse 斜边? included side 夹边? leg 三角形的直角边?median of a triangle 三角形的中线?base 底边，底数（e.g. 2 的5 次方，2 就是底数）? opposite 直角三角形中的对边?midpoint 中点?endpoint 端点?vertex （复数形式vertices）顶点? tangent 切线的? transversal 截线? intercept 截距??7. ?有关坐标??coordinate system 坐标系?rectangular coordinate 直角坐标系origin 原点?abscissa 横坐标?ordinate 纵坐标?number line 数轴? quadrant 象限? slope 斜率? complex plane 复平面??8. ? 其它plane geometry 平面几何?trigonometry 三角学? bisect 平分?circumscribe 外切? inscribe 内切? intersect 相交? perpendicular 垂直?pythagorean theorem 勾股定理congruent 全等的? multilateral 多边的?其它??1. ? 单位类?cent 美分?penny 一美分硬币nickel 5 美分硬币dime 一角硬币dozen 打（12 个）score 廿 （20 个）?Centigrade 摄氏 ?Fahrenheit 华氏 ? quart 夸脱 ?gallon 加仑 （1 gallon = 4 quart ）? yard 码 ?meter 米 ? micron 微米 ? inch 英 寸 ? foot 英尺 ?minute 分（角度的度量单位， 60 分 =1 度）? square measure 平方单位制 ? cubic meter 立方米 ?pint 品脱（ 干量或液量的单位 ）??2. ?有关文字叙述题，主要是有关商业 intercalary year （leap year ） 闰年 （366 天）? common year 平年 （365 天 ）?depreciation 折旧 ? down payment 直接付款 ?discount 打折 ? margin 利润 ? profit 利 润 ? interest 利息 ?simple interest 单 利 ? compounded interest 复利 ? dividend 红利 ?decrease to 减少到 decrease by 减少了 increase to 增加到 ? increase by 增加了 denote 表示 ? list price 标价 ? markup 涨 价 ? per capita 每人 ? ratio 比率 ? retail price 零售价 ? tie 打Chapter one function notation quadratic functions quadratic equations chapter two Equivalent algebraic expressions等价代数表达式rational expression 有理式 有理表达式horizontal and vertical translation of functions函数的水平和垂直的平移reflections of functions 函数的倒映 映射chapter threeExponential functions 指数函数exponential decay 指数式衰减 exponent 指数properties of exponential functions指数函数的特性 chapter fourTrigonometry 三角学 Reciprocal trigonometric ratios 倒数三角函数比Trigonometric functions 三角函数 Discrete functions 离散函数 方程符号 函数符号二次函数 二次方程式 二次等式。

SAT数学考试常用8大公式1.勾股定理：a，b，c分别代表直角三角形的勾、股、弦三边之长(a^2)+(b^2)=(C^2)其变形b^2=c^2-a^2=(c-a)(c+a)a^2=c^2-b^2=(c-b)(c+b)，c^2=2ab+(b-a)^22.某些数列前n项和1+2+3+4+5+6+7+8+9+…+n=n(n+1)/2 1+3+5+7+9+11+13+15+…+(2n-1)=n^22+4+6+8+10+12+14+…+(2n)=n(n+1) 12+22+32+42+52+62+72+82+…+n2=n(n+1)(2n+1)/613+23+33+43+53+63+…n3=n2(n+1)2/4 1*2+2*3+3*4+4*5+5*6+6*7+…+n(n+1)=n(n+1)(n+2)/33.等差数列：1)等差数列通项公式：an=a1+(n-1)d2)前n项和公式：Sn=na1+[n(n-1)d]/2或Sn=n(a1+an)/24.等比数列：1)等比数列通项公式：an=a1??q^(n-1)2) 前n项和公式：当 q= 1时，Sn=na1当q≠1 时, Sn=[a1(1-q^n )] /(1-q)或Sn=(a1-anq)/(1-q)5. 一元一次方程一般形式：ax+b=0(a、b为常数，a≠0)6.一元二次方程：一般形式：ax^2+bx+c=0(a、b、c为常数，a≠0)7. 韦达定理:一元二次方程ax^2+bx+c (a不为0)中设两个根为X1和X2则X1+X2= - b/aX1*X2=c/a8.阶乘1×2×3×……×n=x，x就是n的阶乘以上就是关于SAT数学常用公式的全部信息，包括了在SAT数学考试中常见的勾股定理，数列，方程等方面的公式。

大家可以在解答SAT数学题目的时候，对这些公式进行熟悉和应用，熟练之后，相信会对大家有很大的帮助的。

Math Test – No Calculator25 MINUTES, 20 QUESTIONSTurn to Section 3 of your answer sheet to answer the questions in this section.DirectionsFor questions 1-15, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 16-20, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 16 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work.Notes.The use of a calculator is not permitted. .All variables and expressions used represent real numbers unless otherwise indicated. .Figures provided in this test are drawn to scale unless otherwise indicated. .All figures lie in a plane unless otherwise indicated. .Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f(x) is a real number. Reference1. A painter will paint n walls with the same size and shape ina building using a specific brand of paint. The painter’s fee can be calculated by the expression nKl h, where n is the number of walls, K is a constant with units of dollars per square foot, l is the length of each wall in feet, and h is the height of each wall in feet. If the customer asks the painterto use a more expensive brand of paint, which of the factors in the expression would change?A) hB) lC) KD) n2. If 3r = 18, what is the value of 6r + 3 ?A) 6B) 27C) 36D) 393. Which of the following is equal to a 23, for all values of a ?a 1 3B) a 3C)a 123D) a 234. The number of states that joined the United States between1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true? A) 30x =2 B) 2x =30 C)x2=30D) x +30=25. If 5x=15x +20, what Is the value of 5x?A) 10 B) 5 C) 2 D)126. x −3y = −143x − 2y = −6If (x , y ) is a solution to the system of equations above, what is the value of x −y ? A) −20B) −8C) −4D) 87.The function f is defined by a polynomial. Some values of x and f (x) are shown in the table above. Which of the following must be a factor of f(x)?A) x−2B) x−3C) x−4D) x−58. The line y=kx+4,where k is a constant, is graphed in thexy-plane. If the line contains the point (c, d), where c ¹ 0 and d ¹0, what is the slope of the line in terms of c and d ?A) d-4cB) c-4dC) 4-dcD) 4-cd9.10. In the xy-plane, the parabola with equation
y = (x −11)2 intersects the line with equation y=25at two points, A andB. What is the length of AB ?A) 10B) 12C) 14D) 1611.In the figure above, lines k, l, and m intersect at a point. If x+y=u+w, which of the following must be true?I. x=zII. y=wIII. z=tA) I and II onlyB) I and III onlyC) II and III onlyD) I, II, and III12. y = a(x−2)(x+4)In the quadratic equation above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c, d). Which of the following is equal to d ?A) −9aB) −8aC) −5aD) −2a13. The equation
true for all values of24x2+25x-47ax-2=-8x-3-53ax-2, where a is a constant. What is thevalue of a ?A) −16B) −3C) 3D) 1614. What are the solutions to 3x2+12x+6=0 ?A) x=-2±2B) x=-2±30 3C) x=-6±2D) x=-6±6215. C = 59( F − 3 2 )The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?I. A temperature increase of 1 degree Fahrenheit isequivalent to a temperature increase of 59degreeCelsius. II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III. A temperature increase of 59degree Fahrenheit isequivalent to a temperature increase of 1 degree Celsius..A) I only.B) II onlyC) III only
D) I and II only16. x3(x2 − 5) = − 4xIf x > 0, what is one possible solution to the equation above?17. If 79x-49x=14+512what is the value of x?18.Two isosceles triangles are shown above. If 180−z=2y andy=75,what is the value of x ?19. At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?20. In triangle ABC, the measure of ∠B is 90°,
BC = 16, and AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C,the length of respectively, and each side of triangle DEF is 13the corresponding side of triangle ABC. What is the value of sin F ?Math Test – No Calculator55 MINUTES, 38 QUESTIONSTurn to Section 4 of your answer sheet to answer the questions in this section.DirectionsFor questions 1-30, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 31-38, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 16 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work.Notes.The use of a calculator is not permitted. .All variables and expressions used represent real numbers unless otherwise indicated. .Figures provided in this test are drawn to scale unless otherwise indicated. .All figures lie in a plane unless otherwise indicated. .Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f(x) is a real number. Reference1.The graph above shows Marilyn’s distance from her campsite during a 3‐hour hike. She stopped for
30 minutes during her hike to have lunch. Based on the graph, which of the following is closest to the time she finished lunch and continued her hike?A) 12:40 P.M.B) 1:10 P.M.C) 1:40 P.M.D) 2:00 P.M2.The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is the probability that the winnerwill be either a female under age 40 or a male age 40 or older?A)4 25B) 10 25C)11 25D) 16 253. The graph below shows the total number of music album sales, in millions, each year from 1997 through 2009.Based on the graph, which of the following best describes the general trend in music album sales from 1997 through 2009 ?A) Sales generally increased each year since 1997.B) Sales generally decreased each year since 1997.C) Sales increased until 2000 and then generally decreased.D) Sales generally remained steady from 1997 through 2009.4.The table above shows some values of the linear function f. Which of the following defines f ?A) f(n)=n−3B) f(n)=2n−4C) f(n)=3n−5D) f(n)=4n−65. At Lincoln High School, approximately 7 percent of enrolled juniors and 5 percent of enrolled seniors were inducted into the National Honor Society last year. If there were 562 juniors and 602 seniors enrolled at Lincoln High School last year, which of the following is closest to the total number ofjuniors and seniors at Lincoln High School last year who were inducted into the National Honor Society?A) 140B) 69C) 39D) 306.3x2 − 5x + 25x2 − 2x – 6Which of the following is the sum of the two polynomials shown above?A) 8x2−7x−4B) 8x2+7x−4C) 8x4−7x2−4D) 8x4+7x2−47. If 35w=43,what is the value of w ?A)920B)45C)54D)2098. The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, where
x represents the number of years since2000, and
y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation?A) The total number of students at the school in 2000 B) The average number of students per classroom in 2000 C) The estimated increase in the average number of students per classroom each year D) The estimated difference between the average number of students per classroom in 2010 and in 2000 9. Nate walks 25 meters in13.7 seconds. If he walk sat this same rate, which of the following is closest to the distance he will walk in 4 minutes?A) 150 metersB) 450 metersC) 700 metersD) 1,400 metersQuestions 10 and 11 refer to the following information.The chart above shows approximations of the acceleration due to gravity in meters per second squared (m)for the eight planetssec2in our solar system. The weight of an object on a given planet can be found by using the formula W = mg, where W is the weight of the object measured in newtons, m is the mass of the object measured in kilograms, and g is the acceleration due to gravity on the planet measured in (m)sec210. What is the weight, in newtons, of an object on Mercury witha mass of 90 kilograms?A) 25B) 86C) 101D) 32411. An object on Earth has a weight of 150 newtons. On which planet would the same object have an approximate weight of 170 newtons?A) VenusB) SaturnC) UranusD) Neptune12. If the function f has five distinct zeros, which of the following could represent the complete graph of f in thexy‐plane?13. h = −16t2 + vt + kThe equation above gives the height h, in feet, of a ball t seconds after it is thrown straight up with an initial speed of v feet per second from a height of k feet. Which of the following gives v in terms of h, t, and k ?A) v=h+k−16tB) v=h-k+16tC) v=h-kt-16tD) v=h-kt+16t14. 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+60C) c=60h0.20D) c=0.20h6015. In order to determine if treatment X is successful in improving eyesight, a research study was conducted. From a large population of people with poor eyesight, 300 participants were selected at random. Half of the participants were randomly assigned to receive treatment X, and the other half did not receive treatment X. The resulting data showed thatparticipants who received treatment X had significantly improved eyesight as compared to those who did not receive treatment X. Based on the design and results of the study, which of the following is an appropriate conclusion?A) Treatment X is likely to improve the eyesight of people who have poor eyesight. B) Treatment X improves eyesight better than all other available treatments. C) Treatment X will improve the eyesight of anyone who takes it. D) Treatment X will cause a substantial improvement in eyesight.
16.Graphs of the functions f and g are shown in the xy-plane above. For which of the following values of x does f(x)+g(x)=0?A) −3B) −2C) −1D) 0Questions 17 and 18 refer to the following information.S ( P ) = 1P + 4 02D(P) = 220 −PThe quantity of a product supplied and the quantity of the product demanded in an economic market are functions of theprice of the product. The functions above are the estimated supply and demand functions for a certain product. The function S(P) gives the quantity of the product supplied to the market when the price isP dollars, and the function D(P) gives the quantity of the product demanded by the market when the price is P dollars.17. How will the quantity of the product supplied to the market change if the price of the product is increased by $10 ?A) The quantity supplied will decrease by 5 units.B) The quantity supplied will increase by 5 units.C) The quantity supplied will increase by 10 units.D) The quantity supplied will increase by 50 units.18. At what price will the quantity of the product supplied to the market equal the quantity of the product demanded by the market?.A) $90.B) $120.C) $133.D) $15519. Graphene, which is used in the manufacture of integrated circuits, is so thin that a sheet weighing one ounce can cover up to 7 football fields. If a football field has an area ofapproximately 11acres, about how many acres could 48 ounces of3graphene cover?A) 250B) 350C) 450D) 1,35020.Michael swam 2,000 yards on each of eighteen days. The scatterplot above shows his swim time for and corresponding heart rate after each swim. The line of best fit for the datais also shown. For the swim that took 34 minutes, Michael’s actual heart rate was about how many beats per minutes less than the rate predicted by the line of best fit?A) 1B) 2C) 3D) 421. Of the following four types of savings account plans, which option would yield exponential growth of the money in the account?A) Each successive year, 2% of the initial savings is added to the value of the account.B) Each successive year, 1.5% of the initial savings and $100 is added to the value of the account.C) Each successive year, 1% of the current value is added to the value of the account.D) Each successive year, $100 is added to the value of the account.22. The sum of three numbers is 855. One of the numbers, x, is 50% more than the sum of the other two numbers. What is the value of x ?A) 570B) 513C) 214D) 15523.The angles shown above are acute and
sin(a°) = cos(b°). If a = 4k−22 and b = 6k−13, what is the value of k ?A) 4.5B) 5.5C) 12.5D) 21.524. Mr. Kohl has a beaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are in the class?A) 16B) 21C) 23D) 2625.A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet?A) 261.8B) 785.4C) 916.3D) 1,047.226. In the xy-plane, the line determined by the
points (2, k) and (k, 32) passes through the origin. Which of the following could be the value of k ?A) 0B) 4C) 8D) 1627. A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. If these alterations decreased the area of the rectangle by 12 percent, what is the value of p ?A) 12B) 15C) 20D) 2228. In planning maintenance for a city’s infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 10 percent every 20 years. If the present population of the city is 50,000, which of the following expressions represents the engineer’s estimate of the population of the city t years from now?A) 50,000(0.1)20tB) 50000(0.1)t 20C) 50,000(0.9)20tD) 50000(0.9)t 2029.The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth-grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. If there is a total of 18 left-handed students and 122 right-handedstudents in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.)A) 0.410B) 0.357C) 0.333D) 0.25030. 3x+b=5x-73y+c=5y-7In the equations above, b and c are constants. If b is c minus 12, which of the following is true?A) x is y minus 14 B) x is y minus 5p 4C) x is y minus 1D) x is y plus 1231. Tickets for a school talent show cost $2 for students and $3 for adults. If Chris spends at least $11 but no more than $14 on x student tickets and 1 adult ticket, what is one possible value of x ?32.The table above lists the ages of the first 12 United States presidents when they began their terms in office. According to the table, what was the mean age, in years, of these presidents at the beginning of their terms? (Round your answer to the nearest tenth.)34. In a circle with center O , central angle AOB has a measureof 5p 4radians. The area of the sector formed by central angle AOB is what fraction of the area of the circle?35. An online store receives customer satisfaction ratingsbetween 0 and 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?36.In the xy ‐plane, if a point with coordinates (a , b ) lies in the solution set of the system of inequalities above, what isthe maximum possible value of b ?Questions 37 and 38 refer to the following information.If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for an average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N = rT. This relationship is known as Little’s law.The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little’s law to estimate that there are 45 shoppers in the store at any time.37.Little’s law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?38. The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in theoriginal store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1)。

sat最难数学题
摘要：
1.SAT 数学考试简介
2.SAT 数学中最难的题目类型
3.如何准备和应对这些难题
4.结论
正文：
1.SAT 数学考试简介
SAT（Scholastic Assessment Test）是美国大学入学考试的一种，其数学部分对于许多学生来说是一项挑战。

SAT 数学考试分为两部分，分别是数学（Math）和数学2（Math 2），总共有58 道题目，考试时间为80 分钟。

题目涵盖了代数、几何、统计学和数据分析等数学领域。

2.SAT 数学中最难的题目类型
在SAT 数学考试中，最难的题目通常涉及复杂的代数问题、需要高级几何知识的题目以及需要深入理解概率和统计学的题目。

这些题目的难点在于需要学生运用所学的知识解决实际问题，同时需要具备良好的逻辑思维和分析能力。

3.如何准备和应对这些难题
要应对SAT 数学中最难的题目，学生需要做好充分的准备。

首先，要熟练掌握代数、几何、统计学和数据分析等数学领域的基本概念和公式。

其次，要通过大量练习提高解题速度和准确率，特别是对于难题，要能够快速找到解题思路。

此外，还要学会利用排除法、代入法等解题技巧，以提高解题效率。

在考试中，对于遇到的难题，学生可以先跳过，等其他题目完成后再回来解决。

这样可以避免在难题上花费过多时间，导致其他较容易的题目没有时间完成。

同时，学生要保持冷静，不要因为遇到难题而影响自己的情绪。

4.结论
虽然SAT 数学考试中最难的题目可能让学生感到压力，但只要做好充分的准备，掌握解题技巧，就能应对这些挑战。

SAT 数学题分成了选择题和计算题，相对于 SAT 数学选择题,答案还有一些提示的作用,SAT 数学计算题就需要大家自己进行解答了。

下面为大家推荐的这道 SAT 数学计算题是非常典 型的代数方程类的题目,大家一起来看看吧。

What value of satisfies both of the equations above？ The correct answer is1/2 or 。

5 Explanation Difficulty: MediumSince， the value ofis either or 。

ORThe two values of that satisfy the first equation are and .Since， the value ofis either or .ORThe two values of that satisfy the second equation are and .You are asked to find the value of that satisfies both equations. That value is 。

The answer can be entered in the grid asor 。

下面是两道 SAT 数学练习题,都是选择题，后面附有答案及其解析。

SAT 数学练习题可以让 大家更快更好的了解 SAT 数学考试的出题方式以及应对方式.下面是详细内容,我们一起来 看一下这些 SAT 数学练习题的吧。

1、 Cone A has volume 24。

When its radius and height are multiplied by the same factor， the cone’s surface area doubles. What is Cone A’s new volume?（A）(B)48（C)（D）96 （E)Not enough information to tell 2、 A rectangle stands so that its 6 inch side lies flat against the ground。

SAT数学考试计算器使用方法1、必须用计算器的操作，主要是指次方，对数，三角函数和反三角函数值的计算。

基础好的学霸，简易的"卖菜计算器'就够用了。

其它一些操作视自己的基础和题目而定。

SAT2数学计算器使用说明1. 排列(permutation)、组合(combination)的公式老是记不住。

84的计算器，math按键，调到最右边，会看到对应按键。

比如计算7P5：7math--向右到第四个--nPr--5--enter得解。

组合的计算类似。

阶乘(fACTorial)也在那块。

Nspire，选择计算后，按menu，概率，排列/组合。

2. 想按负号不要按成了减号。

负号是数字按键那块右下角带括号的那个。

3. 角度(degree)和弧度(radian)的转换。

84在mode里选择对应的按enter就行。

按完后clear或quit就能去进行更改后的计算了。

Nspire按数字5进入设置，常规里有选择(其中浮点表示小数位)。

4. Complex number的计算实在不会时，84把"mode'调成a + bi 的模式，i的输入，按2nd，最下面那行中间的.就是。

Nspire的i在的按键里(键盘左下角)。

5. 次方(power)怎么按?84是clear按键下面的三角，nspire 是等于号下面的三角号。

这个次方也可以是分数次方。

6. 常见的一些按键84的基本就在键盘上了。

其中logab在math--logbase里。

Nspire的按ctrl--10x按键。

2SAT数学考试冲分方法定量学习应用类型部分应用类型的题目会在题干上会增加同学的阅读难度，例如生词或一次多义。

对待这部分的题目同学应当通过大量的学习识记高频的词汇，学会提取关键信息。

更高效地完成题目。

草稿清楚有序在学习过程中，草稿清楚可以帮助同学在整理错题的时候清楚地找到自己的错误点;在考试过程中，可以帮助同学检查过程。

限时模考非常重要不要以为数学简单就不去模考，从而在考试过程中产生不必要的紧张情绪; 先跳过或者换种思路，一定注意从问题入手找到必须要的信息，条件尽量都用到。