SAT数学练习2.2
SAT 2 数学2 college board官网全部原题加答案讲解 SAT Subject Test Math Level 2
SAT Subject Test Practice - Results Summary Mathematics Level 21Your answer Omitted!What is the distance in space between the points with coordinates and ?(A)(B)(C)(D)(E)ExplanationDifficulty: EasyThe correct answer is D.The distance between the points with coordinates and is given by the distance formula: .Therefore, the distance between the points with coordinates and is:,which simplifies to .2Your answer Omitted!If , what value does approach as gets infinitely larger?(A)(B)(C)(D)(E)ExplanationDifficulty: EasyThe correct answer is E.One way to determine the value that approaches as gets infinitely larger is to rewrite the definition of the function to use only negative powers of and then reason about the behavior of negative powers of as gets infinitely larger. Since the question is only concerned with what happens to as gets infinitely larger, one can assume that is positive. For , theexpression is equivalent to the expression . As gets infinitely larger, the expression approaches the value , so as gets infinitely larger, the expression approaches the value . Thus, as gets infinitely larger, approaches .Alternatively, one can use a graphing calculator to estimate the height of the horizontal asymptote for the function . Graph the function on an interval with “large”, say, from to .By examining the graph, the all seem very close to . Graph the function again, from, say, to .The vary even less from . In fact, to the scale of the coordinate plane shown, the graph of the function is nearly indistinguishable from the asymptotic line . This suggests that as gets infinitely larger, approaches , that is, .Note: The algebraic method is preferable, as it provides a proof that guarantees that the value approaches is . Although the graphical method worked in this case, it does not provide a complete justification; for example, the graphical method does not ensure that the graph resembles a horizontal line for “very large”such as .3Your answer Omitted!If is a factor of , then(A)(B)(C)(D)(E)ExplanationDifficulty: EasyThe correct answer is A.By the Factor Theorem, is a factor of only when is a root ofthat is, , which simplifies to . Therefore, .Alternatively, one can perform the division of by and then find a value for so that the remainder of the division is .Since the remainder is , the value of must satisfy . Therefore, .4Your answer Omitted!Alison deposits into a new savings account that earns percent interest compounded annually. If Alison makes no additional deposits or withdrawals, how many years will it take for the amount in the account to double?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumAfter year, the amount in the account is equal to . After years, the amount isequal to , and so on. After years, the amount is equal to . You needto find the value of for which . There are several ways to solve this equation. You can use logarithms to solve the equation as follows.Since , it will take more than years for the amount in the account to double. Thus, you need to round up to .Another way to find is to use your graphing calculator to graph and . From the answer choices, you know you need to set the viewing window with values from to about and values extending just beyond . The of the point of intersection is approximately . Thus you need to round up to .5Your answer Omitted!In the figure above, when is subtracted from , what is the length of the resultant vector?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe resultant of can be determined by . The length of the resultant is:6Your answer Omitted!In the -plane, what is the area of a triangle whose vertices are , , and ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumIt is helpful to draw a sketch of the triangle:The length of the base of the triangle is and the height of the triangle is . Therefore, the area of the triangle is . The correct answer is B.7Your answer Omitted!A right circular cylinder has radius and height . If and are two points on its surface, what is the maximum possible straight-line distance between and ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe maximum possible distance occurs when and are on the circumference of opposite bases: You can use the Pythagorean Theorem:The correct answer is (B).8Your answer Omitted!Note: Figure not drawn to scale.In the figure above, and the measure of is . What is the value of ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThere are several ways to solve this problem. One way is to use the law of sines. Since ,the measure of is and the measure of is . Thus, and . (Make sure your calculator is in degree mode.)You can also use the law of cosines:Since is isosceles, you can draw the altitude to the triangle.9Your answer Omitted!The function is defined by for .What is the difference between the maximum and minimum values of ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumIt is necessary to use your graphing calculator for this question. First graph the function. It is helpful to resize the viewing window so the -values go fromto . On this interval the maximum value of is and the minimum value of is. The difference between these two values is , which rounds to .10Your answer Omitted!Suppose the graph of is translated units left and unit up. If the resulting graph represents , what is the value of ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumIt may be helpful to draw a graph of and .The equation for is . Therefore,. The correct answer is B.11Your answer Omitted!A sequence is recursively defined by , for . If and , what is the value of ?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe values for and are given. is equal to . is equal to. is equal to . is equal to.If your graphing calculator has a sequence mode, you can define the sequence recursively and findthe value of . Let , since the first term is . Define . Let , since we have to define the first two terms and . Then examining a graph or table, you can find .12Your answer Omitted!The diameter and height of a right circular cylinder are equal. If the volume of the cylinder is , what is the height of the cylinder?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe correct answer is A.To determine the height of the cylinder, first express the diameter of the cylinder in terms of theheight, and then express the height in terms of the volume of the cylinder.The volume of a right circular cylinder is given by , where is the radius of the circular base of the cylinder and is the height of the cylinder. Since the diameter and height are equal, . Thus . Substitute the expression for in the volume formula to eliminate :. Solving for gives . Since the volume of the cylinder is , theheight of the cylinder is .13Your answer Omitted!If ,then(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe correct answer is E.One way to determine the value of is to apply the sine of difference of two angles identity: . Since and , the identity gives . Therefore, .Another way to determine the value of is to apply the supplementary angle trigonometric identity for the sine: . Therefore, .14Your answer Omitted!A line has parametric equations and , where is the parameter. The slope of the line is(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe correct answer is B.One way to determine the slope of the line is to compute two points on the line and then use the slope formula. For example, letting gives the point on the line, and letting gives the point on the line. Therefore, the slope of the line is equal to .Alternatively, one can express in terms of . Since and , it follows that . Therefore, the slope of the line is .15Your answer Omitted!What is the range of the function defined by ?(A) All real numbers(B) All real numbers except(C) All real numbers except(D) All real numbers except(E) All real numbers between andExplanationDifficulty: MediumThe correct answer is D.The range of the function defined by is the set of such thatfor some .One way to determine the range of the function defined by is to solve the equation for and then determine which correspond to at least one . To solve for , first subtract from both sides to get and then take the reciprocal of both sides to get . The equation shows that for anyother than , there is an such that , and that there is no such for . Therefore, the range of the function defined by is all real numbers except .Alternatively, one can reason about the possible values of the term . The expression can take on any value except , so the expression can take on any value except . Therefore, the range of the function defined by is all real numbers except .16Your answer Omitted!The table above shows the number of digital cameras that were sold during a three-day sale. The prices of models , , and were , , and , respectively. Which of the following matrix representations gives the total income, in dollars, received from the sale of the cameras for each of the three days?(A)(B)(C)(D)(E)ExplanationDifficulty: MediumThe correct answer is C.A correct matrix representation must have exactly three entries, each of which represents the total income, in dollars, for one of the three days. The total income for Day is given by the arithmetic expression , which is the single entry of the matrix product; in the same way, the total income for Day is given by, the single entry of ; and the total income for Day is given by , the single entry of. Therefore, the matrix representationgives the total income, in dollars, received from the sale of the cameras for each of the three days. Although it is not necessary to compute the matrix product in order to answer the question correctly, equals .17Your answer Omitted!The right circular cone above is sliced horizontally forming two pieces, each of which has the sameheight. What is the ratio of the volume of the smaller piece to the volume of the larger piece?(A)(B)(C)(D)(E)ExplanationDifficulty: HardIt is helpful to label the figure.The top piece is a cone whose height is one-half the height of the original cone . Using the properties of similar right triangles, you should realize the radii of these two cones must be in the same ratio. So if the top cone has radius , the original cone has radius .The volume of the top piece is equal to . The volume of the bottom piece is equal to the volume of the original cone minus the volume of the top piece.The ratio of the volume of the smaller piece to the volume of the larger piece is .18Your answer Omitted!In the figure above, is a regular pentagon with side of length . What is the -coordinate of ?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe sum of the measures of the interior angles of a regular pentagon is equal to . Each interior angle has a measure of . Using supplementary angles, has a measure of . You can use right triangle trigonometry to find the -coordinate of point .Since , is about . Since the length of each side of the pentagon is , the -coordinate of point is . Putting the information together tells us that the -coordinate of point is . The correct answer is (B).19Your answer Omitted!For a class test, the mean score was , the median score was , and the standard deviation of the scores was . The teacher decided to add points to each score due to a grading error. Which of the following statements must be true for the new scores?I. The new mean score is .II. The new median score is .III. The new standard deviation of the scores is .(A) None(B) only(C) only(D) and only(E) , , andExplanationDifficulty: HardFor this type of question you need to evaluate each statement separately. Statement is true. If you add to each number in a data set, the mean will also increase by . Statement is also true. The relative position of each score will remain the same. Thus, the new median score will be equal to more than the old median score. Statement is false. Since each new score is more than the old score, the spread of the scores and the position of the scores relative to the mean remain the same. Thus, the standard deviation of the new scores is the same as the standard deviation of the old scores.20Your answer Omitted!A game has two spinners. For the first spinner, the probability of landing on blue is . Independently, for the second spinner, the probability of landing on blue is What is the probability that the first spinner lands on blue and the second spinner does not land on blue?(A)(B)(C)(D)(E)ExplanationDifficulty: HardSince the two events are independent, the probability that the first spinner lands on blue and the second spinner does not land on blue is the product of the two probabilities. The first probability is given. Since the probability that the second spinner lands on blue is the probability that thesecond spinner does not land on blue is Therefore, . The correct answer is (E).21Your answer Omitted!In January the world’s population was billion. Assuming a growth rate of percent per year, the world’s population, in billions, for years after can be modeled by theequation . According to the model, the population growth from January to January was(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is C.According to the model, the world’s population in January was and in January was . Therefore, according to the model, the population growth from January to January , in billions, was , or equivalently,.22Your answer Omitted!What is the measure of one of the larger angles of a parallelogram in the that has vertices with coordinates , , and ?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is C.First, note that the angle of the parallelogram with vertex is one of the two larger angles of the parallelogram: Looking at the graph of the parallelogram in the makes this apparent. Alternatively, the sides of the angle of the parallelogram with vertex are a horizontal line segment with endpoints and and a line segment of positive slope with endpoints and that intersects the horizontal line segment at its left endpoint , so the angle must measure more than Since the sum of the measures of the four angles of aparallelogram equals , the angle with vertex must be one of the larger angles.One way to determine the measure of the angle of the parallelogram with vertex is to apply the Law of Cosines to the triangle with vertices , , and . The length of the two sides of the angle with vertex are and; the length of the side opposite the angle is . Let represent the angle with vertex and apply the Law of Cosines: , so. Therefore, the measure of one of the larger angles of the parallelogram is .Another way to determine the measure of the angle of the parallelogram with vertex is to consider the triangle , , and . The measure of the angle of this triangle with vertex is less than the measure of the angle of the parallelogram with vertex . The angle of the triangle has opposite side of length and adjacent side of length , so the measure of this angle is . Therefore, the measure of the angle of the parallelogram withvertex is .Yet another way to determine the measure of the angle of the parallelogram with vertex is to use trigonometric relationships to find the measure of one of the smaller angles, and then use the fact that each pair of a larger and smaller angle is a pair of supplementary angles. Consider the angle of the parallelogram with vertex ; this angle coincides with the angle at vertex of the right triangle with vertices at , , and , with opposite side of lengthand adjacent side of length , so the measure of this angle is . This angle, together with the angle of the parallelogram with vertex , form a pair of interior angles on the same side of a transversal that intersects parallel lines, so the sum of the measures of the pair of angles equals . Therefore, the measure of the angle of the parallelogram with vertex is.23Your answer Omitted!For some real number , the first three terms of an arithmetic sequence are, and . What is the numerical value of the fourth term?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is E.To determine the numerical value of the fourth term, first determine the value of and then apply the common difference.Since , and are the first three terms of an arithmetic sequence, it must be true that, that is, Solving for gives . Substituting for in the expressions of the three first terms of the sequence, one sees that they are , , and , respectively. The common difference between consecutive terms for this arithmetic sequence is , and therefore, the fourth term is .24Your answer Omitted!In a group of people, percent have brown eyes. Two people are to be selected at random from the group. What is the probability that neither person selected will have brown eyes?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is A.One way to determine the probability that neither person selected will have brown eyes is to count both the number of ways to choose two people at random from the people who do not have brown eyes and the number of ways to choose two people at random from all people, and then compute the ratio of those two numbers.Since percent of the people have brown eyes, there are people with brown eyes, and people who do not have brown eyes. The number of ways of choosing two people, neither of whom has brown eyes, is : there are ways to choose a first person and ways to choose a second person, but there are ways in which that same pair of people could be chosen. Similarly, the number of ways of choosing two people at random from the people is . Therefore, the probability that neither of the two people selected has brown eyes is.Another way to determine the probability that neither person selected will have brown eyes is to multiply the probability of choosing one of the people who does not have brown eyes at random from the people times the probability of choosing one of the people who does not have brown eyes at random from the remaining people after one of the people who does not have brown eyes has been chosen.Since percent of the people have brown eyes, the probability of choosing one of the people who does not have brown eyes at random from the people is . If one of the people who does not have brown eyes has been chosen, there remain people who do not have brown eyes out of a total of people; the probability of choosing one of the people who does not have brown eyes at random from the people is . Therefore, if two people are to be selected from the group at random, the probability that neither person selected will have brown eyes is .25Your answer Omitted!If , what is ?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is E.One way to determine the value of is to solve the equation for . Since , start with the equation , and cube both sides to get. Isolate to get , and apply the cube root to both sides of the equation to get .Another way to determine the value of is to find a formula for and then evaluate at Let and solve for : cubing both sides gives , so , and. Therefore, , and .26Your answer Omitted!Which of the following equations best models the data in the table above?(A)(B)(C)(D)(E)ExplanationDifficulty: HardThe correct answer is D.One way to determine which of the equations best models the data in the table is to use a calculator that has a statistics mode to compute an exponential regression for the data.The specific steps to be followed depend on the model of calculator, but can be summarized as follows: Enter the statistics mode, edit the list of ordered pairs to include only the four points givenin the table and perform an exponential regression. The coefficients are, approximately, for the constant and for the base, which indicates that the exponential equation is the result of performing the exponential regression. If the calculator reports a correlation, it should be a number that is very close , to which indicates that the data very closely matches the exponential equation. Therefore, of the given models, best fits the data.Alternatively, without using a calculator that has a statistics mode, one can reason about the data given in the table.The data indicates that as increases, increases; thus, options A and B cannot be candidates for such a relationship. Evaluating options C, D and E at shows that option D is the one that gives a value of that is closest to In the same way, evaluating options C, D and E at each of the other given data points shows that option D is a better model for that one data point than either option C or option E. Therefore, is the best of the given models for the data.27Your answer Omitted!The linear regression model above is based on an analysis of nutritional data from 14 varieties of cereal bars to relate the percent of calories from fat to the percent of calories from carbohydrates . Based on this model, which of the following statements must be true?I. There is a positive correlation between and .II. When percent of calories are from fat, the predicted percent of calories from carbohydrates is approximately .III. The slope indicates that as increases by , decreases by .(A) II only(B) I and II only(C) I and III only(D) II and III only(E) I, II, and IIIExplanationDifficulty: HardThe correct answer is D.Statement I is false: Since , high values of are associated with low values of which indicates that there is a negative correlation between and .Statement II is true: When percent of calories are from fat, and the predicted percent of calories from carbohydrates is .Statement III is true: Since the slope of the regression line is , as increases by , increases by ; that is, decreases by .28Your answer Omitted!The number of hours of daylight, , in Hartsville can be modeled by , where is the number of days after March . The day with the greatest number of hours of daylight has how many more daylight hours than May ? (March and May have days each. April and June have days each.)(A) hr(B) hr(C) hr(D) hr(E) hrExplanationDifficulty: HardThe correct answer is A.To determine how many more daylight hours the day with the greatest number of hours of daylight has than May , find the maximum number of daylight hours possible for any day and then subtract from that the number of daylight hours for May .To find the greatest number of daylight hours possible for any day, notice that the expressionis maximized when , which corresponds to , so. However, for this problem, must be a whole number, as it represents a count of days after March . From the shape of the graph of the sine function, either or corresponds to the day with the greatest number of hours of daylight, and since, the expression is maximized when days after March . (It is not required to find the day on which the greatest number of hours of daylight occurs, but it is days after March ,that is, June .)Since May is days after March , the number of hours of daylight for May is .Therefore, the day with the greatest number of hours of daylight hasmore daylight hours than May .。
SAT考试数学练习题
SAT 考试数学练习题 2来源 : 91SAT 考试网时间 : 2009 年 08 月 20 日1. If f(x) = │(x² –50)│, what is the value of f( -5) ?A. 75B. 25C. 0D. -25E. -752. ( √2 - √3 )² =A. 5 - 2√6B. 5 - √6C. 1 - 2√6D. 1 - √2E. 13. 230 + 230 + 230 + 230 =A. 8120B. 830C. 232D. 230E. 2264. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?A. 10B. 8C. 6D. 4E. 25. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?A. 18B. 13.5C. 9D. 4.5E. 3答案：1.Correct Answer: BExplanation:If x = -5, then (x² – 50) = 25 – 50 = -25But the sign │x│ means the absolute value of x (the distance between the number and zero on the number line). Absolute values are always positive.│-25 │ = 252.Correct Answer: AExplanation:Expand as for (a + b)2.(√2 - √3)(√2 - √3) = 2 - 2(√2 + √3) + 3 = 5 - 2 √63.Correct Answer: CExplanation:All four terms are identical therefore we have 4 (230).But 4 = 22, and so we can write 22. 230Which is equivalent to 2324. Correct Answer: BExplanation:Amy can travel clockwise or anticlockwise on the diagram.Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes. Similarly, anticlockwise she has four different routes.Total routes = 85.Correct Answer: DExplanation:If we take AE as the base of triangle AEC, then the height is CD.The height of the triangle is therefore, 9 (given).To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1.The area of AEC = ½ base x heigh t=1/2 x 9 = 4.5SAT 考试数学练习题 3来源 : 91SAT 考试网时间 : 2009 年 08 月 20 日1.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 35small cakes per hour.The kitchen is available for 3hours and20 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 5to 2and the ratio of Indian to British stamps is 5to 1,what is the ratio of US to British stamps?A. 5 : 1B. 10 : 5C. 15 : 2D. 20 : 2E. 25 : 24.A 3by 4rectangle is inscribed in circle.What is the circumference of the circle?A.2.5πB.3πC.5πD.4πE. 10π5.Two sets of 4consecutive 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.答案：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 < 180 The only value of x which satisfies this relation is 20.2.Correct Answer: AExplanation:20large cakes will require the equivalent of 10helpers 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 10helpers.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,n n d ian :British =5: 1.Multiply the first by 5,and the second by 2.Now US : Indian = 25 : 10, and Indian : British = 10 : 2 Hence 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 3,4,5triangle,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 3more than the equivalent term in the first set.Since there are four terms the total of the differences will be 4x 3=12SAT 考试数学练习题 4来源 : 91SAT 考试网时间 : 2009 年 08 月 20 日1. 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)2. 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. 63. If n ≠ 0, which of the following mus t be greater than n?I 2nII n²III 2 - nA. I onlyB. II onlyC. I and II onlyD. II and III onlyE. None4. 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. 3.25. 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答案：1.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 itlooks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.2.Correct Answer: DExplanation:(Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral 9 - (2 x ½ x 3 x 1.5) = 4.53.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 ½ then n2 will be less than n. Incase III, if n is 2, then 2-n = 0, which is less than n. Therefore, none of the choices must be greaterthan n4.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 = 85.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 p To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9 n + p = 5 + 9 = 14SAT 考试数学练习题 5来源 : 太傻网考试频道整理时间 : 2009 年 08 月 27 日1. If f(x) = x² – 3, where x is an integer, which of the following could be a value of f(x)?I 6II 0III -6A. I onlyB. I and II onlyC. II and III onlyD. I and III onlyE. I, II and IIICorrect Answer: A解析:Choice I is correct because f(x) = 6 when x=3. Choice II is incorrect because to make f(x) =0, x² would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x) = 0, x² would have to be –3 but squares cannot be negative. (The minimum value for x2 is zero; hence, the minimum value for f(x) = -3)2. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?A. 48B. 49C. 50D. 51E. 52Correct Answer: C解析:1 < 4n + 7 < 200. n can be 0, or -1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1. The largest value for n will be an integer < (200 - 7) /4. 193/4 = 48.25, hence 48. The number of integers between -1 and 48 inclusive is 503. In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?A. 23B. 22C. 18D. 16E. 14Correct Answer: B解析:First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99). Therefore in the given problem D must be 1. Now use trial and error to satisfy the sum 5A +BC = 143. A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13. With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8. A + C + B + D = 13 + 8 + 1 = 224. 12 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth, and 40 cm height. How high (in cm) will the water rise?(1 litre = 1000cm³)A. 6B. 8C. 10D. 20E. 40Correct Answer: B解析:Total volume of water = 12 liters = 12 x 1000 cm3. The base of the aquarium is 50 x 30 = 1500cm3. Base of tank x height of water = volume of water. 1500 x height = 12000; height = 12000 / 1500 = 85. Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?A. 11/P + 6B. P/11 +6C. 17 - P/6D. 17/PE. 11.5PCorrect Answer: A解析:Let Ben’s age now be B. Anita’s age now is A. (A - 6) = P(B - 6)But A is 17 and therefore 11 = P(B - 6). 11/P = B-6(11/P) + 6 = BSAT 考试数学练习题 6来源 : 太傻网考试频道整理时间 : 2009 年 08 月 27 日1. The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance from A to C?I 11II 1III 7A. I onlyB. II onlyC. I and II onlyD. II and III onlyE. I, II, or III. Correct Answer: E 解析:Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11, but anywhere in between is possible.2. √5 percent of 5√5 =A. 0.05B. 0.25C. 0.5D. 2.5E. 25Correct Answer: B解析:We can write the statement mathematically, using x to mean ‘of’ and /100 for ‘per cent’ . S o ( √5/100) x 5√5 = 5 x 5 /100 = 0.253. If pqr = 1 , rst = 0 , and spr = 0, which of the following must be zero?A. PB. QC. RD. SE. TCorrect Answer: D解析:If pqr = 1, none of these variable can be zero. Since spr = 0 , and since p and r are not zero, s must be zero. (Note that although rst = 0, and so either s or t must be zero, this is not sufficient to state which must be zero)4.A. 1/5B. 6/5C. 6³D. 64 / 5E. 64Correct Answer: E解析:65 = 64x 6(64 x 6) - 64 = 64(6 - 1) = 64 x 5 Now, dividing by 5 will give us 645. -20 , - 16 , - 12 , -8 ....In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence?A. 0B. 200C. 440D. 668E. 762Correct Answer: E解析:All terms in the sequence will be multiples of 4. 762 is not a multiple of 4SAT 考试数学练习题 7来源 : 太傻网考试频道整理时间 : 2009 年 08 月 27 日1. If a² = 12, then a4 =A. 144B. 72C. 36D. 24E. 16Correct Answer:A解析:a4 = a2 x a2 = 12 x 12 = 1442. If n is even, which of the following cannot be odd?I n + 3II 3nIII n² - 1A. I onlyB. II onlyC. III onlyD. I and II onlyE. I, II and IIICorrect Answer: B解析:In case I , even plus odd will give odd. In case II, odd times even will give even. In case III even squared is even, and even minus odd is odd. (You can check this by using an easy evennumber like 2 in place of n). Only case II cannot be odd.3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?I 24II 20III 5A. I onlyB. II onlyC. III onlyD. II and III onlyE. I, II and IIICorrect Answer: D解析:The maximum area of the triangle will come when the given sides are placed at right angles. If we take 8 as the base and 5 as the height the area = ½ x 8 x 5 = 20. We can alter the angle between the sides to make it less or more than 90, but this will only reduce the area. (Draw it out for yourself). Hence the area can be anything less than or equal to 20.4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?A. 12B. 11C. 10D. 9E. 8Correct Answer: E解析:Food consumed per day = 39/6. In the remaining days it will consume 91 - 39 pounds = 52 pounds. Now divide the food by the daily consumption to find the number of days. 52 / (39/6) = 52 x (6 / 39) = 85. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?A. 8pB. pqC. pq + 27D. -pE. (p - q)6Correct Answer: C解析:A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5. Consider the answer choices in turn. 8 is the cube of 2, and p is a cube, and so the product will also be a cube. pq will also be a cube as shown above.pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube. -p will be a cube. Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).SAT 考试数学练习题 8来源 : 太傻网考试频道整理时间 : 2009 年 08 月 27 日6. What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)?A. 3B. √31C. √41D. 7E. 9Correct Answer: C解析:Sketch a diagram and calculate the distance (hypotenuse of a right triangle) using Pythagoras theorem.Vertical height of triangle = 5 ; horizontal side = 4 ; hypotenuse = √(25 + 16) = √417. n is an integer chosen at random from the set{5, 7, 9, 11 }p is chosen at random from the set{2, 6, 10, 14, 18}What is the probability that n + p = 23 ?A. 0.1B. 0.2C. 0.25D. 0.3E. 0.4Correct Answer:A解析:Each of the integers in the first set could be combined with any from the second set, giving a total of 4 x 5 = 20 possible pairs. Of these the combinations that could give a sum of 23 are (5 + 18), and (9 + 14). This means that the probability of getting a sum of 23 is 2/20 = 1/108. A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?A. 0.75DB. 0.76DC. 0.765DD. 0.775DE. 0.805DCorrect Answer: C解析:If the price is reduced by 15 %, then the new price will be 0.85D. If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D9. All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?A. 2B. 2√2C. 3D. √ 10E. √20Correct Answer: E解析:The longest line segment that can be drawn without passing through any dots other than those at the beginning and end of the segment, such a line could go from the middle dot in the top row to either the bottom left or right dot. In any case the segment will be the hypotenuse of a right triangle with sides 2 and 4. Using Pythagoras theorem the hypotenuse will be √(2 ² + 4 ² ) = √2010. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?A. 9B. 10C. 11D. 12E. 13Correct Answer: D解析:If the radius is 7, the circumference = 14π . The length of the arc is 100/360 of the circumference. Taking π as 22/7 we get. (100 x 14 x 22) / (360 x 7) which reduces to 440/ 36 = 12.22 (i.e. approx. 12)。
美国“高考”SAT考试的数学题
美国“高考”SAT考试的数学题数学第一部分时间（25分钟）16个问题说明：这部分包含有两种类型的问题。
你将有25分钟时间来完成他们。
对于1—8，在所给选项中选出一个最佳答案，然后再答题卡上填上相应的圆圈，你可以使用任何可用的草稿纸空间。
注释：1、可以使用计算器。
2、所有使用的数字均为实数。
3、在测试中，问题中所提供的数字或图表都包含一定的信息，这对于解题很有帮助。
所有图表都是比较准确的，除非在某些具体问题中，图表没有按比例绘制。
所有数字都呈现于平面上，除非另有说明。
4、除非另有规定，对于任何函数f 的值域都是所有实数x 的集合，并使得f(x) 是实数。
可能用到的公式：1、If 4(t+u) + 3 =19, then t+u=如果4(t+u) + 3 =19, 那么t+u=A 3B 4C 5D 6E 72、如图，三条直线相交于一点。
如果f=85, e=25, 那么a 的值是多少？A 60B 65C 70D 75E 853、如果玛丽开车行驶n 英里用了t 小时，那么下列哪个可以表示她行驶的平均速度，英里/小时？A n/tB t/nC 1/ntD ntE n²t4、如果a 是一个奇数，b 是一个偶数，那么选项中哪一个是奇数？A 3bB a+3C 2(a+b)D a+2bE 2a+b5、在平面坐标内，F(-2,1),G(1,4), H(4,1)在以P为圆心的圆上，那么点P的坐标是什么？A（0,0）B（1,1）C（1,2）D（1，-2）E（2.5,2.5）6、如图，如果-3≤x≤6，那么x 有几个值，使得f(x)=2?A 零B 一个C 两个D 三个E 三个以上7、如果t 和t+2 的算术平均值是x, t 和t-2的算术平均值是y，那么x 和y 的算术平均值是多少？A 1B 1/2C tD t+1/2E 2t8、对于任何数x 和y,假设x△y=x²+xy+y²,那么（3△1）△1等于多少？A 5B 13C 27D 170E 1839、摩根的植物在一年之内从42厘米长到57厘米。
sat数学试题
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 Math Practice Test Two SAT数学模拟试题二
16 A B C D E
234
Practice Test II
Practice Test IIA: 25 Minutes, 18 Questions (8 Multiple-Choice and 10 Grid-in) Practice Test IIB: 25 Minutes, 20 Multiple-Choice Questions Practice Test IIC: 20 Minutes, 16 Multiple-Choice Questions
235
Part III: Math Practice Tests
Practice Test IIA
Time: 25 minutes 18 questions (8 multiple-choice and 10 grid-in)
Directions: This section is composed of two types of questions. Use the 25 minutes allotted to answer both question types. For Questions 1–8, select the one correct answer of the five choices given and mark the corresponding circle on your answer sheet. Your scratch work should be done on any available space in the section.
A. –12 B. –4 C. 0 D. 3 E. 4
sat数学考试试题(可编辑修改版)
sat数学考试试题(可编辑修改版) SAT数学考试试题(可编辑修改版)在这份SAT数学考试试题中，我们为您精心挑选了一些题目，希望能够帮助您进行备考和巩固数学知识。
请您认真阅读题目，并尽量独立思考和解答。
每道题后面都附带了详细的解答和解题思路，以供参考。
祝您考试顺利！题目一：若a和b都是正整数，且a/b = 1/4，那么a+b的值是多少？A. 5B. 8C. 14D. 16E. 20解答一：我们可以通过代入法求解这道题。
假设a=1，b=4，则a/b=1/4。
因此，a+b=1+4=5。
所以，选项A是正确答案。
题目二：某公司的年度收入增长率为20%，每年的增长幅度相同。
如果这家公司在2018年的年度收入为100万美元，那么在2021年的年度收入是多少？A. 120万美元B. 160万美元C. 140万美元D. 180万美元E. 200万美元解答二：我们可以使用复合增长率的方法来解决这道题。
首先，我们假设2018年的年度收入为x万美元。
根据题目的信息，可得以下等式：x * (1 + 0.2) * (1 + 0.2) * (1 + 0.2) = 100解方程可得：(1.2)^3 * x = 1001.728x = 100x ≈ 57.87（万美元）因此，2021年的年度收入约为57.87 * (1 + 0.2) * (1 + 0.2) * (1 + 0.2) ≈ 140（万美元）。
所以，选项C是正确答案。
题目三：在直角三角形ABC中，角A是直角，边AC = 10，边BC = 24。
点D位于边BC上，使得边AD垂直于边BC。
求边AD的长度是多少？A. 7B. 8C. 12D. 15E. 20解答三：由题目可知，三角形ABC是一个直角三角形。
根据勾股定理，可得：AC^2 + BC^2 = AB^210^2 + 24^2 = AB^2100 + 576 = AB^2676 = AB^2因此，AB = √676 = 26。
sat数学练习题
SAT数学练习题一、代数基础1. 如果3x 5 = 7，那么x的值是多少？2. 解方程：2(3x 4) + 4 = 5x + 23. 已知a ≠ 0，求表达式(a 3)²的最小值。
4. 简化表达式：(2x³ 3x²) (4x³ 5x²)5. 若x + y = 10，x y = 4，求x和y的值。
二、几何图形1. 计算直角三角形的斜边长度，已知两条直角边分别为3和4。
2. 在一个等边三角形中，每条边的长度为6，求该三角形的周长。
3. 已知圆的半径为5，求该圆的面积。
4. 计算长方体的体积，长、宽、高分别为8、6和4。
5. 若一个正方形的对角线长度为10，求正方形的面积。
三、数据分析、统计与概率2. 从一副52张的扑克牌中随机抽取一张，求抽到红桃的概率。
3. 一个袋子里有5个红球、3个蓝球和2个绿球，随机抽取一个球，求抽到蓝球或绿球的概率。
5. 某班级有30名学生，其中18名喜欢篮球，15名喜欢足球，5名两者都喜欢。
求至少喜欢一项运动的学生人数。
四、函数与方程1. 已知函数f(x) = 2x + 3，求f(5)的值。
2. 若g(x) = 3x² 4x + 1，求g(1)的值。
3. 解不等式：2x 5 > 74. 已知函数h(x) = x² 4x + 4，求h(x)的最小值。
5. 求函数k(x) = |x 3|在x = 2时的导数值。
五、数列与级数1. 计算数列1, 3, 5, 7, 9的前5项和。
2. 已知等差数列的第3项为7，第5项为11，求首项和公差。
3. 求等比数列8, 24, 72的下一项。
4. 计算数列2, 4, 8, 16, 32的第6项。
5. 已知数列的通项公式为an = 3n 2，求前5项的和。
六、实际问题解决1. 小明购买了3本书和2支笔，共花费了45元。
如果每本书比每支笔贵5元，求每本书和每支笔的价格。
2. 一辆汽车以60公里/小时的速度行驶，另一辆汽车以80公里/小时的速度行驶。
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 .。
SAT2数学习题6套
(a) ¶ (b) 2 ·¶ (c) 3 ·¶ (d) 4 ·¶ (e) ¶/2
o Answer: OAB equilateral so angleAOB is equal to 60o. The ratio between the AOB angle and 360o is equal to the ratio between the length of the arc AB and the circumference of the circle. 60o/360o = arcAB / (2 ¶·9) arcAB = 3 ·¶
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更多 SAT 考试资料，请访问 Question #2: What is the length of the arc AB, if O is the center of the circle and triangle
Question #6: If 2x < 100 and x is an integer, how many of the 2x + 2 integers will be divisible by 3 and by 2?
(a) 1
(b) 2
(c) 3
(d) 4
(d) 5 o Answer: 26 = 64 and 27 = 128. If 2x < 100, then the highest value of x is 6. Possible values for x: 0 , 1 , 2 , 3 , 4, , 5 , 6. 2x + 2 can take the values 3 , 4 , 6 , 10 , 18 , 34 , 66. Out of these values, only 6 , 18 and 66 are divisible by 3 and by 2. The correct answer is (c).
SAT强化班讲义--万一叶ver2.2
SAT 强化填空讲义Ver 2.2一. SAT填空简介(1) 你最好和他商量一下，------他会生气的。
(A)如果 (B)要么 (C)可是 (D)于是(2) By the end of 2015, the population of India ------ surpassed that of China.(A) will (B) will have (C) have (D) had(3) 好人是------。
(A) 爱好和平的 (B) 可耻的 (C) 受到尊敬的 (D) 不坏的 (E) 公平的(4)张飞，三国时期的将领，是________; 他外表彪悍，能智擒马岱。
(A) 易怒的 (B) 武力高超的 (C) 仗义的 (D) 有谋略的 (E) 多才多艺的(5) Rather than enhancing a country’s security, the successful development of nuclear weapons could serve at first to increase that country’s ------.(A) bravery (B) influence (C) responsibility (D) moderation (E) vulnerability(6)张飞，三国时期的将领，是------; 他不仅武艺高超，而且善于画美女。
(A) 易怒的 (B) 爱美女的 (C) 仗义的 (D) 有谋略的 (E) 多才多艺的(7) A true rebel, Leslie often did what was ------ simply to demonstrate her inclination to disobey taboos.(A) courageous (B) monotonous (C) customary (D) arduous (E) forbidden1.5 重复的两种考察方式1.5.1 空格与题干的重复(1) That critic’s writing is so obscure upon first reading, one finds its ------ hard to penetrate.(A) brevity (B) rigidity (C) floridity(D) harmony (E) opacity(2) To avoid being ------, composer Stephen Sondheim strives for an element of surprise in his songs.(A) erratic(B) informal (C) elaborate (D) predictable (E) idiosyncratic(3) As a person who combines care with ------, Marisa completed her duties with ------ as well as zeal.(A) levity .. resignation(B) geniality .. ardor(C) vitality .. willingness(D) empathy .. rigor(E) enthusiasm .. meticulousness1.5.2考察空格与空格的关系(1) Although the bystander’s account of the car accident at first seemed ------, the police officer was surprised, on further investigation, to find that it was ------.(A) dubious .. erroneous(B) incongruous .. inconsistent(C) implausible .. correct(D) logical .. pertinent(E) probable .. coherent(2) As scientists at the Smithsonian have observed, the institution’s range of scientific inquiry may be ------, but its financial resources are far less ------.(A) restricted .. substantial(B) unbounded .. confined(C) admirable .. limited(D) vast .. extensive(E) diminishing .. stable(3) Improvements in refrigeration and transportation in the nineteenth century ------ the ------ of available food for many families in the United States.(A) slowed .. distribution(B) accelerated .. perishability(C) expanded .. variety(D) lowered .. amount(E) created .. dearth二. SAT填空解题步骤2.1(1) The ------ of Maria Irene Fornes’play Mud—a realistic room perched on a dirt pile—challenges conventional interpretations of stage scenery.(A) appeal (B) plot(C) setting(D) mood(E) rehearsal(2)张飞的 ------, 经过千锤百炼，当今的科学家希望通过相变来模拟它的制造，超过历史上任何一件兵器。
SAT数学练习题(四)-智课教育出国考试.
智课网 S A T 备考资料SAT数学练习题(四-智课教育出国考试SAT数学练习题 1If f(x = x2 – 3, where x is an integer, which of the following could be a value of f(x?I 6II 0III -6A. I onlyB. I and II onlyC. II and III onlyD. I and III onlyE. I, II and IIICorrect Answer: A解析:Choice I is correct because f(x = 6 when x=3. Choice II is incorrect because to make f(x = 0, x2 would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x = 0, x2 would have to be –3 but squares cannot be negative. (The minimum value for x2 is zero; hence, the minimum value for f(x = -3SAT数学练习题 2For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?A. 48B. 49C. 50D. 51E. 52Correct Answer: C解析:1 < 4n + 7 < 200. n can be 0, or -1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be lessthan1. The largest value for n will be an integer < (200 - 7 /4. 193/4 = 48.25, hence 48. The number of integers between -1 and 48 inclusive is 50SAT数学练习题 3In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?A. 23B. 22C. 18D. 16E. 14Correct Answer: B解析:First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99. Therefore in the given problem D must be 1. Now use trial and error to satisfy the sum 5A + BC = 143. A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13. With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8. A + C + B + D = 13 + 8 + 1 = 22SAT数学练习题 412 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth, and 40 cm height. How high (in cm will the water rise?(1 litre = 1000cm3A. 6B. 8C. 10D. 20E. 40Correct Answer: B解析:Total volume of water = 12 liters = 12 x 1000 cm3. The base of the aquarium is 50 x 30 = 1500cm3. Base of tank x height of water = volume of water. 1500 x height = 12000; height = 12000 / 1500 = 8SAT数学练习题 5Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?A. 11/P + 6B. P/11 +6C. 17 - P/6D. 17/PE. 11.5PCorrect Answer: A解析:Let Ben’s age now be B. Anita’s age now is A. (A - 6 = P(B - 6 But A is 17 and therefore 11 = P(B - 6. 11/P = B-6(11/P + 6 = B。
数学选修2-2自主练习：2.2.2间接证明 含解析 精品
自主广场我夯基 我达标1.设a 、b 是异面直线，在a 上任取两点A 1、A 2，在b 上任取两点B 1、B 2，试证：A 1B 1与A 2B 2也是异面直线.思路解析：证明异面直线常用反证法.证明：假设A 1B 1与A 2B 2不是异面直线,则A 1B 1与A 2B 2确定一个平面α.∴A 1、B 1、A 2、B 2∈α.∴A 1A 2⊂α,B 1B 2⊂α,即a ⊂α,b ⊂α.∴a 、b 共面于α,与a 、b 是异面直线矛盾.∴假设不成立.∴A 1B 1与A 2B 2也是一异面直线.2.设a 、b 、c 都是正数，则三个数ac c b b a 1,1,1+++( ) A.都大于2 B.至少有一个大于2C.至少有一个不小于2D.至少有一个不大于2 思路解析：)1()1()1()1()1()1(cc b b a a a c c b b a +++++=+++++≥2+2+2=6,当且仅当a=b=c=1时取“=”.答案:C3.求证：一个三角形中至少有一个内角不小于60°.思路分析：“至少”问题可用反证法，根据三角形的内角之和为180°解答.证明：假设△ABC 的三个内角A 、B 、C 都小于60°,即∠A ＜60°，∠B ＜60°,∠C ＜60°,相加得∠A+∠B+∠C ＜180°.这与三角形内角和定理矛盾，∴∠A 、∠B 、∠C 都小于60°的假定不能成立.∴一个三角形中，至少有一个内角不小于60°.4.如图2-2-3所示，在△ABC 中，AB ＞AC ，AD 为BC 边上的高线，AM 是BC 边上的中线，求证：点M 不在线段CD 上.图2-2-3思路分析：点M 不在线段CD 上不易证出，可假设M 在线段CD 上，用反证法证明. 证明：假设M 在线段CD 上，则BD ＜BM=CM ＜CD ，且AB 2=BD 2+AD 2,AC 2=AD 2+CD 2.∴AB 2=BD 2+AD 2＜BM 2+AD 2＜CD 2+AD 2=AC 2，即AB 2＜AC 2,AB ＜AC.这与AB ＞AC 矛盾，∴点M 不在线段CD 上.5.求证：若a≥b ＞0,n 为正整数，且n≥2，则n a ≥n b .思路分析：开方不易运算，可转为乘方运算.证明：假设n n b a <,则n n n n b a )()(<,即a ＜b.这与a≥b ＞0矛盾， ∴n a ≥n b 成立.6.设正实数a 、b 、c 满足a+b+c=1,则a 、b 、c 中至少有一个数不小于______________. 思路解析：假设a 、b 、c 中至少有一个数不小于x 的反命题成立.假设a 、b 、c 都小于x ，即a ＜x,b ＜x,c ＜x,∴a+b+c ＜3x.∵a+b+c=1,∴3x ＞1.∴x ＞31,若取x=31就会产生矛盾. 答案:31 我综合 我发展7.下列命题错误的是( )A.三角形中至少有一个内角不小于60°B.四面体的三组对棱都是异面直线C.闭区间［a 、b ］上的单调函数f(x)，至多有一个零点D.设a 、b ∈Z ,若a+b 是奇数，则a 、b 中至少有一个是奇数思路解析：逐一用反证法判断.答案:D8.平面上有四个点，没有三点共线，证明以每三点为顶点的三角形不可能都是锐角三角形. 思路分析：命题的结论是以否定形式给出，宜采用反证法.证明：假设以每三个点为顶点的四个三角形都是锐角三角形.记这四个点为A 、B 、C 、D ，考虑点D 在△ABC 之内或之外两种情况：(1)如果点D 在△ABC 之内，由假设围绕点D 的三个角都是锐角，其和小于270°，这与一个周角等于360°矛盾.(2)如果点D 在△ABC 外，∵∠A 、∠B 、∠C 、∠D 都小于90°与四边形ABCD 的内角和为360°相矛盾. 综上，假设不成立，∴原结论成立.9.已知f(x)=x 2+px+q.(1)求证:f(1)+f(3)-2f(2)=2;s(2)求证：|f(1)|,|f(2)|,|f(3)|中至少有一个不小于21. 思路分析：本题可用反证法，借助第(1)问的结论得到矛盾.证明：(1)f(1)+f(3)-2f(2)=(1+p+q)+(9+3p+q)-2(4+2p+q)=2.(2)假设|f(1)|、|f(2)|、|f(3)|中至少有一个不小于12不成立.则假设|f(1)|、|f(2)|、|f(3)|都小于21. 则|f(1)|+2|f(2)|+|f(3)|＜2.而|f(1)|+2|f(2)|+|f(3)|≥f(1)+f(3)-2f(2)=(1+p+q)+(9+3p+q)-(8+4p+2q)=2. 与|f(1)|+2|f(2)|+|f(3)|＜2相矛盾，故假设不成立.1∴|f(1)|、|f(2)|、|f(3)|中至少有一个不小于.2。
高中数学人教B必修三优质练习：2.2.2 用样本的数字特征估计总体的数字特征 Word含答案
2.2.2 用样本的数字特征估计总体的数字特征课后篇巩固探究A 组1.能反映一组数据的离散程度的是( )A.频数B.平均数C.标准差D.极差解析:本题考查数据的基本特征量以及它们的含义,因为标准差反映数据的波动大小及离散程度,所以应选C. 答案:C2.如右的茎叶图记录了甲、乙两组各五名学生在一次英语听力测试中的成绩(单位:分). 已知甲组数据的中位数为15,乙组数据的平均数为16.8,则x ,y 的值分别为( ) A.2,5B.5,5C.5,8D.8,8解析:由甲组数据中位数为15,可得x=5;而乙组数据的平均数16.8=,可解得y=8.故选C. 答案:C3.某同学使用计算器求30个数据的平均数时,错将其中一个数据105输入为15,则由此求出的平均数减去实际平均数的值是( ) A.3.5B.-3C.3D.-0.5答案:B4.(2017安徽宣城高三模拟)若样本数据x1,x2,…,x10的标准差为8,则数据2x1-1,2x2-1,…,2x10-1的标准差为()A.8B.15C.16D.32解析:设样本数据x1,x2,…,x10的平均数为,由方差定义知--…-=64,又数据2x1-1,2x2-1,…,2x10-1的平均数为2-1,则其方差为------…---=4--…-=4×64,故其标准差为16.答案:C5.甲、乙两人在一次射击比赛中各射靶5次,两人成绩的条形统计图如图所示,则()A.甲的成绩的平均数小于乙的成绩的平均数B.甲的成绩的中位数等于乙的成绩的中位数C.甲的成绩的方差小于乙的成绩的方差D.甲的成绩的极差小于乙的成绩的极差(4+5+6+7+8)=6,解析:甲(5×3+6+9)=6,甲的成绩的方差为(22×2+12×2)=2,乙的成绩的方差为(12×3+32×1)=2.4.乙答案:C6.对某同学的6次物理测试成绩(满分100分)进行统计,作出的茎叶图如图所示,给出关于该同学物理成绩的以下说法:①中位数为84;②众数为85;③平均数为85;④极差为12.其中,正确说法的序号是()A.①②B.③④C.②④D.①③解析:中位数是=84,众数为83,平均数是=85,极差是91-78=13,故选D.答案:D7.10名工人某天生产同一零件,生产的件数分别是15,17,14,10,15,17,17,16,14,12.设平均数为a,中位数为b,众数为c,则a,b,c的大小顺序为.答案:c>b>a8.一组数据x1,x2,…,x n的方差为9,则数据3x1,3x2,…,3x n的方差是,标准差是.答案:8199.甲、乙两种水稻试验品种连续4年的单位面积平均产量如下:其中产量比较稳定的水稻品种是.解析:甲种水稻单位面积平均产量的平均值为10,则方差为----=0.025;乙种水稻单位面积平均产量的平均值为10,则方差为----=0.045;∵0.025<0.045,∴甲种水稻产量比较稳定.答案:甲10.导学号17504031甲、乙两位学生参加数学竞赛培训.现分别从他们在培训期间参加的若干次预赛成绩中随机抽取8次,记录如下:甲8281797895889384乙9295807583809085(1)用茎叶图表示这两组数据.(2)现要从中选派一人参加数学竞赛,从统计学的角度考虑,你认为选派哪位学生参加合适?请说明理由.解:(1)作出茎叶图如下:(2)派甲参赛比较合适.理由如下:(70×2+80×4+90×2+8+9+1+2+4+8+3+5)=85,甲(70×1+80×4+90×3+5+0+0+3+5+0+2+5)=85,乙[(78-85)2+(79-85)2+(81-85)2+(82-85)2+(84-85)2+(88-85)2+(93-85)2+(95-85)2]=35.5, 甲[(75-85)2+(80-85)2+(80-85)2+(83-85)2+(85-85)2+(90-85)2+(92-85)2+(95-85)2]=41, 乙因为,甲乙甲乙所以甲的成绩较稳定,派甲参赛比较合适.B组1.已知数据x1,x2,x3,…,x n是某市普通职工n(n≥3,n∈N+)个人的年收入,设这n个数据的中位数为x,平均数为y,方差为z,如果再加上世界首富的年收入x n+1,那么关于这n+1个数据,下列说法中正确的是()A.年收入平均数大大增大,中位数一定变大,方差可能不变B.年收入平均数大大增大,中位数可能不变,方差变大C.年收入平均数大大增大,中位数可能不变,方差也不变D.年收入平均数可能不变,中位数可能不变,方差可能不变答案:B2.为比较甲、乙两地某月14时的气温状况,随机选取该月中的5天,将这5天中14时的气温数据(单位:℃)制成如图所示的茎叶图.考虑以下结论:①甲地该月14时的平均气温低于乙地该月14时的平均气温;②甲地该月14时的平均气温高于乙地该月14时的平均气温;③甲地该月14时的平均气温的标准差小于乙地该月14时的气温的标准差;④甲地该月14时的平均气温的标准差大于乙地该月14时的气温的标准差.其中根据茎叶图能得到的统计结论的编号为()A.①③B.①④C.②③D.②④解析:甲地数据为:26,28,29,31,31;乙地数据为:28,29,30,31,32.所以甲=29,乙=30,甲×[(26-29)2+(28-29)2+(29-29)2+(31-29)2+(31-29)2]=3.6,乙×[(28-30)2+(29-30)2+(30-30)2+(31-30)2+(32-30)2]=2,所以s 甲= ,s 乙= ,s 甲>s 乙. 即正确的有①④. 答案:B3.在某地区某高传染性病毒流行期间,为了建立指标来显示疫情已受控制,以便向该地区居民显示可以过正常生活,有公共卫生专家建议的指标是“连续7天每天新增感染人数不超过5”,根据连续7天的新增病例数计算,下列各选项中,一定符合上述指标的是( )①平均数x ≤3;②标准差s ≤2;③平均数x ≤3且标准差s ≤2;④平均数x ≤3且极差小于或等于2;⑤众数等于1且极差小于或等于4. A.①②B.③④C.③④⑤D.④⑤解析:本题考查平均数、标准差、极差、众数的统计意义.假设连续7天新增病例数为1,2,3,3,3,3,6,易知满足平均数x ≤3且标准差s ≤2,但是不符合指标,所以①②③错误.若极差等于0或1,在平均数x ≤3的条件下显然符合指标;若极差等于2,则极小值与极大值的组合可能有:(1)0,2;(2)1,3;(3)2,4;(4)3,5;(5)4,6.在平均数x ≤3的条件下,只有(1)(2)(3)成立,且显然符合指标,所以④正确.又易知⑤正确,故选D.答案:D4.如图是一个容量为100的样本的重量频率分布直方图,则由图可估计样本重量的中位数为 .解析:根据频率分布直方图,得∵0.06×5=0.3<0.5,0.3+0.1×5>0.5,令0.3+0.1x=0.5,解得x=2,∴中位数是10+2=12.答案:125.在发生某公共卫生事件期间,有专业机构认为该事件在一段时间没有发生大规模群体感染的标准为“连续10天,每天新增疑似病例不超过7人”.根据过去10天甲、乙、丙、丁四地新增疑似病例的数据,一定符合该标准的是.(填序号)①甲地:总体均值为3,中位数为4②乙地:总体均值为1,总体方差大于0③丙地:中位数为2,众数为3④丁地:总体均值为2,总体方差为3解析:根据信息可知,连续10天内,每天的新增疑似病例不能有超过7的数,选项①中,中位数为4,可能存在大于7的数;同理,在选项③中也有可能;选项②中的总体方差大于0,叙述不明确,如果数目太大,也有可能存在大于7的数;选项④中,根据方差公式,如果有大于7的数存在,那么方差就大于3,故答案选④.答案:④6.据报道,某公司的32名职工的月工资(单位:元)如下:(1)求该公司职工工资的平均数、中位数、众数.(精确到1元)(2)假设副董事长的工资从5 000元提升到20 000元,董事长的工资从5 500元提升到30 000元,那么新的平均数、中位数、众数又是什么?(精确到1元)(3)你认为哪个统计量更能反映这个公司员工的工资水平?结合此问题谈一谈你的看法.解:(1)平均数为=≈2 091(元).中位数是1 500元,众数是1 500元.(2)平均数为=≈3 288(元).中位数是1 500元,众数是1 500元.(3)在这个问题中,中位数或众数均能反映该公司员工的工资水平,因为公司中少数人的工资额与大多数人的工资额差别较大,这样导致平均数与中位数偏差较大,所以平均数不能反映这个公司员工的工资水平.7.导学号17504032对某校高三年级学生参加社区服务次数进行统计,随机抽取M名学生作为样本,得到这M名学生参加社区服务的次数,根据此数据作出了频数与频率的统计表和频率分布直方图如图所示.[25,30]20.05合计M1(1)求出表中M,p及图中a的值;(2)若该校高三学生有240人,试估计该校高三学生参加社区服务的次数在区间[10,15)内的人数;(3)估计这次学生参加社区服务次数的众数、中位数以及平均数.解:(1)由分组[10,15)内的频数是10,频率是0.25,知=0.25,所以M=40.因为频数之和为40,所以10+24+m+2=40,m=4,p==0.10.因为a是对应分组[15,20)的频率与组距的商,所以a==0.12.(2)因为该校高三学生有240人,分组在[10,15)内的频率是0.25,所以估计该校高三学生参加社区服务的次数在此区间内的人数为240×0.25=60.(3)估计这次学生参加社区服务次数的众数是=17.5.因为n==0.6,所以样本中位数是15+-≈17.1,估计这次学生参加社区服务次数的中位数是17.1,样本平均数是12.5×0.25+17.5×0.6+22.5×0.1+27.5×0.05=17.25,估计这次学生参加社区服务人数的平均数是17.25.8.导学号17504033在每年的春节后,某市政府都会发动公务员参与到植树绿化活动中去.林业管理部门为了保证树苗的质量,都会在植树前对树苗进行检测.现从甲、乙两种树苗中各抽测了10株树苗,量出它们的高度如下(单位:cm),甲:37,21,31,20,29,19,32,23,25,33;乙:10,30,47,27,46,14,26,10,44,46.(1)画出两组数据的茎叶图,并根据茎叶图对甲、乙两种树苗的高度作比较,写出两个统计结论;(2)设抽测的10株甲种树苗高度平均值为x,将这10株树苗的高度依次输入,按程序框图(如图)进行运算,问输出的s的大小为多少?并说明框图中s的统计学意义.解:(1)茎叶图如图所示(单位:cm):统计结论:(任意两个即可)①甲种树苗的平均高度小于乙种树苗的平均高度;②甲种树苗比乙种树苗长得整齐;③甲种树苗的中位数为27,乙种树苗的中位数为28.5;④甲种树苗的高度基本上是匀称的,而且大多数集中在均值附近,乙种树苗的高度分布比较分散.高中数学必修3(2)x=27,s=35,s表示10株甲种树苗高度的方差.。
高中数学2.2二项分布及其应用2.2.2事件的相互独立性优化练习新人教A版选修2-3
2.2.2 事件的相互独立性[课时作业] [A 组 基础巩固]1．把标有1,2的两张卡片随机地分给甲、乙；把标有3,4的两张卡片随机地分给丙、丁，每人一张，事件“甲得1号纸片”与“丙得4号纸片”是( ) A ．互斥但非对立事件 B ．对立事件 C ．相互独立事件D ．以上答案都不对解析：相互独立的两个事件彼此没有影响，可以同时发生，因此它们不可能互斥．故选C. 答案：C2．两个实习生每人加工一个零件，加工为一等品的概率分别为23和34，两个零件是否加工为一等品相互独立，则这两个零件中恰有一个一等品的概率为( ) A.12 B.512C.14D.16解析：设“两个零件中恰有一个一等品”为事件A ，因事件相互独立，所以P (A )＝23×14＋13×34＝512. 答案：B3．设两个独立事件A 和B 都不发生的概率为19，A 发生B 不发生的概率与B 发生A 不发生的概率相同，则事件A 发生的概率P (A )是( ) A.29 B.118C.13D.23解析：由P (A B )＝P (B A )得P (A )P (B )＝P (B )·P (A )，即P (A )[1－P (B )]＝P (B )[1－P (A )]，∴P (A )＝P (B )．又P (A B )＝19，∴P (A )＝P (B )＝13.∴P (A )＝23.答案：D4．在如图所示的电路图中，开关a ，b ，c 闭合与断开的概率都是12，且是相互独立的，则灯亮的概率是( )A.18B.38C.14D.78解析：设开关a ，b ，c 闭合的事件分别为A ，B ，C ，则灯亮这一事件E ＝ABC ∪AB C ∪A B C ，且A ，B ，C 相互独立，ABC ，AB C ，A B C 互斥，所以P (E )＝P (ABC ∪AB C ∪A B C )＝P (ABC )＋P (AB C )＋P (A B C )＝P (A )P (B )P (C )＋P (A )P (B )P (C )＋P (A )P (B )P (C ) ＝12×12×12＋12×12×⎝ ⎛⎭⎪⎫1－12＋12×⎝ ⎛⎭⎪⎫1－12×12＝38.答案：B5．甲、乙两名学生通过某种听力测试的概率分别为12和13，两人同时参加测试，其中有且只有一人能通过的概率是( ) A.13 B.23 C.12D ．1解析：设事件A 表示“甲通过听力测试”，事件B 表示“乙通过听力测试”． 依题意知，事件A 和B 相互独立，且P (A )＝12，P (B )＝13.记“有且只有一人通过听力测试”为事件C ，则C ＝(A B )∪(A B )，且A B 和A B 互斥．故P (C )＝P ((A B )∪(A B ))＝P (A B )＋P (A B )＝P (A )P (B )＋P (A )P (B )＝12×⎝ ⎛⎭⎪⎫1－13＋⎝ ⎛⎭⎪⎫1－12×13＝12. 答案：C6．某条道路的A ，B ，C 三处设有交通灯，这三盏灯在一分钟内平均开放绿灯的时间分别为25秒、35秒、45秒，某辆车在这条路上行驶时，三处都不停车的概率是________． 解析：P ＝2560×3560×4560＝35192.答案：351927．某天上午，李明要参加“青年文明号”活动．为了准时起床，他用甲、乙两个闹钟叫醒自己．假设甲闹钟准时响的概率是0.80，乙闹钟准时响的概率是0.90，则两个闹钟至少有一个准时响的概率是________．解析：至少有一个准时响的概率为1－(1－0.90)(1－0.80)＝1－0.10×0.20＝0.98. 答案：0.988．如图所示，在两个圆盘中，指针落在本圆盘每个数所在区域的机会均等，那么两个指针同时落在奇数所在区域的概率是________．解析：左边圆盘指针落在奇数区域的概率为46＝23，右边圆盘指针落在奇数区域的概率为23，所以两个指针同时落在奇数区域的概率为23×23＝49.答案：499．从一副除去大小王的扑克牌(52张)中任取一张，设事件A 为“抽得K ”，事件B 为“抽得红牌”，事件A 与B 是否相互独立？是否互斥？是否对立？为什么？解析：由于事件A 为“抽得K ”，事件B 为“抽得红牌”，故抽到的红牌中可能抽到红桃K 或方块K ，故事件A 与B 有可能同时发生，显然它们不是互斥或对立事件．下面判断它们是否相互独立：“抽得K ”的概率为P (A )＝452＝113，“抽得红牌”的概率为P (B )＝2652＝12，“既是K 又是红牌”的概率为P (AB )＝252＝126.因为126＝113×12，所以P (AB )＝P (A )P (B )．因此A 与B 相互独立．10．某班甲、乙、丙三名同学竞选班委，甲当选的概率为45，乙当选的概率为35，丙当选的概率为710.(1)求恰有一名同学当选的概率； (2)求至多有两人当选的概率．解析：设甲、乙、丙当选的事件分别为A 、B 、C ， 则P (A )＝45，P (B )＝35，P (C )＝710.(1)易知事件A 、B 、C 相互独立， 所以恰有一名同学当选的概率为P (AB －C －)＋P (A B C )＋P (A －B －C )＝P (A )P (B )P (C )＋P (A )P (B )P (C )＋P (A )P (B )P (C ) ＝45×25×310＋15×35×310＋15×25×710＝47250. (2)至多有两人当选的概率为1－P (ABC )＝1－P (A )P (B )P (C )＝1－45×35×710＝83125.[B 组 能力提升]1．国庆节放假，甲，乙，丙去北京旅游的概率分别为13，14，15.假定三人的行动相互之间没有影响，那么这段时间内至少有1人去北京旅游的概率为( ) A.5960 B.35 C.12D.160解析：因甲，乙，丙去北京旅游的概率分别为13，14，15.因此，他们不去北京旅游的概率分别为23，34，45，所以，至少有1人去北京旅游的概率为P ＝1－23×34×45＝35. 答案：B2．从甲袋中摸出一个红球的概率是13，从乙袋中摸出一个红球的概率是12且从两个袋中摸球相互之间不受影响，从两袋中各摸出一个球，则23等于( )A ．2个球不都是红球的概率B ．2个球都是红球的概率C ．至少有1个红球的概率D ．2个球中恰有1个红球的概率解析：分别记从甲、乙袋中摸出一个红球为事件A ，B ，则P (A )＝13，P (B )＝12，由于A ，B相互独立，所以1－P (A )P (B )＝1－23×12＝23.根据互斥事件可知C 正确．答案：C3．甲袋中有8个白球，4个红球；乙袋中有6个白球，6个红球．从每袋中任取一个球，则取得同色球的概率为________．解析：设从甲袋中任取一个球，事件A 为“取得白球”，则事件A 为“取得红球”，从乙袋中任取一个球，事件B 为“取得白球”，则事件B 为“取得红球”． ∵事件A 与B 相互独立，∴事件A 与B 相互独立． ∴从每袋中任取一个球，取得同色球的概率为P ((A ∩B )∪(A ∩B ))＝P (A ∩B )＋P (A ∩B )＝P (A )P (B )＋P (A )P (B )＝23×12＋13×12＝12. 答案：124．设甲、乙、丙三台机器是否需要照顾相互之间没有影响，已知在某一小时内，甲、乙都需要照顾的概率为0.05.甲、丙都需要照顾的概率为0.1，乙、丙都需要照顾的概率为0.125.则求甲、乙、丙每台机器在这个小时内需要照顾的概率分别为________，________，________. 解析：记“机器甲需要照顾”为事件A ，“机器乙需要照顾”为事件B ，“机器丙需要照顾”为事件C ，由题意可知A ，B ，C 是相互独立事件． 由题意可知⎩⎪⎨⎪⎧P AB ＝P A P B ＝0.05，P AC ＝P A P C ＝0.1，P BC ＝P B P C ＝0.125，得⎩⎪⎨⎪⎧P A ＝0.2，P B ＝0.25，P C ＝0.5.所以甲、乙、丙每台机器需要照顾的概率分别为0.2，0.25，0.5. 答案：0.2 0.25 0.55．某商场举行的“三色球”购物摸奖活动规定：在一次摸奖中，摸奖者先从装有3个红球与4个白球的袋中任意摸出3个球，再从装有1个蓝球与2个白球的袋中任意摸出1个球．根据摸出4个球中红球与蓝球的个数，设一、二、三等奖如下：(1)求一次摸奖恰好摸到1个红球的概率； (2)求摸奖者在一次摸奖中获奖金额X 的分布列．解析：设A i (i ＝0,1,2,3)表示摸到i 个红球，B j (j ＝0,1)表示摸到j 个蓝球，则A i 与B j 独立．(1)恰好摸到1个红球的概率为 P (A 1)＝C 13C 24C 37＝1835.(2)X 的所有可能值为：0,10,50,200，且 P (X ＝200)＝P (A 3B 1)＝P (A 3)P (B 1)＝C 33C 37·13＝1105；P (X ＝50)＝P (A 3B 0)＝P (A 3)P (B 0)＝C 33C 37·23＝2105，P (X ＝10)＝P (A 2B 1)＝P (A 2)P (B 1)＝C 23C 14C 37·13＝12105＝435，P (X ＝0)＝1－1105－2105－435＝67. 综上可知，获奖金额X 的分布列为6.方案一：考三门课程至少有两门及格为考试通过；方案二：在三门课程中，随机选取两门，这两门都及格为考试通过．假设某应聘者对三门指定课程考试及格的概率分别为0.5，0.6,0.9，且三门课程考试是否及格相互之间没有影响．(1)求该应聘者用方案一通过的概率； (2)求该应聘者用方案二通过的概率．解析：记“应聘者对三门考试及格”分别为事件A ，B ，C .则P (A )＝0.5，P (B )＝0.6，P (C )＝0.9.(1)该应聘者用方案一通过的概率为P 1＝P (AB C )＋P (A BC )＋P (A B C )＋P (ABC )＝0.5×0.6×0.1＋0.5×0.6×0.9＋0.5×0.4×0.9＋0.5×0.6×0.9 ＝0.03＋0.27＋0.18＋0.27＝0.75. (2)应聘者用方案二通过的概率为P 2＝13P (AB )＋13P (BC )＋13P (AC )＝13(0.5×0.6＋0.6×0.9＋0.5×0.9) ＝13×1.29＝0.43.。
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1.Erica has $50.00 saved and receives an allowance of $20.00 each week. Her older brother, Paolo,has $20.00 saved and receives an allowance of $25.00 each week. Which of the following equations best models the number of weeks, w, that must pass for the siblings to have the same amount of money saved? Assume that Erica and Paolo save all of their money during this time period.A.50.00+20.00w=20.00+25.00wB.50.00w+20.00=20.00w+25.00C.20.00(50.00+w)=25.00(20.00+w)D.20.00w+25.00w=50.00+20.002.The mass of a liquid solution is 25 grams (g) and its volume is 40 milliliters (ml). A second liquidsolution has the same density () and a volume of 200 ml. Which of the following equations best models the mass in grams, mm, of the second liquid solution?A.200m = (25)(40)B.200m =C. =D. =3.Two interior angles of a triangle are complementary. The measure of the first angle is half themeasure of the second angle, which has a measure of xx degrees. Which of the following equations best models the sum of the interior angles of this triangle?A.x+2x+90=180B.+x+90=180C.(x+2x+90)=180D.+x+2x=1804. A park shaped like a pentagon has four equal length sides and one unequal side whose length is35 feet (ft). The perimeter of the park is 195 ft. What is the length in feet of one of the equal sides?5.Sasha has $2.65 in change in her pocket. The $2.65 is made up of one quarter plus an equalnumber of nickels and dimes. How many nickels does Sasha have in her pocket?6.The number of subscribers to a certain newspaper decreases by about 2,000 each year. In 2010,there were 19,000 subscribers. In what year should the newspaper expect to have approximately 7,000 subscribers?7.An airplane begins its descent to land from a height of 35,000 feet (ft) above sea level. Theairplane's height changes by about −4000 ft every 3 minutes. Rounded to the nearest minute, in approximately how many minutes will the plane land? Assume that the airport runway is at sea level.8. A car driving on a straight path travels about 260 feet (ft) in 3 seconds. Rounded to the nearestsecond, approximately how many seconds will it take for the car to travel 1 mile (mi) at the samerate? 1 mi=5,280 ft.9.As an object's depth below the surface of a body of salt water increases, so does the pressureacting on the object due to atmospheric and water conditions. The rate at which pressure increases is approximately 11 pounds per square inch (psi) for every increase in depth of 25 feet (ft). The pressure at the surface of the water is 15 psi. Rounded to the nearest foot, at what depth will the pressure acting on the object be 50 psi?10.A piece of wood has a mass of 30 grams (g) and a volume of 40 cubic centimeters (cm3). Asecond piece of wood has the same density () and a volume of 240 cm3. What is the mass in grams of the second piece of wood?11.A meteorologist estimates that on a sunny day, the air temperature decreases by about 4° F forevery 1,000 feet (ft) of elevation gain. On a certain day, the air temperature outside an airplane flying above Seattle is −58° F, and the ground level temperature in Seattle is 70°F. If x is the height, in feet, at which the plane is flying, which of the following best models the situation?A.70= − x − 58B.70= x − 58C.−58 = − 4x + 70D.−58 = 4x + 7012.A taut string of length 10 inches is plucked at the center. The vibration travels along the string at aconstant rate of c inches per millisecond in both directions. If x represents the position on the string from the left-most end, so that 0≤x≤10, which of the following equations can be used to find the location x of the vibration after 0.3 milliseconds?A.| x -5 | =0. 3B.∣cx−5∣=0.3C.| x -0.3 | = 5D.| x - 10 | =0.3c13.In the year 2006, the average home price per square foot in a certain county was$98. For eachyear before or after 2006, the average price per square foot increased by approximately $3.50. In what years could the average home price per square foot be $119?A.2003 and 2009B.2002 and 2010C.2000 and 2012D.1999 and 201314.Oliver mows lawns in his neighborhood. He charges $10 for each regular yard he mows, and hecharges an extra $5 for each large yard that he mows. In one week he mowed 6 more large yards than regular yards and made $265. If r represents the number of regular yards that Oliver mowed, which equation best models the situation?A.10(r+6)+15r=265B.10(r+6) + 5r=265C.10r+15(r+6)=265D.10r + 5(r+6)=26515.Anna spent 3 hours in her garden planting 6 rosebushes. To plant a rosebush, she first dug the hole,then refilled the hole with the root ball, dirt, and compost. She spent twice as long digging the hole for each plant as she did refilling it. If m represents the minutes spent digging a hole for a single rosebush, which equation best models the situation?A.6m+6(2m)=3B.6m+6( )=3C.6m+6(2m)=180D.6m+6( )=18016. Jennifer wants to spend no more than $300 on school clothes. She spends $75 on a jacket and wants to buy some shirts that are on sale for $10 each. Which inequality represents the number, s, of shirts Jennifer can buy?A.B.C.D.17. Teddy is delivering boxes of paper to each floor of an office building. Each box weighs 56 pounds, and Teddy himself weighs 140 pounds. If the maximum capacity of an elevator is 2,000 pounds, or one ton, which of the following inequalities describes how many b boxes Teddy can safely take on each elevator trip without going over the capacity?A.B.C.D.18. A small airplane can carry less than 1050 pounds of luggage and mail. Tuesday's load of mail weighs 490 pounds. If each passenger brings 70 pounds of luggage, what is the greatest possible number of passengers that can travel on the airplane on Tuesday?A.7B.8C.14D.1519. Trevon is going to buy a coat and a hat. The coat costs 3 times as much as the hat. He must spend less than $94. If the cost of the hat costs x dollars, which inequality best models this situation?A.B.C.D.20. A shipping company charges $3.46 for the first pound of a package and $1.53 for each additional pound of the package. If Robin wants to spend under $100 on shipping, which inequality best represents how many pounds, p, Robin can have in her particular package?A.B.C.D.21. Members of the wrestling team are planning to sell pre-ordered programs at matches. The cost to print the programs is $150 plus $0.50 per program. They plan to sell each program for $2. If profit is the amount of money earned from selling programs minus the expenses of printing the programs, how many programs must they sell to make a profit of at least $500?A.260B.261C.433D.43422. Christopher has at most $18.50 to spend at a convenience store. He buys one bag of bananas for $1.50 and a bottle of apple juice for $1.55. If gasoline at this store costs $2.35 per gallon, which of the following number of gallons can he buy for his car without exceeding his budget?A. 4.23B.7.61C.10.82D.15.1723. Jonas is traveling by bus to visit a friend who lives 300 miles away. The friend has asked Jonas to call at least 30 minutes before arriving, so he can pick up Jonas. Jonas's bus travels at a constant speed of 45 miles per hour. Which inequality shows the number of travel hours, t, before which Jonas should call his friend?A.B.C.D.24. One particular hotel in the downtown area costs $90 a night. An additional 10% tax is added to the original cost of the hotel room. There is also a one-time $12 parking charge, and a family can expect to spend $30 on tips during their stay. How many nights can a family spend at the hotel without exceeding their budget of $600?A. 5B. 6C.62D.66。