《GMAT数学讲义》PPT课件.ppt

有关数学的运算,Add,plus Subtract Difference Multiply, times Product divide,有关数学的运算,Add,plus Subtract Difference Multiply,times Product divide,加 减 差 乘 积 除,有关数学的运算,Divisible Divided evenly Divident Divisor Quotient Remainder,有关数学的运算,Divisible Divided evenly Divident Divisor Quotient Remainder,可被整除的 被整除 被除数，红利 因子，除数 商 余数,Which of the following could be the remainder when four consecutive positive integers are each divided by 3? A. 1,2,3,1 B. 1,2,3,4 C. 0,1,2,3 D. 0,1,2,0 E. 0,2,3,0,Power Radical sign,root sign factorial,乘方 方根,阶乘 N!=1*2*3*(N-2)*(N-1)*N 且规定0!=1 例如 8!=1*2*3*4*5*6*7*8,Power Radical sign,root sign factorial,1、根号8除以2倍根号2,If United States imports increased 20 percent and export decreased 10 percent during a certain year,the ratio of imports to exports at the end of the year was how many times the ratio at the beginning of the year? A. 12/11 B. 4/3 C.11/8 D. 3/2 E.2,有关数学的运算,Round off Round to,熟悉： sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236,有关数学的运算,Round off Round to,四舍五入 四舍五入,熟悉： sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236,有关集合,Set Subset Proper subset Solution set Complementary set intersection,有关集合,Set Subset Proper subset Solution set Complementary set intersection,集合 子集 真子集 解集 补集 交集,最近演了3部电影。调查了100个人，其中20人看了所有3部，10人什么都没看。看了每部电影的人数分别为：47，48，55。问：只看了2部的人数？ A 20， B 30， C 40， D 70， E 90。,代数式 方程 不等式,Algebraic Like terms,similar terms Inequality Triangle inequality,代数式 方程 不等式,Algebraic Like terms,similar terms Inequality Triangle inequality,代数项 同类项 不等式 三角不等式,Original equation Equivalent equation Linear equation Quadratic equation,Original equation Equivalent equation Linear equation Quadratic equation,原方程 同解方程， 等价方程 一次方程 二次方程,1.00001*0.99999+1.00002*0.99998=?,分数,fraction improper fraction proper fraction denominator numerator Mixed number,分数,分数 假分数 真分数 分母 分子 带分数,fraction improper fraction proper fraction denominator numerator Mixed number,小数,Decimal Infinite decimal Recurring decimal tenths digit tenth units digit 3-digit number,小数,Decimal Infinite decimal Recurring decimal tenths digit tenth units digit 3-digit number,小数 无穷小数 循环小数 十位 十分位 个位 三位数,基本数论,integer Irrational Real number, rational number multiplier multiple natural number reciprocal,基本数论,整数 无理数 有理数 乘数 倍数 自然数 倒数,integer Irrational Real number, rational number multiplier multiple natural number reciprocal,Positive number Negative number Odd number Even number Composite number Prime number,Positive number Negative number Odd number Even number Composite number Prime number,正数 负数 奇数 偶数 合数 质数,Multiple Factor Greatest common factor Least common multiple,Multiple Factor Greatest common factor Least common multiple,倍数 约数 最大公约数 最小公倍数,Domain range,定义域 值域,Domain range,mean arithmatic mean geometric mean,平均数 算术平均数 几何平均数（几何平均数） n个数之积的n次方根,mean arithmatic mean geometric mean,median,median,（中数） 将一堆数排序之后，正中间的一个数（奇数个数字）， 或者中间两个数的平均数（偶数个数字） e.g. median of 1,7,4,9,2,2,2,2,2,5,8 is 2 median of 1,7,4,9,2,5 is (5+7)/2=6,mode,mode,众数 一堆数中出现次数最多的数 Eg. 1、2、3、2、4、2 1、1、2、3、3,三角形 余玄定理 两线垂直的条件为K1K2=(-1) 三的倍数的特点：所有位数之和可被3整除,In the xy-plane,point R(2,3) and point S(5,6) are two vertices of triangle RST.if the sum of the slopes of the sides of the triangle is 1,which of the following angles could be a right angle? 1.R 2.S 3.T A.none B.1only C.3only D.1and3 only E.1,2and3,.2/3 as many A as B .twice as many. A as B,A=2/3*B A=2*B,Sequence arithmetic progression geometric progression,Sequence arithmetic progression geometric progression,数列 等差数列 等比数列,一个电影院，第一排有16个位置，每后一排多两个，最后一排64，问总共多少？,一个球落下弹回原高度75%，到第三次落地共旅程为2146CM，问最初高度？,Function Inverse function Exponent Logarithm Complementary function Linear function Quadratic function,Function Inverse function Exponent Logarithm Complementary function Linear function Quadratic function,函数 反函数 指数 对数 余函数 一次函数 二次函数,For all positive values of x ,the function f is defined by .of the following,which is the best approximation of f(x)for value of x greater than 1000?,Abscissa ordinate Quadrant Coordinate Slope intercede,Abscissa ordinate Quadrant Coordinate Slope intercede,横坐标 纵坐标 象限 坐标 斜率 截距,排列(permutation) 组合(combination),有两个老师三个学生排队，老师只能在最前或最后，有多少种排法？,6本书其中 paper book 4 本,hard book 2本.求取3本至少1本hard book, 有多少种取法 (2次),w,概率(probability),t,On Monday,Anderson High Schools basketball team will play the team from Baker High School.On Wednesday, Bakers team will play the team from Cole High School.On Friday, Cole will play Anderson.in each game,either team has a 50 percent chance of winning. (a)what is the probability that Anderson will win both its game? (b)what is the probability that Baker will lose both its game? (c)what is the probability that Anderson will win both its game and Baker will lose both its game?,抛三次硬币，相同的面朝上的概率,on the desk show above,a player spins the arrow twice.the fraction is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number is the sector where the arrow stops after the second spin.on every spin,each of the numbered sectors has an equal probability of being the sector on which the arrow stops.what is the probability that the fraction is greater than 1? A. B. C. D. E.,Included angle Interior angle Exterior angle Ajacent angle,Included angle Interior angle Exterior angle Ajacent angle,夹角 内角 外角 邻角,Straight angle Supplementary angles complementary angles,Straight angle Supplementary angles complementary angles,平角 补角 余角,Acute angle Obtuse angle Right angle,Acute angle Obtuse angle Right angle,锐角 钝角 直角,Central angle Round angle,Central angle Round angle,圆心角 圆周角,Triangle Equilateral triangles Isosceles triangles Pythagorean theorem,Triangle Equilateral triangles Isosceles triangles Pythagorean theorem,三角形 等边三角形 等腰三角形 毕达哥拉斯定理,Congruent triangles Similar triangles,Congruent triangles Similar triangles,全等三角形 相似三角形,一个三角形，一个角60度，另一个45度，45度角对应的边长10，问60度对应的边长。,In PQR above, and . what is the value of the fraction,In the figure above, arc SBT is one quarter of a circle with center R and radius 6.if the length plus the width of rectangle ABCR is 8,then the perimeter of the shaded region is A. B. C. D. E.,Quadrilaterals Parallelograms Rectangles Squares Trapezoid rhombus,Quadrilaterals Parallelograms Rectangles Squares Trapezoid rhombus,四边形 平行四边形 矩形 正方形 梯形 菱形,In the figure show above,lengthsAB,BD,and CDare all units.angles Aand C are both .what is the perimeter of ABCD? What is the area of ABCD?,diagonal segment length width perimeter area,diagonal segment length width perimeter area,对角线 线段 长 宽 周长 面积,Polygon Pentagon Hexagon heptagon,Polygon Pentagon Hexagon heptagon,多边形 五边形 六边形 七边形,Octagon enneagon=nonagon decagon,Octagon enneagon=nonagon decagon,八边形 九边形 十边形,Circles Diameter Radius Arc chord,Circles Diameter Radius Arc chord,圆 直径 半径 弧 弦,Tangent circumference,Tangent circumference,切线 周长,In the figure show above,A is center of a circle whose area is 25 .B and C are points on the circle.the measure of angle ABC is .what is the length of line segment BC?,Cubes Rectangular solids Prisms Cylinders Cone Spheres pyramids,Cubes Rectangular solids Prisms Cylinders Cone Spheres pyramids,立方体 长方体 棱柱 圆柱 圆锥 球 棱锥,increase by increase to in terms of ,increase by increase to in terms of ,增加了 增加到 用表达,In the xy-plane above,point Q and S are the centers of the ciecles,which are tangent to the x-axis.what is the slop of line QS? A.1/8 B.1/4 C.1/2 D.7/8 E.1,A wheel has an outer diameter of 11 inchs,as shown above.the rim is 1 inch wide and the diameter of the hub is 2 inches.if each spoke extend inch into the hub and inch into the rim,what is the sum of the length of the 5 spokes,in inches?,The figure above shows the remaining pieces of a paper chain from which a section has been removed.the first link of the original chain was red and the colors of the links formed the repeating pattern of red(R),yellow(Y),green(G),white(W)and blue(B)from left to right.which of the following could be the number of links in the section that was removed? A.60 B.61 C.62 D.63 E.64,In a plane,two regions,S and T,are called “unlinked” if (1)S has no points in common with T. (2)any line segment that can be drawn with both endpoints in S has no points in common with any line segment that canbe draw with both endpoints in T. Which of the following shows a pair of regions that are unlinked?,3, 5, -5, The first term in the sequence of numbers show above is 3.each even-numbered term is 2 more than the previous term and each odd-numbered term,after the first, is -1 times the previous term .for example,the second term is 3+2,and the third term is .what is the 55th term of the sequence? A.-5 B.-3 C.-1 D.3 E.5,5.101001000100001 The decimal number above consists of only 1s and 0s to the right of the decimal point.the first 1 is followed by one 0, the second 1 is followed by two 0s, the third 1 is followed by three 0s,and so on.what is the total number of 0s between 98th and the 101st 1 in this decimal number? A.288 B.291 C.294 D.297 E.300, If the 5 cards show above are placed in a row so that is never at either end ,how many different arrangements are possible?, If the 5 cards show above are placed in a row so that is never at either end ,how many different arrangements are possible? 79,Ellipse hyperbola parabola,Ellipse hyperbola parabola 椭圆 双曲线 抛物线,The figure above shows the graphs of y=x2 and y=a-x2 for some constant a.if the length of PQ is equal to 6,what is the value of a? A.6 B.9 C.12 D.15 E.18,The quadratic function g is given by ,where a and c are negative constants.which of the following could be the graph of g?,The figure above shows the graph of a quadratic function f that has a minimum at the point (1,1).if f(b)=f(3),which of the following could be the value of b? A.-3 B.-2 C.-1 D. 1 E.5,In the figure above,ABCD is a rectangle.points A and C lie on the graph of ,where p is a constantif the area of ABCD is 4,what is the value of p?,Point O has coordinates (0,0),point P lies on the graph of ,and point B has coordinates .if OP=BP,the area of triangle OPB is A.1.7 B.3.0 C.3.5 D.4.7 E.5.2,Lilys lock combination consists of 3 two-digit number.the combination satisfies the three conditions below. One number is odd. One number is a multiple of 5. One number is the day of the month of lilys birthday. If each number satisfies exactly one of the conditions,which of the following could be the combination to the lock? A.14-20-13 B.14-25-13 C.15-18-16 D.20-15-20 E.34-30-21,N, _, 2n, _ The first number in the sequence above is n,and each number after the first is p units greater than the previous number.in terms of p,what is the sixth number in the sequence A.3p B.4p C.5p D.6p E.7p,1/x=0.0N 1/y=0.00P The fractions 1/x and 1/y can be written as decimals as show above,where N and P represent different digits.which of the following is equal to 1/xy is S equals N times P and S is a digit? A.0.0000S B.0.000S C.0.00S D.0.0S E.0.S,The figure above showsa cylinder with radius 2 and hight 5.if points A and B lie on the circumference or the top and bottom of the cylinder,respectively,what is the greatest possible straight-line distance between A and B? A.3 B.5 C.7 D. E.,1,234,1,920,21,484,490 The integer above is formed by writing the integers from 1 to 50,in older,next to each other.if the integer is read from left to right,what is the 50th digit from the left? A.0 B.1 C.2 D.3 E.9,A circle of radius rolls to the right along the line shown above without slipping.in the starting position,point Aon the circle touches the line for the first time at point 0 on the line. At what point on the line will point A touch the line for the fourth time? A.12 B.10 C.8 D.6 E.4,Which of the following has the same volume as the cylinder shown above with radius x and height 2x? A.a cylinder with radius 2x and height x B. A cylinder with radius and height x C.A cube with edge 2x D.A cube with edge E.A rectangular solid with dimensions x,2x,In the schedule above,each session is to be1.5 hours long,each break is to be hour long,and lunch is to be 1 hour long.if session 4 is to end at 4:30 P.M,at what time should session 1 begin? A. 8:15 A.M B. 8:30 A.M C. 8:45 A.M D. 9:00 A.M E. 9:15 A.M,A merchant sells three types of clocks that chime as indicated by the check marks in the table above.what is the total number of chimes of the inventory of clocks in the 90-minute period from 7:15 to 8:45?,a, 3a, The first term in the sequence above is a,and each term after the first is 3 times the preceding term.if the sum of the first 5 term is 605.what is the value of a?,In the figure above,ABCD is a rectangle with BC=4 and AB=6 Points P,Q,and R are different points on a line (not shown) that is parallel to AD.points P and Q are symmetric about line AB and points Q and R are symmetric about line CD.what is the length of PR? A.6 B.8 C.10 D.12 E.20,Number of siblings per student in a preschool class,The table above shows how many students in a class of 12 preschoolers had 0,1,2,or 3 siblings.later,a new student joined the class,and the average(arithmetic mean) number of siblings per students became equal to the median number of siblings per student.how many siblings did the new students have? A.0 B.1 C.2 D.3 E.4,If p,r,and s are three different prime numbers greater than 2,and n=prs,how many positive factors,including 1 and n,does n have?,How many integers greater than 20 and less than 30 are each the preduct of exactly two different numbers,both of which are prime? A.zero B.one C.two D.three E.four,If i= ,for which of the folloeing values of n does have a positive value? A.23 B.24 C.25 D.26 E.27,Two identical spheres of radius 6 intersect so that the distance between their centers is 10.the points of intersection of the two spheres from a circle.what is the area of this circle? A. B. C. D. E.,Each of the 3 circles is tangent to the other 2,and each side of the equilateral triangle is tangent to 2 of the circles.if the length of one side of the triangle is x,what is the radius,in terms of x,of one of the circles? A. B. C. D. E.,In a remainder of 4 is obtained when is divided by x-2,what is the value of k? A.4 B.6 C.10 D.12 E.14,In the stop sign shown in the figure above,all sides have equal length and all angles have equal measure.if the figure could be rotated 225 degrees in a clockwise direction,point G would be in the position of point A. I B.J C.K D.L E.M,A school bus has 10 double seats in each of 2 rows.two students can sit in each double seat.if an empty bus starts out and makes two stops,picking up three times the number of students at the second stop as at the first stop,and if the bus is then filled to seating capacity,how many students got on the bus at the second stop? A.5 B.10 C.15 D.20 E.30,KN KN KN KN +_ 232,If K and N are digits in the two digit numbers in the sum above,then K+N=,In the figure above,the circle inscribed in PQRS has radius 3.what is the perimeter of square PQRS? A.9 B.24 C.36 D.54 E.81,In a list of numbers,the first number is 3.the second is 4.and each subsequent number is the sum of all the proceeding numbers in the list.if the 20th number in the list is x.what is the 25th number in the list? A.7X B.16X C.32X D.35X E.161X,In the figure above if the area of the inscribed rectangular region is 32,then the circumference of the circle is A. B. C. D. E.,A certain integer n is a multiple of both 5 and 9.which of the following must be true? . n is an odd integer . n is equal to 45 .n is a multiple of 15 A. only B. and only C. and only D. and only E. , and ,In the figure above,the circle is inscribed in the square.if the square has side of length 100,then the perimeter of the square is approximately how much greater than the circumference of the circle? A.9686 B.2150 C.243 D.100 E.86,A secretary typed 6 letters,each of which had either 1 or 2 pages.if the secretary typed 10 pages in all,how many of the letters had 2 pages? A.1 B.2 C.3 D.4 E.5,At 9:00 a.m.train T left the train station and two hours later train S left the same station on a parallel track.if train T averaged 60 kilometers per hour and train S averaged 75 kilometers per hour until S passed T,at what time did S pass T? A.2:00p.m B.5:00p.m C.6:00p.m D.7:00p.m E.9:00p.m,The volume of the cube in the figure above is 64.if the vertices ofPQR are midpoints of the cubes edges,what is the perimeter of PQR? A.6 B. C. D. 12 E.,The figure above shows the path traced by the end of a pendulum as it moves from point X to point Y .how many centimeters does the end of the pendulum travel along the arc from X to Y? A. B. C. D .E.,Three individuals contributed $800 each toward the purchase of a computer.if they bought the computer on sale for $1950 plus 10 percent sales tax,how much money should be refunded to each individual? A.$65 B.$85 C.$150 D.$195 E.$255,In the figure above,arcs PR and QS are semicircles with centers at Q and R respectively. if PQ=5,what is the perimeter of the shaded region? A. B. C. D. E.,Which of the following statements must be true about the cube above? .plane FEH is parallel to plane GDC .BG is perpendicular to plane FED .FE is parallel to BC. A. only B. omly C. only D. and E. , and ,If PQR and PRS above are equilateral, what fraction of PQRS is shaded? A.1/3 B.1/4 C.1/6 D.1/9