数学点题班讲义答案!.pdf

移向运算 乘除法运算 表述运算 角度运算 指数运算 二次函数运算 比较大小 奇偶性 等式间的联立 2 不等式 3 不等式与组合 整数与不等式 数轴 算术平均数 2 中位数和值域 比例 2 比率 等差数列 非等差非等比数列 数字运算应用题 2 比例应用题 3 比率应用题 3 散点图应用题 折线图应用题 维恩图 平面直角坐标系 一元二次方程 一次函数图像 斜率 2 平面直角坐标系与平面几何 2 三角形 3 勾股定理 2 圆 2 圆与三角形 立方体体对角线 立体几何 逻辑推理 If w x y z what is the average arithmetic mean of w x y and z in terms of w If n is any prime number greater than 2 which of the following CANNOT be a prime number A n 4 B n 3 C n 1 D n 2 E n 5 If 4 less than 3 times a certain number is 2 more than the number what is the number A number is added to 9 less than twice the number If the result is 180 what is the number A fitness center purchased a number of exercise machines 4 costing 1700 each 8 costing 1300 each and x costing 1200 each where x is a positive odd integer If the median price for all the exercise machines purchased by the fitness center was 1300 what is the greatest possible value of x A car traveled 10 miles at an average speed of 20 miles per hour and them traveled the next 10 miles at an average speed of 40 miles per hour What was the average speed in miles per hour of the car for the 20 miles If x and y are integers and 2 xyx is odd which of the following statements must be true I x is odd II y is odd III x y is odd A I only B III only C I and II D I and III E II and III For how many integers n is 2n 1 3n 11 a negative number What is the smallest possible integer value of x for which x 8 x 5 0 A 8 B 7 C 6 D 5 E 4 If x is an integer and 2 x1 On the number line above there are 9 equal intervals between 0 and 1 What is the value of x Sixty eight people are sitting in 20 cars and each car contains at most 4 people What is the maximum possible number of cars that could contain exactly 1 of the 68 people If United States imports increased 20 percent and exports 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 If the length of the rectangle is increased by 30 and the width of the same rectangle is decreased by 30 what is the effect on the area of the rectangle A It is increased by 60 B It is increased by 30 C It is unchanged D It is decreased by 15 E It is decreased by 9 If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair what fraction of those who do not have brown hair have red hair A 1 4 B 4 11 C 4 9 D 5 9 E 4 5 The pyramid shown above has altitude h and a square base of side m The four edges that meet at V the vertex of the pyramid each have length e If e m what is the value of h in terms of m There was a 100 day period when the number of bees in a certain hive could be modeled by the function n above In the function k is a constant and n t represents the number of bees on day number t for 0 t 99 On what number day was the number of bees in the hive the same as it was on day number 10 Tim ran a quarter mile five times yesterday The table above shows the time of each run in minutes and seconds For example the time 1 07represents 1 minute and 7 seconds What is the range in seconds of the times of Tim s five runs A 3 B 4 C 6 D 8 E 11 The first term of a sequence is 100 Each term after the first term is equal to the preceding term divided by half of that preceding term For example the third term is equal to the second term divided by half of the second term How many terms in the sequence are greater than 2 A One B Two C Three D Four E More than four The temperature in a certain laboratory does not deviate from 22 by more than 4 If T is the temperature in degrees Celsins in the laboratory which of the following represents all possible values of T A T 4 22 B T 4 22 C T 22 4 D T 22 4 E T 26 22 The figure above shows the graph of the quadratic function with equation y ax2 bx c where a b and c are constants Which of the following is true about a A a 1 B 1 a 0 C 0 a1 In the figure above X and Y are the centers of the circles and the perimeter of the shaded region is 24 What is the total length of the darkened arcs A 12 B 16 C 18 D 20 E 24 6 7 10 12 x The average arithmetic mean of the 5 numbers in the list above equals the median What is one possible value of x a b 10 The first term in the sequence above is a and each term after the first is obtained by subtracting 2 from 3 times the preceding term What is the value of a A 0 B 2 C 3 D 4 E 8 In the figure above the line is the graph of function f and the curve is the entire graph of function g Which of the following describes al values of x for which g x f x A 2 x 4 B 2 x 6 C 3 x 9 D 3 x 12 E 0 x 2 or x 6 At a certain high school there are 9 students on the math team and 10 students on the academic team There are a total of 11 students who are on exactly one of the teams Of those students who are on the math team how many are also on the academic team A 0 B 1 C 2 D 4 E 5 The scatter plot above shows the number of books read and the number of videos watched by each of 12 students in one month For how many of the students was the number of books read greater than the number of video watched A Three B Four C Five D Six E Seven If 3x k what does 32x 1 equal in terms of k A 3k2 B 9k3 C k2 3 D 2k 3 E 2k 1 The parabola above is the graph of y x2 K where k is a constant if AB 1o what is the slope of AP A 2 B 5 2 C 5 D 10 E 20 The cube shown in the figure above is made from 27 small cubes each with an edge of length 1 If the shaded cube is removed What will be the surface area of the remaining solid The bar graph above shows the number of students who were absent from Jackson High School each day last week Of those students 8 were absent exactly 2 days each 1 was absent 3 days and no students were absent more than 3 days If 5 percent of the students in the school were absent at least 1 day last week how many students are enrolled in Jackson High School The lengths of two sides of a triangle are 5 and 12 and the length of the third side is an integer What is the greatest possible perimeter of the triangle A 22 B 29 C 30 D 33 E 34 By Saturday afternoon 374 tickets had been sold for a Saturday evening performance at a theater with a capacity of 500 seats After those 375 tickets were sold half the members of a group of 210 people each purchased a ticket If no other tickets were sold prior to the performance how many tickets remained unsold at the time of the performance On the number line what is one possible number that is less than 5 units from both 1 and 10 xy 4096 In the equation above x and y are positive integers What is the greatest possible value of x y Which of the follwing CANNOT be folded along the dashed lines to form a closed cube If ax 1 1 where a is a positive even integer which of the following CANNOT be a value of x2 A 0 B 1 4 C 1 2 D 1 E 4 The function f is defined by f x 2x2 5 What are all possible values of f x where 2 x 2 A 5 f x 0 B 5 f x 3 C 0 f x 3 D 0 f x 8 E 2 f x x B y xz C wx xy D w x y E x w 2 z The figure above represents a right circular cylinder made of paper It has a height of 20 centimeters and a diameter of 8 centimeters and it is open at both ends Of the following which is closest to the surface area in square centimeters of the outside of the paper cylinder A 450 B 475 C 500 D 525 E 550 Carol has 5 scarves and 5 sweaters and each scarf matches a different sweater If she chooses one of these scarves and one of these sweaters at random what is the probability that they will not match 36x 81a2 In the equation above x is a positive integer and a 0 If 27x ka what is the value of k If 1 2y 0 what is one possible value of y y The integer n is equal to k2 for some integer k If n is divisible by 24 and by 10 what is the smallest possible positive value of n In the xy plane above point D not shown lies on line l If the slope of AD is 2 3 what is the length of BD A 2 B 3 C 9 D 10 E 15 The figure above is made up of two identical 270 degree arcs Each arc is part of a circle of radius 8 What is the area of the figure A 96 B 128 C 48 64 D 96 32 E 96 64 Let the compactness index of a rectangle be defined as 2lw l2 w2 where l and w represent the length and width respectively of the rectangle Each of the following rectangles has an area of 36 Which one has a compactness index closest to 3 4 When the area of a certain circle is divided by the result is the square of an integer Which of the following could be the diameter of the circle A 12 B 11 C 9 D 7 E 5 If n 2 which of the following has the least value A 1 n2 B 1 n2 C 1 n D 1 n 1 E 1 n 1 The figure above is a pyramid with a square base and four equilateral triangular faces Points P Q R and S not shown are the midpoints of the edges that are not drawn on the triangular faces such that each segment connects two of these points Which of the following is a representation of how these dashed line segments could appear if viewed through the square base The positive number n is the product of three different prime numbers greater than 2 If the sum of these three prime numbers is also prime what is the smallest possible value for n A grocery customer spent a total of 9 60 for ground beef and coffee The coffee cost 2times as much per pound as the fround beef and the customer bought 3 times as many pounds of ground beef as pounds of coffee How much in dollars did the customer spend on coffee The volume of a right circular cylinder is 64 cubic inches If the height and base radius of the cylinder are equal what is the height of the cylinder A 4 inches B 6 inches C 8 inches D 16 inches E 32 inches x 3 5 y 4 3 If x and y satisfy the inequalities above then xy could be any of the following EXCEPT A 16 B 8 C 4 D 2 E 1 The integers 1 through 6 appear on the six faces of a cube one on each face If three such cubes are rolled what is the probability that the sum of the numbers on the top faces is 17 or 18 A 1 108 B 1 54 C 1 27 D 1 18 E 1 16 What is the greatest four digit integer that meets the following three restrictions 1 All of the digits are different 2 The greatest digit is the sum of the other three digits 3 The product of the four digits is divisible by 10 and not equal to zero The first term of a sequence is a Each term after the first is p more than the preceding term Which of the following expressions is the sum of the first 6 terms of the sequence A 6a 5p B 6a 15p C 6a 18p D 12a 5p E 12a 30p The graph above shows the advertised number of miles per gallon of gasoline used by a group of cars that were tested by a consumers group What is the median advertised gas mileage for these cars in miles per gallon A 26 B 26 5 C 26 75 D 27 E 27 5 R S and J are positive single digit integers Which of the following is equal to R 105 S 104 J 101 A R S00 0J0 B R S00 00J C RS0 J00 D RS0 0J0 E RS J00 the sum of r and 5 is less than the square of the difference between r and 5 but greater than the square of one half r Which of the following is equivalent to the statement above A r2 4 r 5 r 5 2 B r2 4 r 5 r2 5 C r2 2 r 5 r 5 2 D r2 2 r 5 r2 5 E r2 2 r2 5 r2 5 The integer x is the sum of 3 different positive integers each less than 10 The integer y is the sum of 3 different positive integers each less than 20 What is the smallest possible value of x y The function f is defined by f x x x 4 2 What are all values of x for which f x is NOT defined A x 0 and x 2 B x 0 and x 4 C x 2 and x 4 D x 2 and x 6 E x 4 and x 6 If 1 x 0 and 0 y 1 which of the following must be true I 1 xy 0 II 1 x y 0 III y x 1 A I only B II only C III only D I and III only E I II and III The lengths of the sides of an isosceles triangle are 20 n and n If n is an integer what is the smallest possible perimeter of the triangle A 40 B 41 C 42 D 44 E 60 When the positive integers w and n are divided by 6 the remainders are 3 and 2 respectively What is the remainder when the product wn is divided by 6 In the xy plane the points with coordinates 0 1 and 4 t lie on line l If the slope of l is greater than 3 4 and less than 1 what is one possible value of t The sum of the areas of the 3 circles above is The radius of circle II is 1 2 the radius of circle I and the radius of circle III is 1 3 the radius of circle I What is the radius of circle I A 6 11 B 4 7 C 6 7 D 7 6 E 9 4 1 SAT 数学数学词汇词汇 题型介绍 1 选择题 multiple choice questions 2 自答题 student produced response questions 考查内容 Number and Operations Integer whole number odd integer even integer consecutive integer Elementary Number Theory real number rational number irrational number composite number prime number reciprocal common divisor multiple common multiple least common multiple factors common factor greatest common factor ordinary scale decimal scale nonnegative Number Lines Squares and Square Roots Fractions and Rational Numbers atordeno numerator min least common denominator reducing to lowest terms 化简至最简形式 Place Value and Scientific Notation 百位 hundreds 十位 tens 个位 units decimal 十分位 tenths 百分位 hundredths Ratios Proportions and Percents Sequence arithmetic sequence 等差数列 geometric sequence 等比数列 2 the sum of certain terms in a sequence 前 n 项和 the average of certain terms in a sequence 前 n 项平均数 the value of a specific term in sequence 第 n 项 Sets element union intersection Operations add plus and 加 sum 和 subtract 减 difference 差 multiply times 乘 product 积 divide 除 quotient 商 remainder 余数 divisible 可被整除的 divided evenly 被整除 dividend 被除数 divisor 因子 除数 factorial 阶乘 power 乘方 root 根 square root cubic root radical sign root sign 根号 round to the nearest 四舍五入精确到 Counting Principle Permutations and Combinations Algebra and Functions factoring 因式分解 exponents 指数 幂 base 底数 absolute value 绝对值 inequality quadratic equations 二次方程 directly proportional