SAT2数学习题6套

更多 SAT 考试 资料 新概念英语资料下载李居明饿命改运学pdf成本会计期末资料社会工作导论资料工程结算所需资料清单 ，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com SAT II 数学 Level 1 & Level 2 练习题 http://sat.tiandaoedu.com 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com SAT2 数学 Level 1 习题 1 Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)? x = 1 x1 = 1, x2 = -1 x1 = 1, x2 = 0 x = 0 x = -1 Question #2: What is the length of the arc AB in the figure below, if O is the center of the circle and triangle OAB is equilateral? The radius of the circle is 9. ¶ 2 · ¶ 3 · ¶ 4 · ¶ ¶ / 2 Question #3: What is the probability that someone that throws 2 dice gets a 5 and a 6? Each dice has sides numbered from 1 to 6. 1/2 1/6 1/12 1/18 1/36 Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He bikes from A to B at a speed of 15 miles/hour while his return speed is 10 miles/hour. What is the 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com distance between the 2 towns? 11 miles 18 miles 15 miles 12 miles 10 miles Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1. What is the height of C2? 2·a / ¶ a / ¶ a / (2·¶) a / ¶ a + ¶ Question #6: How many integers x are there such that 2 x < 100, and at the same time the number 2 x + 2 is an integer divisible by both 3 and 2? 1 2 3 4 5 Question #7: sin(x)cos(x)(1 + tan 2 (x)) = tan(x) + 1 cos(x) sin(x) tan(x) sin(x) + cos(x) Question #8: If 5xy = 210, and x and y are positive integers, each of the following could be the value of x + y except: 13 17 23 15 43 Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y? 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com 11 17 13 15 9 Question #10: The inequality |2x - 1| > 5 must be true in which one of the following cases? I. x < -5 II. x > 7 III. x > 0 II only I, II and II I and II only I and III only I only  Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)? (a) x1 = 1, x2 = -1 (b) x1 = 1, x2 = 0 (c) x = 1 (d) x = 0 (e) x = -1 o Answer: x = √x, if we square the left and right terms of the equation we get x2 = x. x·(x-1) = 0 and x1 = 1, x2 = 0 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com  Question #2: What is the length of the arc AB, if O is the center of the circle and triangle OAB is equilateral? The radius of the circle is 9. (a) ¶ (b) 2 · ¶ (c) 3 · ¶ (d) 4 · ¶ (e) ¶/2 o Answer: OAB equilateral so angleAOB is equal to 60 o . The ratio between the AOB angle and 360 o is equal to the ratio between the length of the arc AB and the circumference of the circle. 60 o /360 o = arcAB / (2 ¶ · 9) arcAB = 3 · ¶  Question #3: What is the probability that someone that throws 2 dice gets a 5 and a 6? Each dice has sides numbered from 1 to 6. (a) 1/6 (b) 1/12 (c) 1/18 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com (d) 1/36 (e) 1/2 o Answer: The probability to have a (5,6) combination is equal to the probability that dice1 is 5 and dice2 is 6, plus the probability that dice2 is 5 and dice1 is 6. P = 1/6· 1/6 + 1/6· 1/6 = 1/36 + 1/36 = 1/18. (c) is the correct answer.  Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He bikes from A to B at a speed of 15 miles/hour, while his return speed is 10 miles/hour. What is the distance between the 2 towns? (a) 18 miles (b) 15 miles (c) 12 miles (d) 10 miles (e) 11 miles o Answer: The total time t = tAB + tBA = dAB/(15 miles/hour) + dAB/(10 miles/hour) = dAB/(6 miles/hour). dAB = dAB/(6 miles/hour) · 3 hours = 18 miles. (a) is the correct answer.  Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1. What is the height of C2? (a) a / ¶ (b) a / (2·¶) (c) a / ¶ (d) 2·a / ¶ 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com (e) a + ¶ o Answer: The volume of the cube is a 3 . This is equal to half the volume of the cylinder C2. a 3 = ¶ · a 2 · h/2 , where h is the height of the cylinder 2 · a 3 = ¶ · a 2 · h , 2 · a = ¶ · h, so h = 2 · a / ¶ and (d) is the correct answer.  Question #6: If 2 x < 100 and x is an integer, how many of the 2 x + 2 integers will be divisible by 3 and by 2? (a) 1 (b) 2 (c) 3 (d) 4 (d) 5 o Answer: 2 6 = 64 and 2 7 = 128. If 2 x < 100, then the highest value of x is 6. Possible values for x: 0 , 1 , 2 , 3 , 4, , 5 , 6. 2 x + 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).  Question #7: sin(x)cos(x)(1 + tan 2 (x)) = (a) tan(x) + 1 (b) cos(x) (c) sin(x) (d) tan(x) (e) sin(x) + cos(x) o Answer: sin(x)cos(x)(1 + tan 2 (x)) =sin(x)cos(x)(1 + sin 2 (x)/cos 2 (x)) = sin(x)cos(x)[(cos 2 (x) + sin 2 (x))/cos 2 (x)] = sin(x)cos(x)[1/cos 2 (x)] = sin(x)/cos(x) = tan(x) 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com  Question #8: If 5xy = 210, and x and y are positive integers, each of the following could be the value of x + y except: (a) 13 (b) 17 (c) 23 (d) 15 (e) 43 o Answer: 5xy = 210 so xy = 42. 42 = 2 · 3 · 7. The following products of integers equal to 42: (6 · 7) or (2 · 21) or (14 · 3) or (42 · 1). 6 +7 = 13, 2 + 21 = 23, 14 + 3 = 17 42 + 1 = 43 The only answer that is NOT 43, 13, 23 or 17 is (d), 15.  Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y? (a) 11 (b) 17 (c) 13 (d) 15 (e) 9 o Answer: The average of the 5 numbers is (24 + 6 + 12 + x + y)/5. (24 + 6 + 12 + x + y)/5 = 11 24 + 6 + 12 + x + y = 11 · 5 24 + 6 + 12 + x + y = 55 x + y = 13 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com  Question #10: The inequality |2x - 1| > 5 must be true in which one of the following cases? I. x < -5 II. x > 7 III. x > 0 (a) II only (b) I, II and II (c) I and II only (d) I and III only (e) I only o Answer: |2x - 1| > 5, -5 > 2x - 1 or 2x - 1 > 5 -4 > 2x or 2x > 6 -4 > 2x results in x < -2 2x > 6 results in x > 3 I answer is true, II answer is also true, but III answer is false, so the correct answer is (c) SAT2 数学 Level 1 习题 2 Question #1: 50% of US college students live on campus. Out of all students living on campus, 40% are graduate students. What percentage of US students are graduate students living on campus? 90% 5% 40% 20% 25% 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com Question #2: In the figure below, MN is parallel with BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC? 5/9 2/3 4/9 1/2 2/9 Question #3: If a 2 + 3 is divisible by 7, which of the following values can be a? 7 8 9 11 4 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com Question #4: What is the value of b, if x = 2 is a solution of equation x 2 - b · x + 1 = 0? 1/2 -1/2 5/2 -5/2 2 Question #5: Which value of x satisfies the inequality | 2x | < x + 1 ? -1/2 1/2 1 -1 2 Question #6: If integers m > 2 and n > 2, how many (m, n) pairs satisfy the inequality m n < 100? 2 3 4 5 7 Question #7: The US deer population increase is 50% every 20 years. How may times larger will the deer population be in 60 years ? 2.275 3.250 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com 2.250 3.375 2.500 Question #8: Find the value of x if x + y = 13 and x - y = 5. 2 3 6 9 4 Question #9: US UK Medals 3 2 gold 1 4 silver 4 1 bronze The number of medals won at a track and field championship is shown in the table above. What is the percentage of bronze medals won by UK out of all medals won by the 2 teams? 20% 6.66% 26.6% 33.3% 10% Question #10: The edges of a cube are each 4 inches long. What is the surface area, in square inches, of this cube? 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com 66 60 76 96 65 参考 答案 八年级地理上册填图题岩土工程勘察试题省略号的作用及举例应急救援安全知识车间5s试题及答案  Question #1: 50% of US college students live on campus. Out of all students living on campus, 40% are graduate students. What percentage of US students are graduate students living on campus? (a) 90%? (b) 5% ? (c) 40%? (d) 20%? (e) 25%?  Answer: If x = US college students, y = US graduate students, z = US graduate students living on campus, y = .4x and z = .4·y = .4·(.5x) = .2·x The percentage of US students that are graduate students living on campus is 20%. 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com  Question #2: In the figure below, MN is parallel with BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC? (a) 5/9 (b) 2/3 (c) 4/9 (d) 1/2 (e) 2/9  Answer: Triangles ABC and AMN are similar, so the lengths of their corresponding sides are proportional. This means MN/BC = 2/3 and the ratio between their altitudes is also 2/3. The area of triangle ABC is (BC · H)/2 where H is the altitude of ABC. The area of triangle AMN is (MN · h)/2 where h is the altitude of AMN. AreaAMN / AreaABC = (2/3) · (2/3) = 4/9 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com  Question #3: If a 2 + 3 is divisible by 7, which of the following values can be a? (a) 7 (b) 8 (c) 9 (d) 11 (e) 4 o Answer: 7 2 + 3 = 52 = 2 · 2 · 13 8 2 + 3 = 67 9 2 + 3 = 84 = 2 · 2 · 3 · 7 11 2 + 3 = 124 = 2 · 2 · 31 4 2 + 3 = 17 The correct answer is a = 9  Question #4: What is the value of b, if x = 2 is a solution of equation x 2 - b · x + 1 = 0? (a) 1/2 (b) -1/2 (c) 5/2 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com (d) -5/2 (e) 2 o Answer: x = 2 is a solution of the equation, so 2 2 - b · 2 + 1 = 0. 4 - 2 · b + 1 = 0, b = 5/2.  Question #5: Which value of x satisfies the inequality | 2x | < x + 1 ? (a) -1/2 (b) 1/2 (c) 1 (d) -1 (e) 2 o Answer: We can write the inequality as -(x + 1) < 2x OR 2x < x + 1 -x - 1 < 2x; 3x + 1 >0 x > -1/3 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com 2x < x + 1 x < 1 Out of the given answers, the only x that satisfies the inequality is x = 1/2.  Question #6: If integers m > 2 and n > 2, how many (m, n) pairs satisfy the inequality m n < 100? (a) 2 (b) 3 (c) 4 (d) 5 (e) 7 o Answer: The lowest m n possible is for m = 3 and n = 3. m n = 27. This pair satisfies the inequality. m = 3 and n = 4 then m n = 81. This is also less than 100. This pair also satisfies the inequality. m = 3 and n = 5 then m n = 243. For all n > 5, m n > 100. m = 4 and n = 3 then m n = 64. This is also less than 100. This pair satisfies the inequality. m = 4 and n = 4 then m n = 256. For all n > 4, m n > 100. In conclusion there are only 3 combinations that satisfy the inequality. 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com  Question #7: The US deer population increase is 50% every 20 years. How may times larger will the deer population be in 60 years ? (a) 2.275 (b) 3.250 (c) 2.250 (d) 3.375 (e) 2.500 o Answer: x being the present number of deer, in 20 years, the number will be (1 + .5)x. In 40 years the number will be (1 + .5)·(1 + .5)·x and in 60 years (1 + .5) · (1 + .5) · (1 + .5)x = (1 + .5) 3 x. The answer will be (1 + .5) 3 = 3.375  Question #8: Find the value of x if x + y = 13 and x - y = 5. (a) 2 (b) 3 (c) 6 (d) 9 (e) 4 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com o Answer: We notice that if we add the 2 equations we get 2x = 18, then x = 9 is the correct answer.  Question #9: US UK Medals 3 2 gold 1 4 silver 4 1 bronze  The number of medals won at a track and field championship is shown in the table above. What is the percentage of bronze medals won by UK out of all medals won by the 2 teams?   (a) 20%   (b) 6.66%   (c) 26.6%   (d) 33.3%   (e) 10%  o Answer: The numbers of medals won by the 2 teams is 3 + 2 + 1 + 4 + 4 + 1 = 15. The number of bronze medals won by UK is 1. The percentage will be 1/15 · 100 = 6.66%  Question #10: The edges of a cube are each 4 inches long. What is the surface area, in square inches, of this cube? (a) 66 (b) 60 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com (c) 76 (d) 96 (e) 65 o Answer: Each face of the cube has an area of 4×4 = 16 square inches The total surface area of the cube is (6 faces)x(16 square inches) = 96 square inches. SAT2 数学 Level 1 习题 3  Question #1: The sum of the two solutions of the quadratic equation f(x) = 0 is equal to 1 and the product of the solutions is equal to -20. What are the solutions of the equation f(x) = 16 - x ? (a) x1 = 3 and x2 = -3 (b) x1 = 6 and x2 = -6 (c) x1 = 5 and x2 = -4 (d) x1 = -5 and x2 = 4 (e) x1 = 6 and x2 = 0 o Answer: If a, b are the solutions of the equation f(x) = 0, ab = -20 a + b = 1 We solve this system of equations, and a = 5, b = -4. Then f(x) = (x-5)(x+4) f(x) = x 2 - x - 20. f(x) = 16 - x x 2 - x - 20 = 16 - x x 2 = 36, x1 = 6 and x2 = -6   Question #2: In the (x, y) coordinate plane, three lines have the equations: l1: y = ax + 1 l2: y = bx + 2 l3: y = cx + 3 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com Which of the following may be values of a, b and c, if line l3 is perpendicular to both lines l1 and l2? (a) a = -2, b = -2, c = .5 (b) a = -2, b = -2, c = 2 (c) a = -2, b = -2, c = -2 (d) a = -2, b = 2, c = .5 (e) a = 2, b = -2, c = 2 o Answer: If line l3 is perpendicular to both lines l1 and l2, then l1 must be parallel to l2. The slopes of l1 and l2 should be equal, slopel1 = slopel2, and the slopel3 = -1/slopel1. a = -2, b = -2, c = .5 is the only answer that satisfies these conditions.  Question #3: The management team of a company has 250 men and 125 women. If 200 of the managers have a master degree, and 100 of the managers with the master degree are women, how many of the managers are men without a master degree? (a) 125 (b) 150 (c) 175 (d) 200 (e) 225 o Answer: If 200 of the managers have a master degree, and 100 of the managers with a master degree are women, then 100 of the managers with a master degree are men. The company has 250 men managers and 100 of the managers with a master degree are men, so the number of managers that are men without a master degree is 250 - 100 = 150.  Question #4: In the figure below, the area of square ABCD is equal to the sum of the areas of triangles ABE and DCE. If AB = 6, then CE = 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com (a) 5 (b) 6 (c) 2 (d) 3 (e) 4 o Answer: AreaABCD = AB 2 AreaABE = AB·BE/2 AreaDCE = DC·CE/2 = AB·CE/2 The problem states that the area of square ABCD is equal to the sum of the areas of triangles ABE and DCE. AB 2 = AB·BE/2 + AB·CE/2 AB = BE/2 + CE/2 BE = CE + AB AB = CE/2 + AB/2 + CE/2 AB/2 = CE/2 + CE/2 CE = AB/2 CE = 3 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com  Question #5: If α and β are the angles of the right triangle shown in the figure above, then sin2α + sin2β is equal to: (a) cos(β) (b) sin(β) (c) 1 (d) cos 2(β) (e) -1 o Answer: sin 2α + sin2β = sin2α + sin2(90o - α) = sin2α + cos2α = 1.  Question #6: The average of numbers (a + 9) and (a - 1) is equal to b, where a and b are integers. The product of the same two integers is equal to (b - 1) 2 . What is the value of a? (a) a = 9 (b) a = 1 (c) a = 0 (d) a = 5 (e) a = 11 o Answer: 1/2(a + 9 + a - 1) = b (a + 9)(a - 1) = (b - 1) 2 We need to solve this system of equations. 1/2(2a + 8 ) = b a + 4 = b (a + 9)(a - 1) = (a + 3) 2 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com a 2 + 9a - a - 9 = a 2 + 6a + 9 2a = 18 a = 9 SAT2 数学 Level 2 习题 1 转载请注明来自天道留学  Question 1: What is the closest approximation of the solution of the equation 2 x - 1 = 3 x + 1 ? (a) -4.42 (b) -5.81 (c) -3.22 (d) 4.93 (e) 3.33 o log(2 x - 1 ) = log(3 x + 1 ) (x - 1)log2 = (x + 1)log3 x(log2 - log3) = log3 + log2 x = (log3 + log2)/(log2 - log3) x is aprox. = -4.418  Question #2: What is the range of (x - y) if 3 < x < 4 and -2 < y< -1? (a) 4< x-y <5 (b) 1< x-y <3 (c) 1< x-y <5 (d) 4< x-y <6 (e) 3< x-y <6 o Answer: We can determine the range of -y: 1 < -y < 2 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com We determine the range of x-y by adding the ranges of x and -y: Therefore, 4< x-y <6  Question #3: A bus travels the distance d from New York to Boston. t1 hours after the bus left New York, a car starts to travel the same distance d from New York to Boston. Both vehicles reach Boston at the same time. Find an expression for d as a function of t1, the speed of the bus v1 and the speed of the car v2. (a) d = v1t1/(v2 - v1) (b) d = v1v2t1/(v2 - v1) (c) d = v1t1/(v2 + v1) (d) d = v1v2t1/(v2 + v1) (e) d = v1v2t1 o Answer: If t is the duration of the travel of the bus, d = v1t d = v2(t - t1) Therefore, v1t = v2(t - t1) t = v2t1 / (v2 - v1) d = v1v2t1 / (v2 - v1)  Question #4: Find the value of x if: x + y + z = 5 x + y - z = 3 x - y = 2 (a) -3 (b) -1 (c) 1 (d) 3 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com (e) 5 o Answer: We notice that if we add equations 1 and 2 we can eliminate z: x + y + z + x + y - z = 5 + 3 2·(x + y) = 8 x + y = 4 At this point we have a system of 2 linear equations with 2 variables, x and y: x - y = 2 x + y = 4 If we add these 2 equations, we get 2·x = 6 and x = 3.  Question #5: A camera has a price of 300 dollars. Its price is lowered 10% and then increased 10%. What is the final selling price of the camera? (a) $297 (b) $303 (c) $310 (d) $330 (e) $303 o Answer: After it is lowered by 10%, the price is $300 - $30 = $270. A 10% increase of a $270 price is $27, so the final price is $270 + $27 = $297.  Question #6: The equation 2x 2 - 2x - 60 = 0 has the following 2 solutions: (a) {-5, 5} (b) {5, -6} (c) {-5, -6} (d) {-5, 6} (e) {5, 6} 更多 SAT 考试资料，请访问 http://sat.tiandaoedu.com 天道留学 www.tiandaoedu.com o Answer: 2x 2 - 2x - 60 = 0 x 2 - x - 30 = 0 The sum of the solutions is 1 and the product is -30 so the solutions are {-5, 6} 参考答案  Question #7: The side of a cube is two times the radius of a sphere. What is the ratio of the volume of the cube to the volume of the sphere? (a) 6/¶ (b) 3/¶ (c) ¶/6 (d) ¶/4 (e) ¶ o Answer: If l is the side of the cube, the volum