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1、 SAT II 数学 Level 1 & Level 2 练习题 SAT2 数学数学 Level 1 习题习题 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 trian
2、gle 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. H
3、e 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? 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 r
4、adius 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 2x 5 must be true in which one of the following cases? I. 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 a
5、nd 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 Question #2: What is the length of the arc AB, if O is t
6、he 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 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 cir
7、cle. 60o/360o = 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 (d) 1/36 (e) 1/2 o Answer: The probability to have a (5,6) combination is equal to the probability that d
8、ice1 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 s
9、peed 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 a
10、nswer. 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 / (e) a + o Answer: The volume of the cube is a3. This is equal to
11、 half the volume of the cylinder C2. a3 = a2 h/2 , where h is the height of the cylinder 2 a3 = a2 h , 2 a = h, so h = 2 a / and (d) is the correct answer. Question #6: If 2x 5 must be true in which one of the following cases? I. x 7 III. x 0 (a) II only (b) I, II and II (c) I and II only (d) I and
12、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 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 数学数学 Level 1 习题习题 2 Question #1: 50% of US college students live on campus. Out of al
13、l students living on campus, 40% are graduate students. What percentage of US students are graduate students living on campus? 90% 5% 40% 20% 25% 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?
14、 5/9 2/3 4/9 1/2 2/9 Question #3: If a2 + 3 is divisible by 7, which of the following values can be a? 7 8 9 11 4 Question #4: What is the value of b, if x = 2 is a solution of equation x2 - b x + 1 = 0? 1/2 -1/2 5/2 -5/2 2 Question #5: Which value of x satisfies the inequality | 2x | 2 and n 2, how
15、 many (m, n) pairs satisfy the inequality mn 0 x -1/3 2x 2 and n 2, how many (m, n) pairs satisfy the inequality mn 5, mn 100. m = 4 and n = 3 then mn = 64. This is also less than 100. This pair satisfies the inequality. m = 4 and n = 4 then mn = 256. For all n 4, mn 100. In conclusion there are only 3 combinations that satisfy the inequality. 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, t
