SAT2数学Level 1习题一.

SAT2数学Level 1习题一

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 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 + tan²(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? 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

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• 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

  • Answer: x = √x, if we square the lt 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 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

  • Answer: OAB equilateral so angle_AOB 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 = arc_AB / (2 ¶ · 9) arc_AB = 3 · ¶

SAT2数学Level 1习题一

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

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