SAT考試Grid-in練習題3.

Question 1: If a§b = 2a - 3b for all real numbers a and b, what is 2^(3§2)?

Question 2: A regular polygon has 6 sides. What is the degree measure of the angle, within the polygon, between any two sides?

Question 3: A cubic box &aposA&apos has sides of length a and another cubic box &aposB&apos has sides of length 3a. How many boxes A could fit into a single box B?

Question 4: If a two-sided coin is flipped 4 times, what is the probability that at least one head will show up?

Question 5: What is the value of (2^{x + 1} - 2^x) / (2^x - 2^{x - 1})?

Question 6: Side AB of the ABCD square is 10, AE = ED and BF = FC. What is the ratio between the area of parallelogram BFDE and the area of triangle AEB?

Question 7: If 15% of x is 45, what is 20% of x?

Question 8: Given the | x - 3 | = 5 equation, what is the average of its solutions?

Question 9: In the x, y plane, what is the area of the quadrilateral delimited by the x axis, the y axis, the x = 5 line and the y = -5 line?

Question 10: If the average of x and y is 3, what is the average of x, y and 6?

SAT考試Grid-in練習題3參考答案

Question 1: If a§b = 2a - 3b for all real numbers a and b, what is 2^(3§2)?

Answer: 1 Explanation: 2^(3§2) = 2^{(2·3 - 3·2)} = 2⁰ = 1

Question 2: A regular polygon has 6 sides. What is the degree measure of the angle, within the polygon, between any two sides?

Answer: 120 Explanation: The sum of all of the angles of a polygon is (n - 2)·180^o, where n is the number of sides of the polygon. For a polygon with 6 sides, this is (6 - 2)·180^o = 720^o The polygon is regular, so all angles are congruent. The degree measure of the angle, within the polygon, between any two sides is 720^o/6 = 120^o.

Question 3: A cubic box &aposA&apos has sides of length a and another cubic box &aposB&apos has sides of length 3·a. How many boxes &aposA&apos could fit into a single box &aposB&apos?

Answer: 27 Explanation: The volume of box &aposA&apos is a³ while the volume of box &aposB&apos is (3·a)³. The number of boxes A that could fit into a box B is the ratio between the volumes of the 2 boxes. This is (3·a)³ / a³ = 27

Question 4: If a two-sided coin is flipped 4 times, what is the probability that at least one head will show up?

Answer: 15/16 Explanation: p₁ = the probability that at least one head will show up when the coin is flipped 4 times p₂ = the probability that no heads will show up when the coin is flipped 4 times p₁ + p₂ = 1 The probability that no heads will show up when the coin is flipped 4 times = the probability that the head will not show up when the coin is flipped the 1st time OR the head will not show up when the coin is flipped the 2nd time OR the head will not show up when the coin is flipped the 3rd time OR the head will not show up when the coin is flipped the 4th time. The probability that no heads will show up when the coin is flipped 4 times, p₂ = (1/2) ·(1/2) ·(1/2) ·(1/2) = 1/16 p₁ = 1 - p₂ = 1 - (1/16) = 15/16

Question 5: What is the value of (2^{x + 1} - 2^x) / (2^x - 2^{x - 1})?

Answer: 2 Explanation: (2^{x + 1} - 2^x) / (2^x - 2^{x - 1}) = 2·(2^x - 2^{x - 1}) / (2^x - 2^{x - 1}) = 2

Question 6: Side AB of the ABCD square is 10, AE = ED and BF = FC. What is the ratio between the area of parallelogram BFDE and the area of triangle AEB?

Answer: 2 Explanation: The area of triangle AEB A₁ = (1/2) · AB · AE = (1/2) · 5 · 10 = 25. The area of triangle CDF A₂ = (1/2) · FC · DC = (1/2) · 5 · 10 = 25. The area of square ABCD A₃ = AB · AD = 10 · 10 = 100. The area of parallelogram BFDE = A₃ - A₁ - A₂ = 100 - 25 - 25 = 50 A₃ / A₁ = 50 / 25 = 2

Question 7: If 15% of x is 45, what is 20% of x?

Answer: 60 Explanation: 15% of x is (15/100)·x (15/100)·x = 45 x = 45·(100/15) = 300 The problem asks you to calculate 20% of x: 20%(300) = 60

Question 8: Given the | x - 3 | = 5 equation, what is the average of its solutions?

Answer: 3 Explanation: Since |x - 3| = 5, the value of x - 3 is either 5 or -5.

Question 9: In the x, y plane, what is the area of the quadrilateral delimited by the x axis, the y axis, the x = 5 line and the y = -5 line?

Answer: 25 Explanation: The geometric figure delimited by the 4 given lines is a square with the side equal to 5. The area of the square is 5² = 25.

Question 10: If the average of x and y is 3, what is the average of x, y and 6?

Answer: 3 Explanation: (x + y)/2 = 3 x + y = 6 (x + y + 6)/3 = (6 + 6)/3 = 4

Question 1: If a§b = 2a - 3b for all real numbers a and b, what is 2^(3§2)?

Question 2: A regular polygon has 6 sides. What is the degree measure of the angle, within the polygon, between any two sides?

Question 3: A cubic box &aposA&apos has sides of length a and another cubic box &aposB&apos has sides of length 3a. How many boxes A could fit into a single box B?

Question 4: If a two-sided coin is flipped 4 times, what is the probability that at least one head will show up?

Question 5: What is the value of (2^{x + 1} - 2^x) / (2^x - 2^{x - 1})?

Question 6: Side AB of the ABCD square is 10, AE = ED and BF = FC. What is the ratio between the area of parallelogram BFDE and the area of triangle AEB?

Question 7: If 15% of x is 45, what is 20% of x?

Question 8: Given the | x - 3 | = 5 equation, what is the average of its solutions?

Question 9: In the x, y plane, what is the area of the quadrilateral delimited by the x axis, the y axis, the x = 5 line and the y = -5 line?

Question 10: If the average of x and y is 3, what is the average of x, y and 6? 上12下

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