SAT考试Grid-in练习题1.

Question 1: How many integers between 1 and 50 contain the digit 3?

Question 2: |2·x + 1| = 3 |x + 5| = 6 What value of x satisfies both of the equations above?

Question 3: The length of rectangle B is 50% longer than the length of rectangle A and the width of rectangle B is 50% shorter than the width of rectangle A. What is the ratio between the area of rectangle B and the area of rectangle A?

Question 4: If a§b = a^b + b^a for all real numbers a,b, what is (2§3)§1?

Question 5: What is the value of the x + y sum, if x + 2y = 5 and 2x + y = 7 ?

Question 6: If AC and BD are the diagonals of the ABCD rectangle and EAB is equilateral, what is the value of angle ADE?

Question 7: The average of a set of 11 numbers is 11. If two numbers are removed the average of the remaining numbers is 10. What is the sum of the two numbers removed?

Question 8: Last year, the price of a computer monitor was $300.What is the percent increase in price, if it is available now at $360?

Question 9: In the x, y plane, what is the area of the triangle created by the x axis, the y axis and the y = (-5/4)x + 5 line?

Question 10: If a coin is flipped twice, what is the probability that it will land heads at least once?

参考答案与解析

Question 1: How many integers between 1 and 50 contain the digit 3?

Answer: 14 Explanation: There are 14 integers between 1 and 50 that contain the digit 3: 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43.

Question 2: |2x + 1| = 3 |x + 5| = 6 What value of x satisfies both of the equations above?

Answer: 1 Explanation: Since |2x + 1| = 3, the value of 2x + 1 is either 3 or -3.

Question 3: The length of rectangle B is 50% longer than the length of rectangle A and the width of rectangle B is 50% shorter than the width of rectangle A. What is the ratio between the area of rectangle B and the area of rectangle A?

Answer: .75 Explanation: The area of rectangle A is Area_A = l_A·w_A The area of rectangle B is Area_B = l_B·w_B = 1.5·l_A·.5·w_A = .75·l_A·w_A The ratio between the area of rectangle B and the area of rectangle A is: Area_B/Area_A = (.75·l_A·w_A)/(l_A·w_A) = .75

Question 4: If a§b = a^b + b^a for all real numbers a,b, what is (2§3)§1?

Answer: 18 Explanation: 2§3 = 2³ + 3² = 8 + 9 = 17 17§1 = 17¹ + 1¹⁷ = 17 + 1 = 18 In conclusion, (2§3)§1 = 18

Question 5: What is the value of the x + y sum, if x + 2y = 5 and 2x + y = 7 ?

Answer: 4 Explanation: The easiest way to find x + y is to realize that by adding the 2 equations, the lt term of the addition is a multiple of x + y: 3(x + y) = 12 x + y = 4 You can also solve the system of 2 equations, find x and y and add them, but this will likely take longer.

Question 6: If AC and BD are the diagonals of the ABCD rectangle and EAB is equilateral, what is the value of angle ADE?

Answer: 30^o Explanation: Rectangles have parallel opposite sides so AD and BC are parallel. The BD diagonal produces congruent angles: angle ADE is equal to angle CBD. ABCD is a rectangle so angle ABC is 90^o. ABE is equilateral so angle ABE is 60^o. Angle ADE = Angle CBD = Angle ABC - Angle ABD = 90^o - 60^o = 30^o

Question 7: The average of a set of 11 numbers is 11. If two numbers are removed the average of the remaining numbers is 10. What is the sum of the two numbers removed?

Answer: 31 Explanation: The average of the 11 numbers is equal with the sum of the numbers divided by 11. 11 = (sum of 11 numbers)/11 Sum of 11 numbers = 11·11 Sum of 11 numbers = 121 If x and y are the 2 numbers removed, [(Sum of 11 numbers) - x - y]/9 = 10 [121 - x - y] = 10·9 [121 - x - y] = 90 x + y = 121 - 90 x + y = 31

Question 8: Last year, the price of a computer monitor was $300.What is the percent increase in price, if it is available now at $360?

Answer: 20% Explanation: The percent increase in price is the actual change in price, divided by the original price, and multiplied by 100. ($360 - $300)·100/$300 = 20%

Question 9: In the x, y plane, what is the area of the triangle created by the x axis, the y axis and the y = (-5/4)x + 5 line?

Answer: 10 Explanation: y = (-5/4)x + 5 intersects the y axis at x = 0 and y = 5 y = (-5/4)x + 5 intersects the x axis at y = 0 and x = 4 The triangle created by the x axis, the y axis and the y = (-5/4)x + 5 line is a right triangle. The area of the triangle is A = (1/2)·4·5 = 10.

Question 10: If a coin is flipped twice, what is the probability that it will land heads at least once?

Answer: .75 Explanation: The 4 possible combinations are (heads,heads), (heads,tails), (tails,heads) and (tails,tails). Three of these four combinations satisfy the conditions that the coin lands heads at least once. The probability is 3/4 = .75.

Question 1: How many integers between 1 and 50 contain the digit 3?

Question 2: |2·x + 1| = 3 |x + 5| = 6 What value of x satisfies both of the equations above?

Question 3: The length of rectangle B is 50% longer than the length of rectangle A and the width of rectangle B is 50% shorter than the width of rectangle A. What is the ratio between the area of rectangle B and the area of rectangle A?

Question 4: If a§b = a^b + b^a for all real numbers a,b, what is (2§3)§1?

Question 5: What is the value of the x + y sum, if x + 2y = 5 and 2x + y = 7 ?

Question 6: If AC and BD are the diagonals of the ABCD rectangle and EAB is equilateral, what is the value of angle ADE?

Question 7: The average of a set of 11 numbers is 11. If two numbers are removed the average of the remaining numbers is 10. What is the sum of the two numbers removed?

Question 8: Last year, the price of a computer monitor was $300.What is the percent increase in price, if it is available now at $360?

Question 9: In the x, y plane, what is the area of the triangle created by the x axis, the y axis and the y = (-5/4)x + 5 line?

Question 10: If a coin is flipped twice, what is the probability that it will land heads at least once? 上12下

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