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1、智 课 网 S A T 备 考 资 料SAT数学Grid-in练习题参考答案(2)-智课教育出国考试SAT数学Grid-in练习题 参考答案与解析 Question 1: In the x,y plane, what is the distance between origin and the (4,3) point? Answer: 5 Explanation: We apply Pythagoras Theorem to the triangle created by the following points: (4,3), (4,0) and (0,0). The distance be
2、tween origin and the (4,3) point is equal to 5, as the other 2 sides of this right triangle are 4 and 3. Question 5: The amount of time taken to build a house is inversely proportional to the number of construction workers on the job. If it takes 6 workers 6 days to complete such a job, how many day
3、s will it take if the job is done by only 4 workers? Answer: 9 Explanation: The amount of time taken to build a house is inversely proportional to the number of construction workers on the job, so Nworkers = k/Ndays k = NworkersNdaysk = 66, as it takes 6 workers 6 days to build the house k = 36 work
4、erdays k = 4 workers Ndays_4workers Ndays_4workers = 36/4 = 9 days Question 6: If side a of triangle ABO is tangent to the circle of center O, what is the value of the radius of the circle in inches? Side a of the ABO triangle is 4 inches and side b of the same triangle is 5 inches. Answer: 3 Explan
5、ation: Side a is tangent to the circle, so the triangle created by the sides a, b and c is right. c2 = b2 - a2c2 = 52 - 42 c2 = 9 c = 3 Question 7: A jar contains a nickel, a dime, and six quarters. Tom draws a nickel from the jar, and then Mary draws a dime from those remaining. If the probability
6、that Tom draws the nickel and Mary draws the dime is 1/x, what is the value of x? Answer: 56 Explanation: The probability that Tom draws the nickel is (number of nickels)/(number of coins in the jar) = 1/8 After Tom draws a coin, the number of coins in the jar is 8 - 1 = 7 The probability that Mary
7、draws the dime is (number of dimes)/(number of coins in the jar) = 1/7 The probability that Tom draws the nickel AND Mary draws the dime is the product of the 2 probabilities calculated above. 1/8 1/7 = 1/56 so x = 56 Question 8: What is the length of the sides of an equilateral triangle, if the len
8、gths of the altitudes of the triangle are 3? Answer: 2Explanation: In the triangle formed by the the altitude a, one side l and the base of the altitude, l2 = a2 + (l/2)2 (3/4)l2 = a2 (3/4)l2 = (3)2 (3/4)l2 = 3 l2 = 4 and l = 2. Question 9: If the population of virus doubles every 90 minutes, the po
9、pulation after 9 hours will be how many times the population at the start? Answer: 64 Explanation:After 90 minutes the virus population will be 2x, where x is the population at the start. After 3 hours the virus population will be 2(2x) = 22x. After 4 hours and 30 minutes, the population will be 23x
10、. After 6 hours, the population will be 24x. After 7 hours and 30 minutes, the population will be 25x. After 9 hours, the population will be 26x. Question 10: f(x) = |x| and g(x) = x - 1. How many solutions x satisfy f(x) = g(x)? Answer: 0 Explanation: The simplest way to solve this problem is to dr
11、aw the 2 functions in the x,y plane. We notice that for any x 0, f(x) is parallel with g(x) and they do not intersect in conclusion there are no x that satisfy f(x) = g(x).Question 6: If side a of triangle ABO is tangent to the circle of center O, what is the value of the radius of the circle in inc
12、hes? Side a of the ABO triangle is 4 inches and side b of the same triangle is 5 inches. Answer: Explanation: Side a is tangent to the circle, so the triangle created by the sides a, b and c is right. c2 = b2 - a2 c2 = 52 - 42 c2 = 9 c = 3 Question 7: A jar contains a nickel, a dime, and six quarter
13、s. Tom draws a nickel from the jar, and then Mary draws a dime from those remaining. If the probability that Tom draws thenickel and Mary draws the dime is 1/x, what is the value of x? Answer: 56 Explanation: The probability that Tom draws the nickel is (number of nickels)/(number of coins in the ja
14、r) = 1/8 After Tom draws a coin, the number of coins in the jar is 8 - 1 = 7 The probability that Mary draws the dime is (number of dimes)/(number of coins in the jar) = 1/7 The probability that Tom draws the nickel AND Mary draws the dime is the product of the 2 probabilities calculated above. 1/8
15、1/7 = 1/56 so x = 56 Question 8: What is the length of the sides of an equilateral triangle, if the lengths of the altitudes of the triangle are 3? Answer: 2 Explanation: In the triangle formed by the the altitude a, one side l and the base of the altitude, l2 = a2 + (l/2)2 (3/4)l2 = a2 (3/4)l2 = (3
16、)2 (3/4)l2 = 3 l2 = 4 and l = 2.Question 9: If the population of virus doubles every 90 minutes, the population after 9 hours will be how many times the population at the start? Answer: 64 Explanation: After 90 minutes the virus population will be 2x, where x is the population at the start. After 3 hours the virus population will be 2(2x) = 22x. After 4 hours and 30 minutes, the population will be 23x. After 6 hours, the population will be 24x. After 7 hours an
