SAT数学 Grid-in 练习题（2）

2017年07月21日13:51 来源：互联网: 参与（0）阅读（5344）

摘要：下面是小站SAT频道为大家整理了SAT数学 Grid-in 练习题(2)，供考生们参考，以下是详细内容。

以下是SAT数学 Grid-in 练习题(2)的详细内容，考生可针对文中介绍的方法进行有针对性的备考。最后祝大家在SAT考试中取得好成绩!

Question 1: In the x,y plane, what is the distance between origin and the (4,3) point?

Question 2: The sum of 4 consecutive integers is 26. What is the product of the 4 numbers?

Question 3: 60% of the players of a team score 5 points each during a basketball game, 30% of players score 1 point each, and 10% score 7 points each. What is the average number of points scored by the players of the team?

Question 4: If f(x) = x - 1, what is the value of x that satisfies the equality f(x) - 1 = f(x2) - x2

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 days will it take if the job is done by only 4 workers?

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.

Question 7: A jar contains a nickel, a dime, and six quarters. Tom draws a coin from the jar, and then Mary draws a coin from those remaining. If the probability that Tom draws the nickel and Mary draws the dime is 1/x, what is the value of x?

Question 8: What is the length of the sides of an equilateral triangle, if the lengths of the altitudes of the triangle are √3?

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?

Question 10: f(x) = |x| and g(x) = x - 1. How many solutions x satisfy f(x) = g(x)?

SAT考试Grid-in数学习题参考答案

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 between origin and the (4,3) point is equal to 5, as the other 2 sides of this right triangle are 4 and 3.

Question 2: The sum of 4 consecutive integers is 26. What is the product of the 4 numbers?

Answer: 1680

Explanation: If m is the least of the integers, m + (m + 1) + (m + 2) + (m + 3) = 26

4m + 6 = 26

m = 5, so the 4 consecutive numbers are 5, 6, 7, 8.

Their product is 5·6·7·8 = 1680

Answer: 4

Explanation: n being the number of players, 60% of the players is .6·n, 30% of the players is .3·n and 10% of the players is .1·n.

The numbers of points scored by players that scored 5 points is (.6·n)·5.

The numbers of points scored by players that scored 1 point is (.3·n)·1.

The numbers of points scored by players that scored 7 points is (.1·n)·7.

The total number of points will be (.6·n)·5 + (.3·n)·1 + (.1·n)·7 = 4·n and the average number of points = ( total number of points)/number of players = 4·n/n = 4

Question 4: If f(x) = x - 1, what is the value of x that satisfies the equality f(x) - 1 = f(x2) - x2

Answer: 1

Explanation:

f(x) - 1 = f(x2) - x2

(x - 1) - 1 = (x - 1)2 - x2

x - 2 = x2 - 2x + 1 - x2

x - 2 = -2x + 1

x = 1

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 = Nworkers·Ndays

k = 6·6, as it takes 6 workers 6 days to build the house

k = 36 worker·days

k = 4 workers · Ndays_4workers

Ndays_4workers = 36/4 = 9 days

Answer: 3

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 quarters. Tom draws a nickel from the jar, and then Mary draws a dime from those remaining. If the probability 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 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 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)2

(3/4)·l2 = 3