SAT数学备考经典模拟题训练31

>>SAT数学模拟题：SAT数学备考经典模拟题训练31

>>SAT考试辅导

练习题内容

· Question #1: In the x,y plane, which of the following statements are true?

I. Line y + x = 5 is perpendicular to line y - x = 5.

II. Lines y + x = 5 and y - x = 5 intersect each other on the y axis.

III. Lines y + x = 5 and y - x = 5 intersect each other on the x axis.

(a) I and III are both true.

(b) I is the only true statement.

(c) II is the only true statement.

(d) I and II are both true.

· Question #2: If a is an integer chosen randomly from the set {3, 5, 6, 9} and b is an integer chosen randomly from the set {2, 3, 4}, what is the probability that a/b is an integer?

(a) .125

(b) .250

(c) .333

(d) .5

(e) .55

解析

o Answer: y + x = 5 can be written as y = -x + 5. The slope of this equation is m1 = -1.

y - x = 5 can be written as y = x + 5. The slope of this equation is m2 = 1.

m2 = -1/m1 so the 2 lines are perpendicular.

We also need to find where the 2 lines intersect. If we add the 2 equations, 2·y = 10, y = 5.

From the first equation, x = 5 - y = 5 - 5 = 0. In conclusion the lines intersect at (0, 5) and this point is on the y axis.

In conclusion I and II statements are correct.

o Answer: We have 4 possible integers for a and 3 for b, so the number of possible combinations for a/b is 4 · 3 = 12.

a/b is an integer only for 4 combinations:

1. a = 3 and b = 3

2. a = 6 and b = 2

3. a = 6 and b = 3

4. a = 9 and b = 3

The probability that a/b is an integer is 4/12 = 1/3 = .333.

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