单选题
Direction: For questions 10 and 11, consider each of the
choices separately and select all that apply.
多选题
If the area of a rectangle is 40, which of the following could be the
perimeter of the rectangle?
Indicate all such areas.
Indicate all such areas.
【正确答案】
B、C、D、E、F
【答案解析】The perimeter of a rectangle whose area is 40 can be as large as we like (for example, if the length is 4,000 and the width is 0.01, the perimeter is 8,000.02). However, the perimeter is the smallest when the rectangle is a square, in which case each side is [*] and the perimeter is [*], the perimeter is greater than 4 × 6 = 24.
So Choice A, 20, is not possible. All of the other choices are possible.
多选题
Which of the following is an equation of a line that is perpendicular to the line whose equation is 2x + 3y = 4?
Indicate all such equations.
A. 3x+ 2y= 4
B. 3x- 2y= 4
C. 2x- 3y= 4
D. 4- 3x = -2y
E. 4 + 2x= 3y
【正确答案】
B、D
【答案解析】Rewriting the equation of the given line, 2x + 3y = 4, in slope-intercept form, we get that [*]. So the slope of the given line is [*].
The slope of any line perpendicular to that line must have a slope of [*], the negative reciprocal of [*].
Rewrite each of the answer choices in slope-intercept form, and see which ones also have a slope of [*].
[*]
Only choices B and D are the equations of lines whose slope is [*].
多选题
In the figure above, the diameter of the circle is 20 and the area of
the shaded region is 8Oft. What is the value of a + b + c + d?
【正确答案】
E
【答案解析】Since the diameter of the circle is 20, the radius is 10 and the area is 100π. Since the area of the shaded region is 80π, it is [*] of the circle, and the white area is [*] of the circle. So the sum of the measures of the two white central angles is [*] of 360°, or 72°. The sum of the measures of all six angles in the two triangles is 360°,
so a+ b+ c+ d+ 72 = 360 [*] a+ b+ c+ d= 288.
填空题
Directions: The answer to the following question is a fraction. Enter the numerator in the upper box and the denominator in the lower box. Each integer from 1 to 50 whose units digit is a 3 is written on a slip of paper and placed in a box. If two slips of paper are drawn at random, what is the probability that both the numbers picked are prime?
