Answers must be exact or must have 4 (or more) significant digits, correctly rounded, unless otherwise noted.
Time limit 10 minutes.
A box contains 20 slips of paper, numbered 1 to 20. Six slips are chosen (without replacement) and laid out in a row. Find the probability that they are in numerical order from smallest to largest.
A is the center of the semicircle on diameter CD. EFGH is a square. If CD=10, find the area of square EFGH.
Time limit 10 minutes.
Solve for x: 2/x + 2 + 2/x +2 = 6
Find the area of the region enclosed by the graphs of y = /x/ - 4 and y = 2 - /x/.
Time limit 10 minutes.
Find the angle formed by the hour and minute hands of a standard 12-hour clock at precisely 4:30.
One of four men (Andy, Bob, Carl, or Dave) committed a crime. Each of the men made two statements (below), one of which is true and the other of which is false. Given the statements below, who committed the crime?
Andy: (1) Dave did it or Bob did it. (2) If Carl did it, then Bob didn't.
Bob: (1) Andy's innocent and I'm innocent. (2) Bob is guilty and Carl is guilty.
Carl: (1) I didn't do it. (2) If Bob did it, then Andy didn't.
Dave: (1) If Carl did it, then Andy did it. (2) I didn't do it.
Time limit 10 minutes.
Solve for the positive integer n: (3!)(5!)(7!)=n!
AB is a minor arc of a circle and CD is the perpendicular bisector of chord AB. If AB=20 and CD=4, find the diameter of the circle.
Time limit 10 minutes.
Find the arithmetic mean of the first 100 positive integers.
ABCD is a rectangle with area 180 and E is the midpoint of side CD. If AF=4, with F on side AB, BC=2x-1, and CE=4x+1, for some x, find the numerical area of triangle AEF.
Time limit 10 minutes.
If f(x)=x3-5 and f o g(x)=x-2, where f and g are real-valued functions, find the value of g(11)
In a standard, well-mixed deck of 52 cards, find the probability that the first card is a king and the second card is a heart.
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