Science Bowl Practice Questions

Math - 4

27.

Short Answer: If both x and y are functions of time, what is the derivative of the PRODUCT of x and y
with respect to time equal to?

ANSWER: x[dy/dt] + y[dx/dt] or y[dx/dt] + x[dy/dt]

28.

Short Answer: If x = t

4

 (read: t raised to the fourth), what is the second derivative of x with respect to t

equal to?

ANSWER: 12t

2

 (read: 12t squared)

29.

Short Answer: In calculus, what is the indefinite integral of the sin(U)dU equal to?

ANSWER: -cos(U) + CONSTANT

30.

Short Answer: Two off-axis lines are perpendicular if and only if the product of their slopes is equal to
what?

ANSWER: -1

31.

Short Answer: Give the equation of one of the circles which satisfy the following criteria: a circle with
a radius of 8 which is tangent to the y-axis and whose center lies on the x-axis.

ANSWER: (x - 8)2 + (y)2 = 82 or (x + 8)2 + (y)2 = 82

32.

Short Answer: What is the sum of the first 100 positive integers?

ANSWER: 5050

33.

Short Answer: What is the name given to the radius of a circle that can be inscribed in any regular
polygon?

ANSWER: APOTHEM

34.

Short Answer: The universal set U contains the elements {1,2,3,4,5}. Set A contains the elements
{1,3}. What elements does the set A' (read: A prime) contain?

ANSWER: {2,4,5}