Science Bowl Practice Questions

Math - 3

16.

Short Answer: What is the log[base 5](1/25) equal to?

ANSWER: -2

17.

Short Answer: Find x if log[base 5](x) = -2.

ANSWER: 1/25 or .04

18.

Short Answer: Given that the log[base 10](2) = .301, what is the log[base 10](8) equal to?

ANSWER: .903

19.

Short Answer: Given that the log[base 10](2) = .30 and that the log[base 10](3) =.48, what is the
log[base 10](1.5) equal to?

ANSWER: .18

20.

Multiple Choice: The trigonometric function cos(2A) (read: cosine of the angle 2A) is equal to which
of the following relationships?

w) 1 - [sin(A)]2 (read: one minus the sine squared of A)
x) [cos(A)]2 - [sin(A)]2 (read: cosine squared of angle A minus the sine squared of
angle A)
y) 2[sin(A)][cos(A)] (read: 2 times the sine of A times the cosine of A)
z) none of the above

ANSWER: X -- [cos(A)]2 - [sin(A)]2

21.

Short Answer: Find the equation of the line that passes through the point (1,2) and is perpendicular to
the line y = 2x + 1.

ANSWER: Y = -(1/2)x + 2.5 or y - 2 = (-1/2)(x - 1)

22.

Multiple Choice: A "reunion of broken parts" is the meaning of the root of what word:

w) algebra
x) calculus
y) mathematics
z) none of the above

ANSWER: W -- ALGEBRA

23.

Short Answer: In what number base does 1 + 2 = 10?

ANSWER: BASE 3

24.

Short Answer: How is the number 14 represented in the hexadecimal system?

ANSWER: E

25.

Short Answer: If an electronic circuit operates in 100 nanoseconds, how many operations can it
perform in one second?

ANSWER: 10 MILLION or 107

26.

Short Answer: What is the imaginary unit "i" when raised to the power 10?

ANSWER: -1