Science Bowl Practice Questions
Math - 8
64.
Short Answer: Express the product of the following complex numbers in the form a + bi (read: a plus b
i) where a and b are real: 4 + 2i and 2 + 5i (read: 4 plus 2 i and 2 plus 5 i)
ANSWER: -2 + 24i (read: minus 2 plus 24 i)
65.
Short Answer: In the complex plane, what are the roots of the equation x2 + 4x + 8 = 0? (read: x
squared plus 4 x plus 8 equals 0)
ANSWER: -2 - 2i and -2 + 2i
66.
Multiple Choice: If log
x
81 = 6 (read: the log base x of 81 equals 6), then x is equal to:
w) 3
x) 9
y) 1/3
z) 9
1/3
(read: the cube root of 9)
ANSWER: Z -- 91/3 (read: the cube root of 9)
67.
Multiple Choice; Matrix C is the product of matrix A times matrix B Which of the following must be
TRUE.
w) The number of rows of A equals the number of rows of B.
x) The number of columns of A equals the number of columns of B.
y) The number of rows of A equals the number of columns of B.
z) The number of columns of A equals the number of rows of B.
ANSWER: Z -- THE NUMBER OF COLUMNS OF A EQUALS THE NUMBER OF
ROWS
68.
Short Answer: For which values of X from the set of real numbers does the following inequality hold:
8x - 6 < 2x + 6 (read: 8 x minus 6 is less than 2 x plus 6)
ANSWER: X < 2 (read: X less than 2)
69.
Short Answer: To what value does the infinite series 1/4 + 1/8 + 1/16 + . . . ..converge? (read: one
fourth plus one eighth plus one sixteenth, etc.)
ANSWER: 1/2
70.
Short Answer: If (sin(3x) + cos(3x))2 = 2 (read: the quantity sine x plus cosine 3 x squared equals 2)
then what does 3sin(3x) cos(3x) (read 3 sine 3 x cosine 3 x) equal?
ANSWER: 3/2
71.
Short Answer: If
θ
= 30
°
, what is csc
2
θ
- cot
2
θ
equal to? (read: If theta equals 30 degrees, what is
cosecant squared theta minus cotangent squared theta equal to?)
ANSWER: 1
72.
Short Answer: A woman is 22 years older than her daughter. Nine years ago she was twice as old as
her daughter. What are their present ages?
ANSWER: THE WOMAN IS 53 YEARS OLD, THE DAUGHTER IS 31 YEARS OLD.
73.
Short Answer: What is the period of the function t = cos 4s? (read: t equals the cosine of 4 s)
ANSWER: p /2 (or 1/2 p)