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Science Bowl Questions (Math)
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Terms in this set (82)
What term BEST describes 2 angles with 90º as the sum of their measurements?
COMPLEMENTARY
Divide the following and give your answer in scientific notation:
8*10^7
________
(4*10^4)^1/2
4 × 10^5
Short Answer Simplify the following expression, where a is not equal to zero if b = 0 or if b = -1: (a^b^2)(a^b)
a^b^2+2
Giving your answer in inches and in simplest radical form, if the hypotenuse of a 45-45-90º triangle is 10 inches, find the length of the other sides:
5sqrt2 (ACCEPT: BOTH 5sqrt2)
Giving your answer in terms of π and in inches, what is the arc-length of a semi-circle whose diameter is 18 inches?
9π
What is the area, in square feet, of a triangle whose perpendicular height is 20 feet with a base of 12 feet?
120
What is the smaller of two integers whose sum is 19 and whose product is 48?
3
Which of the following numbers is evenly divisible by both 11 and 3:
W) 7791
X) 7553
Y) 5181
Z) 8769
Y) 5181
One-fifth of 0.04% is equal to:
W) 8 × 10^-2
X) 8 × 10^-3
Y) 8 × 10^-4
Z) 8 × 10^-5
8 × 10^-5
Find the prime factorization of 240:
2 × 2 × 2 × 2 × 3 × 5 (ACCEPT: 2^4 × 3 × 5)
Giving your answer in centimeters, what is the length of a side of a square whose diagonal measures 12sqrt2 centimeters?
12
Short Answer Multiply the following 4 numbers and give your answer in scientific notation: 30,000 × 3,000 × 30 × 0.1
2.7 × 10^8
Giving your answer in standard form, what is the last term in the binomial expansion of the following: (x + y)^6
y^6
Simplify the following expression by combining like terms:
12.03A - 4.03B - 0.03(A - 40)
12A - 4.03B + 1.2
Simplify the following, giving your answer in proper scientific notation: (6.0 × 10^12)(2.0 × 10^10)^2
2.4 × 10^33
Factor the following expression completely: 81x^2 + 180xy + 100y^2
(9x + 10y)^2
Giving your answer as a proper fraction, what is the cube root of 125/343?
5/7
Find the following product, giving your answer in standard form:
(4x^3 + x)(7x^3 + 4x^2)
28x^6 + 16x^5 + 7x^4 + 4x^3 (ACCEPT: x^3(28x^3 + 16x^2 + 7x + 4))
If triangle ABD is congruent with triangle EFG, which of the following MUST be true:
W) side AB is congruent to side EF
X) side AD is congruent to side FG
Y) measure of angle B = measure of angle G
Z) measure of angle A = measure of angle G
W) SIDE AB IS CONGRUENT TO SIDE EF
If the shortest leg of a 30-60-90 right triangle is 6 inches, what is the measure, in inches, of the other 2 sides?
12 AND 6sqrt3
Consider triangle ABC, where the measure of angle A = 20º, B =117º, and C = 43º. Arrange the 3 sides in order of increasing length:
BC; AB; AC
Simplify the following expression:x^1/2x^2/5
x^9/10 (ACCEPT: 10sqrtx^9)
What is the slope of a line perpendicular to the line given by the graph of the equation, -5x = -6y + 4
-6/5
Which of the following is NOT a Pythagorean triple:
W) 15, 20, 25
X) 10, 24, 26
Y) 16, 24, 30
Z) 33, 44, 55
Y) 16, 24, 30
Evaluate the following expression when a = 1/3, b = 4, c = -1, and
d = -5: 2[3a - (b + c) - 4d]
36
It takes 20 minutes for Janis to prepare lunch. When Kristen helps, it only takes 12 minutes. How many minutes would it take Kristen to prepare the same lunch if she worked alone?
30
In a circle with diameter AB, if the radius is 6 centimeters, find the length in centimeters, giving your answer in terms of π, of the arc AB:
6π
Find the area, in square centimeters, of a rhombus with a diagonal of 6 centimeters and a side of 5 centimeters:
24
A jar of 100 marbles contains only 2 colors of marbles, red and blue. If there are 13 red marbles for every 12 blue marbles, how many blue marbles are in the jar?
48
Solve the following inequality for x: |3 - 2x| ≤ 7 (read as: the absolute value of, 3 minus 2x, close absolute value, is less than or equal to 7)
-2 ≤ x ≤ 5 (ACCEPT: 5 ≥ x ≥ -2)
Assuming that the natural log of 5 = 1.6, find, to the first decimal place, the natural log of 5^13:
0.5
Factor the following expression completely: 100x^2 - 25y^2
25(2x + y)(2x - y)
What is the specific name for a common tangent that intersects the segment joining the centers of 2 circles?
INTERNAL COMMON TANGENT (ACCEPT: INTERNAL or INTERNAL TANGENT)
A flagpole casts a 100-foot long shadow. If a 6-foot tall person standing at the base of the pole casts an 8-foot shadow, how many feet tall is the flagpole?
75
Solve the following equation for x over the integers: x^2 = 3x
0; 3
Factor the following expression completely: 12x^2 + 24x - 36
12(x + 3)(x - 1) (ACCEPT: 12(x - 1)(x + 3))
What is the determinant of a 2-by-2 square matrix whose rows are 4, 2 and -3, -4?
-10
Solve the following equation for x: -2|3 + (x/2)| = -10 (read as: negative 2 times the absolute value of 3 plus, open parenthesis, x divided by 2, close parenthesis, close absolute value, equals negative 10)
4 AND -16
Giving your answer as up, down, left, or right, the graph of the equation x = 5y - 8y^2 - 1 opens in what direction?
LEFT
If $10,000 is placed in a savings account that pays 5% interest compounded annually, what is the total amount of money in the account at the end of 2 years, to the nearest dollar?
$11,025
In what quadrant does θ (read as: theta) terminate if sine θ is positive and secant θ is negative?
2nd (ACCEPT: 2)
Which of the following is NOT true:
W) all central angles in a regular polygon are equal
X) irregular polygons are not considered to have centers and have no central angles
Y) the circumcircle of a regular polygon is the circle that passes through at least one vertex
Z) all regular polygons are convex
Y) THE CIRCUMCIRCLE OF A REGULAR POLYGON IS THE CIRCLE THAT PASSES THROUGH AT LEAST ONE VERTEX
Find the sum of all interior angles, in degrees, in a regular polygon having 100 sides:
17,640
Find 2 mean proportionals between the numbers 3 and 24:
6 AND 12
Find the numerical value of the geometric mean of the following 4 values: 2^1; 2^3; 2^8; 2^8
32 (DO NOT ACCEPT: 2^5)
There are 10 people on a bus who, when ranked from youngest to oldest, all differ from those on the bus closest in age to them by the same number of years. If the youngest is 6 and the oldest is 51, what is the common difference in their age?
5
Solve the following equation for all real values of x: (x + 3)^2 = 16
1 AND -7
Giving your answer in standard form, give the equation of the circle with center at (0, 0) and diameter of 6:
x^2 + y^2 = 9
What is the degree measure of the angle formed by 2 secants intersecting outside a circle if the measures of the intercepted arcs are 80º and 34º?
23
If e^x/5 = 30, which of the following is the value of x, assuming that the natural log of 2 = 0.7, and the natural log of 15 = 2.7:
W) 15
X) 16
Y) 17
Z) 18
Y) 17
If the area of a regular pentagon is 280 square centimeters, what is the length, in centimeters, of each side if the apothem is 16 centimeters?
7
A circle has a diameter of 32 meters. Find the degree measure of the central angle of a sector of the circle if its arc length measures 8π meters:
90
Find the sum of the first 10 terms of the arithmetic sequence whose first three terms are 7, 11, and 15:
250
What is the name for the test that can be used to visually determine whether or not a relation defined by a graph represents a function?
VERTICAL LINE TEST (ACCEPT: VERTICAL LINE)
Find the x and y intercepts of the line passing through the point (4, 8) that is perpendicular to the line 3x - 6y - 12 = 0:
X-INTERCEPT = (8, 0) (ACCEPT: 8); Y-INTERCEPT = (0, 16) (ACCEPT: 16)
Find the cotangent and cosecant, respectively, of a 90º angle:
COTAN = 0; COSECANT = 1
Which of the following points is closest to the point (1, -2):
W) (3, -5)
X) (0, 3)
Y) (3, 0)
Z) (-5, -5)
Y) (3, 0)
What are the leading coefficient and degree, respectively, of the following polynomial: 3x^2 - 6x^5 + 7
LEADING COEFFICIENT = -6; DEGREE = 5
Identify the type of conic section represented by the equation,
x^2 - 16y^2 = 64:
HYPERBOLA
Giving your answer in millimeters squared, find the lateral surface area of a right pentagonal prism whose altitude is 12 millimeters and base has sides of length 8, 10, 12, 14, and 16 millimeters, respectively:
720
If y varies directly as x and z, and y = 12 when x = 4 and z = 5, find y when x = 10 and z = 20:
120
Which of the following is a second quadrant angle in standard position:
W) 500º
X) -180º
Y) -680º
Z) 930º
W) 500º
What is the product of the following 2 values: (1) the greatest common divisor of 7 and 14; and (2) the least common multiple of 7 and 14:
W) 21
X) 49
Y) 98
Z) 196
Y) 98
Multiply the following complex numbers, giving your answer in standard a + bi form: (6 + 3i)(4 + i)
21 + 18i
Which of the following is NOT true of matrices:
W) a square matrix that has an inverse is called invertible
X) a matrix does not have to have an inverse
Y) a matrix that does not have an inverse is called non-singular
Z) a matrix must be square in order to have an inverse
Y) A MATRIX THAT DOES NOT HAVE AN INVERSE IS CALLED NON-SINGULAR
By words or number, name all of the following 3 statements that are TRUE for the function, f(x) = -3x^2 - 2x - 2 = 0:
1) there are no real zeros
2) the graph is a parabola opening downward
3) the graph has no x-intercepts
ALL
Giving your answers in terms of π and in inches squared, find the total surface area of a closed right circular cone whose altitude is 8 inches and radius is 6 inches:
96π
What are the coordinates of the vertex in the graph of the following equation: y = 4x^2 + 8x - 5
(-1, -9)
An object is launched straight up from the ground with an initial velocity of 176 feet per second. What is the height of the object above the ground, in feet, 2 seconds into the flight?
288
A data set has a mean of 10 and variance of 10. If every set element is multiplied by 2, which of the following is TRUE of the new mean and variance:
W) mean is 20, variance is 40
X) mean is 20, variance is 10
Y) mean is 20, variance is 20
Z) mean is 10, variance is 20
W) MEAN IS 20, VARIANCE IS 40
Convert the angle, 18º18'36" (read as: 18 degrees, 18 minutes, 36 seconds) to degrees, to the second decimal place:
18.31
The graph of r = 3 secant (θ) (read as: r = 3 secant theta) is a:
W) parabola
X) circle
Y) hyperbola
Z) line
Z) LINE
Give the resulting vector for the cross product of vector 0,0,1 with vector 1,0,0
0,1,0
What is the angle formed, in degrees, between the hour and minute hand of an analog clock at 10:30 AM?
135
If a point has polar coordinates (3, π), what are the rectangular coordinates?
(-3, 0)
The graph of the polar equation, r = 5 - 5 cosine θ, is a cardioid. In which two quadrants is most of the area of this cardioid?
II AND III (ACCEPT: 2 AND 3 or SECOND AND THIRD)
The point (3, 2) is reflected across the graph of y = 6 and the resulting point is then reflected across the graph of y = x. What are the coordinates of the final point?
(10, 3)
Of the following 5 functions identify all that are NOT differentiable for all real numbers: | x | (read as: absolute value of x); cosine(x); tangent(x); ex; the greatest integer function
TAN(x); THE GREATEST INTEGER FUNCTION
The curve defined by the equation, Ax2 + Bx + Cy2 + Dy + E =0, can be an ellipse if which of the constants are positive?
A AND C
Which of the following is TRUE about any two successive terms in the Fibonacci sequence:
W) their product is a Fibonacci number
X) they are either both odd or both even
Y) they are relatively prime
Z) their quotient is the golden ratio
Y) THEY ARE RELATIVELY PRIME
Which of the following is the equation for the tangent line for y = x4 at the point (1, 1):
W) y = 4x - 3
X) y = 4x - 1
Y) y = 4x + 1
Z) y = 4x + 3
W) y = 4x - 3
Cards numbered 1 through 10 lie on a table. If two cards are picked at random, without replacement, what is the probability, as a fraction in lowest terms, that the two cards will have values within one of each other?
1/5
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