Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

BVSW Scholars Bowl > Varsity - Math > Flashcards

Varsity - Math Flashcards

1
Q

(30 sec) Express two pi over nine radians in degrees.

A

40 degrees

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

(30 sec) What is the mean of all prime numbers between 12 and 24?

A

18

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

(30 sec) What is the perimeter of a square with a diagonal of 10 radical 2?

A

40

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

(60 sec) Give the period, amplitude, and horizontal translation of the function y equals -3 cosine of the quantity 5x minus pi.

A

period is 2 pi over 5, amplitude is 3, and horizontal translation is positive pi over 5 or pi over 5 to the right

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

(30 sec) What is the product of 4 radical 5 and 3 radical 15?

A

60 radical 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

(30 sec) The corners of a parallelogram are at the points (0,0), (6, 0), (3, 4), and (9, 4). What is the area of the parallelogram?

A

24 square units

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

(30 sec) Find the limit of x, divided by the quantity, 2x plus 1, closed quantity, as x approaches infinity.

A

1/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

(45 sec) Find the determinant of the following 3 by 3 matrix: Row 1: -4, 0, -1; Row 2: 2, 2, -1; Row 3: 1, 2, 4.

A

-42

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

(30 sec) Find the sum of the measures of the interior angles of a 15-gon.

A

2340

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

(45 sec) In degrees, find all angles between negative 360 degrees and 360 degrees that have the same sine ratio as 150 degrees.

A

negative 210, 30, negative 330 (-210, 30, -330)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

(30 sec) Multiply the quantity 2 plus 4i times the quantity 5 minus 3i.

A

22 plus 14i (22 + 14i)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

(30 sec) What is the area of an isosceles triangle with side lengths of 4, 4, and 6?

A

3 radical 7

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

(45 sec) Evaluate: 2 sine of pi over six, minus, 3 cosine of pi over 3

A

-1/2 or -.5

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

(45 sec) The sum of three numbers is 40. One number is five more than a second number. The first number is also twice the third. Find all three numbers.

A

18, 13, and 9

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

(30 sec) In terms of pi, state the area of a sector of a circle with a radius of 12 inches and an arc measure of 60 degrees.

A

24 pi square inches or 24 pi inches squared

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

(30 sec) What is the derivative, with respect to x, of y equals 3 x to the 8th, minus, 3 x to the 4th, plus, 2 e to the 3x? (y =
3x^8 - 3x^4+2e^3x)

A

24 x to the seventh, minus, 12 x cubed, plus, 6 e to the 3x (24x^7-12x^3+6e^3x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

(45 sec) A jacket that originally cost $95.00 is on sale for 40% off. If the sales tax were 9%, what is the total amount you will
pay?

A

$62.13

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

(30 sec) What is the length of the line with one endpoint (-2, -4) and midpoint (4, 4)?

A

20

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

(30 sec) The perimeter of a triangle is 36. The second side is four more than the first side. The third side is twice the first
side. What is the length of each side?

A

8, 12, 16

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

(60 sec) Solve for x, if x is in radians between zero and 2 pi: 2 sine x, plus, one, equals zero. (2sin(x) + 1 = 0)

A

11 pi over 6 (11pi/6) -AND- 7 pi over 6 (7pi/6) (must have both)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

(45 sec) The second term in an arithmetic sequence is -2 and the eighth term is 40. What is the first term?

A

-9

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

(45 sec) Tangent x equals radical 3 and x is in quadrant III. Find the exact value of cosine x.

A

negative one-half

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

(30 sec) Two alternate interior angles have measures given as 14x + 9 and 5x + 90. What are the measures of the angles in degrees?

A

135 (degrees)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

(45 sec) Find the radius of a circle with the following equation: x squared plus 4x plus y squared minus 6y minus 12 equals 0.

A

5

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

(30 sec) Simplify the expression: sine x, times cosine x, times secant x, times cotangent x.

A

cosine x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

(30 sec) Jack drove his Harley from one town to the next averaging 64 mph. His average speed for the return trip was 80 mph, and his total travel time was nine hours. How far apart are the towns?

A

320 miles

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

(45 sec) An equilateral triangle has an altitude of 3 square root of 6 and an area of 18 square root of 3. What is the perimeter of the triangle?

A

18 square root of 2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

(60 sec) What is the limit as x approaches 1 of the function quantity, x squared, plus 2x, minus 3, closed quantity, over the quantity x minus 1? (x^2+2x-3)/(x-1)

A

4

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

(30 sec) What is the equation of the line in standard form containing the points 3 comma 9 and -2 comma -1?

A

Accept any one of the following:
2x minus y equals negative 3,
negative 2x plus y equals 3,
2x minus y plus 3 equals zero,
negative 2x plus y minus 3 equals zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

(30 sec) In a right triangle, if the side opposite the acute angle A is 12, and if sine of A is four over five, then what is the length of the hypotenuse?

A

15

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

(60 sec) If you were pouring a concrete slab that had dimensions of 40 feet long by 30 feet wide and 4 inches thick, rounded to the nearest tenth, how many cubic feet of concrete should you order if you intend to order 10% extra?

A

440 (cubic feet)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

(45 sec) How many quarts of 80 percent solution need to be added to 5 quarts of 50 percent solution to produce a mixture of 70 percent solution?

A

10

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

(30 sec) Troop 314 is designing a new campground by first mapping everything on a coordinate plane. They located the mess hall at 40 comma -10,(40,-10) and the showers at -30 comma 64 (-30, 64). They want to put the bathrooms halfway between these two places. What will be the coordinates of the location of the bathrooms?

A

5 comma 27 (5, 27)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

(60 sec) If one card is chosen from a standard deck of 52 cards, and a standard die is rolled once, what are the odds of choosing an ace and rolling a prime number?

A

1 to 25

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

(30 sec) The square root of the quantity 6 times a number plus one, close quantity, is seven. Find the number.

A

8

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

(30 sec) If a square is inscribed into a circle with a radius of 10, what is the area of the inscribed square?

A

200 (square units)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

(10 sec) What term is given to the point where the perpendicular bisectors of the three sides of a triangle intersect?

A

circumcenter

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

(45 sec) What is the equation in slope-intercept form for the line that contains the point 4 comma -6 (4, -6) and is perpendicular to the line 2x plus 8y equals 16. (2x+8y=16)?

A

y equals 4x minus 22 (y=4x-22)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

(30 sec) If the sides of a square are increased by 3, and the resulting area of the square is 144, what was the area of the square before the side length increase?

A

81 (square units)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

(45 sec) Find the area of a right triangle that has a hypotenuse length of 12 and a leg length of 8.

A

16 radical 5 (square units)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

(30 sec) Simplify the following: cosine squared of 3 pi over 4, plus, sine of 5 pi over 6.

A

1

42
Q

(60 sec) Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the average speed in miles per hour of each car for the 2-hour trip?

A

48 and 56

43
Q

(30 sec) RSTU is an isosceles trapezoid with bases of length 6 and 14 and two base angles measuring 45 degrees. What is the area of the trapezoid?

A

40 (units squared)

44
Q

(45 sec) Find the equations of all asymptotes of f of X equals quantity x plus 3, closed quantity over, quantity x squared minus 4x minus 5 closed quantity.

A

Must have all three:
x = 5, x = -1, y = 0

45
Q

(30 sec) Simplify: tangent theta times sine theta divided by secant theta.

A

sine squared theta

46
Q

(30 sec) Each interior angle of a regular polygon measures 160 degrees. How many sides does the polygon have?

A

18

47
Q

(45 sec) A second hand on a clock moves at 60 rotations per hour. In terms of pi, what is its angular velocity in radians per second?

A

pi over 30

48
Q

(30 sec) If f of x equals 2x plus 7and g of x equals x squared, what is g of f of x in simplified form?

A

4x squared, plus 28x plus 49

49
Q

(30 sec) The profit realized by Fred’s Fruitcakes Company varies directly as the number of fruitcakes it sells. If the company makes a profit of $1,500 on the sale of 250 fruitcakes, what is the profit when the company sells 480 fruitcakes?

A

$2880

50
Q

(45 sec) Find the point(s) of inflection of f of x equals x cubed, minus 3x squared, minus 36x plus 5.

A

1 comma -33
(1, -33)

51
Q

(60 sec) Angle A has a measure that is 12 degrees more than three times its supplement. In degrees, what is the measure of angle A’s supplement?

A

42 (degrees)

52
Q

(30 sec) Give the geometric mean of 6 and 96.

A

24

53
Q

(45 sec) Express the product of tangent x times cosecant x as a single trigonometric function.

A

secant x (or 1 over cosine x)

54
Q

(30 sec) Solve the following equation: four times x to the two-thirds power minus 6 equals ten.

A

8 and -8 (need both answers) OR plus or minus 8

55
Q

(30 sec) A high school science teacher got behind in his paperwork and had 2 feet of papers stacked on his desk. If each pageis 1/64th of an inch thick, how many papers are on his desk?

A

1536 (papers)

56
Q

(45 sec) What are the solution(s) for 4x cubed plus 2x squared minus 2x equals 0?

A

-1, 0, 1/2 (Must have all three)

57
Q

(45 sec) A rectangular pool is 4 feet longer than it is wide. Determine the dimensions of the pool, in feet, if it has a uniform depth of 5 feet and holds 300 cubic feet of water when filled to the top.

A

6 (feet) by 10 (feet)

58
Q

(45 sec) Find the 10th term in the series 5, 9, 13, 17…

A

41

59
Q

(30 sec) What is the radius of a sphere whose surface area and volume are numerically identical?

A

3

60
Q

(60 sec) What is the derivative of the function f of x equals the quantity 2x plus one close quantity, divided by the quantity 5 x minus 2 close quantity?

A

negative 9 divided by the quantity 5x minus 2 closed quantity OR negative 9 over 5x minus 2

61
Q

(45 sec) What is the area of a triangle with side lengths of 8, radical 2, and 5, and an included angle of 45 degrees?

A

20

62
Q

(45 sec) A motorboat goes 24 miles upstream in the same length of time it takes to go 36 miles downstream. If the current is flowing at 3 miles per hour, what is the boat’s rate, in miles per hour, in still water?

A

15 (miles per hour)

63
Q

(30 sec) Rectangle ABCD has point A at (4 comma 2), point B at (14 comma 4), and point C at (3 comma 7). Find the
coordinates of point D.

A

13 comma 9 (13, 9)

64
Q

(30 sec) Find the number of diagonals in a decagon.

A

35

65
Q

(30 sec) Find the degree of the following polynomial: -2 x cubed y to the fourth z cubed, plus, 5 x squared y to the sixth z to the fourth, minus, 14 x y cubed z to the fifth.

A

12

66
Q

(60 sec) What is the indefinite integral of 3x squared, minus, 4x, minus 5 cosine of 5x?

A

x cubed, minus, 2 x squared, minus sine 5x plus C

67
Q

(45 sec) If you draw one card from a normal deck of playing cards, what is the fractional probability of drawing a jack, queen, king or a diamond?

A

11 to 26

68
Q

(10 sec) What’s the name given to any value in a set of data that’s more than 1.5 times the interquartile range from the upper or lower quartiles in a box-and-whisker plot?

A

outlier

69
Q

(45 sec) An isosceles trapezoid has a perimeter of 60. Its bases measure 12 and 28. What is the area of the trapezoid?

A

120 (square units)

70
Q

(45 sec) A 5 foot wide path surrounds a rectangular swimming pool. The swimming pool is sixty feet long and twenty feet wide. In square feet, what is the area of the path?

A

900 (square feet)

71
Q

(30 sec) What is the second derivative of 2x to the fourth, plus sine x, minus e to the x?

A

24x squared, minus sine x, minus e to the x

72
Q

(30 sec) How many degrees are in 12.5% of a circle?

A

45 (degrees)

73
Q

(30 sec) Given a bag containing 3 red marbles, 5 blue marbles, and 2 green marbles: what is the probability of choosing a red marble, putting it back in, then choosing first a green marble and then a blue marble without putting the green marble back in?

A

1/30 (1 to 30)

74
Q

(30 sec) What is the log base 2 of the cube root of 4?

A

two-thirds (2/3)

75
Q

(60 sec) One leg and the hypotenuse of a right triangle have lengths of 24 and 74, respectively. What is the length of the other leg?

A

70

76
Q

(30 sec) What is the sum of the interior angles of a heptagon?

A

900

77
Q

(30 sec) In terms of pi, convert 110 degrees to radians

A

11 pi over 18

78
Q

(60 sec) What are the coordinates of the vertex of the parabola formed by the equation y equals 2x squared - 8x + 9?

A

2 comma 1 (2, 1)

79
Q

(10 sec) What is the name given to two coplanar angles with a common side, a common vertex, and no common interior points?

A

Adjacent angles

80
Q

(45 sec) When the expression x squared, plus b ex, minus 24 is factored completely, the difference of the factors is 11. What are the 2 possible values of b?

A

-5 and 5

81
Q

(60 sec) Give the third derivative of the equation 4x to the fifth, plus, 4x to the fourth, plus 3x cubed, minus 2x squared, minus 542.

A

240x squared, plus 96x, plus 18

82
Q

(30 sec) How many unique eight-letter patterns can be formed from the letters of the word parabola?

A

6720

83
Q

(45 sec) What is the domain of f of x equals the square root of the quantity 2x plus 4?

A

x is greater than or equal to -2

84
Q

(30 sec) What is the slope-intercept form of the line that is parallel to y equals 2x plus 7 and goes through the point 4 comma 6?

A

y equals 2x minus 2

85
Q

(45 sec) Three times one number minus a second is 8, and the sum of the numbers is 12. Find the numbers.

A

5 and 7

86
Q

(30 sec) The diagonals of a rhombus have lengths of 16 and 30. Find the perimeter of the rhombus.

A

68

87
Q

(45 sec) The probability model for the number of calls a repair shop receives per hour is 10% of a chance of 0 calls, 30% chance of 1 call, 40% chance of 2 calls, and 20% chance of 3 calls. How many calls should the shop expect per hour?

A

1.7

88
Q

(30 sec) Find the second derivative of y equals x cubed plus sine of x.

A

6x minus sine of x

89
Q

(30 sec) What is the sum of the positive factors of 42?

A

96

90
Q

(45 sec) What is the area of a triangle with vertices at the points with coordinates (1 comma 3), (-2 comma -4), and (4 comma -4)?

A

21 (square units)

91
Q

(45 sec) Find the volume of a right triangular prism with the base lengths 5, 12, and 13 and a height of 9.

A

270

92
Q

(30 sec) Find the number of degrees through which the minute hand of a clock moves in 2 hours and 48 minutes

A

1008

93
Q

(45 sec) Find the coordinates of the vertex of a parabola defined by the equation y equals three x squared minus twelve x plus sixteen?

A

2 comma 4

94
Q

(30 sec) What is the product of 4 minus 5 eye (4-5i) and its conjugate?

A

41

95
Q

(45 sec) Determine the slope of the function, f of x equals x squared plus e to the x, at the point 0 comma 1.

A

1

96
Q

(45 sec) The measure of the largest angle of a triangle is 90 degrees more than the measure of the smallest angle, and the measure of the remaining angle is 30 degrees more than the measure of the smallest angle. Find the measure of each angle, in degrees.

A

20 (degrees), 50 (degrees), 110 (degrees)

97
Q

(60 sec) In slope-intercept form, find the equation of the line that goes through the points (-3 comma 5), and (4 comma -2).

A

y equals negative x plus 2
(y = -x + 2)

98
Q

(45 sec) The perimeter of a triangle is 93. If two sides are equally long and the third side is 9 longer than the others, find the lengths of the three sides.

A

28, 28, 37

99
Q

(30 sec) The angular speed of a bicycle, with tires that have a diameter of 18 inches, is 5pi radians per second. Find the number of revolutions per minute.

A

150 (revolutions per minute)

100
Q

(60 sec) The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240, what are the dimensions of the field?

A

50 by 70

101
Q

(10 sec) What branch of mathematics deals with such concepts as mode, standard deviation, and z-scores?

A

Statistics

102
Q

(30 sec) What must be added to the expression x squared minus 14x to make it a perfect square trinomial?

A

49

BVSW Scholars Bowl (13 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions