Varsity - Math Flashcards
(180 cards)
1
Q
(30 sec) Express two pi over nine radians in degrees.
A
40 degrees
2
Q
(30 sec) What is the mean of all prime numbers between 12 and 24?
A
18
3
Q
(30 sec) What is the perimeter of a square with a diagonal of 10 radical 2?
A
40
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
5
Q
(30 sec) What is the product of 4 radical 5 and 3 radical 15?
A
60 radical 3
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
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
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
9
Q
(30 sec) Find the sum of the measures of the interior angles of a 15-gon.
A
2340
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)
11
Q
(30 sec) Multiply the quantity 2 plus 4i times the quantity 5 minus 3i.
A
22 plus 14i (22 + 14i)
12
Q
(30 sec) What is the area of an isosceles triangle with side lengths of 4, 4, and 6?
A
3 radical 7
13
Q
(45 sec) Evaluate: 2 sine of pi over six, minus, 3 cosine of pi over 3
A
-1/2 or -.5
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
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
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)
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
18
Q
(30 sec) What is the length of the line with one endpoint (-2, -4) and midpoint (4, 4)?
A
20
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
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)
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
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
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)
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
25
(30 sec) Simplify the expression: sine x, times cosine x, times secant x, times cotangent x.
cosine x
26
(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?
320 miles
27
(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?
18 square root of 2
28
(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)
4
29
(30 sec) What is the equation of the line in standard form containing the points 3 comma 9 and -2 comma -1?
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
30
(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?
15
31
(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?
440 (cubic feet)
32
(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?
10
33
(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?
5 comma 27 (5, 27)
34
(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?
1 to 25
35
(30 sec) The square root of the quantity 6 times a number plus one, close quantity, is seven. Find the number.
8
36
(30 sec) If a square is inscribed into a circle with a radius of 10, what is the area of the inscribed square?
200 (square units)
37
(10 sec) What term is given to the point where the perpendicular bisectors of the three sides of a triangle intersect?
circumcenter
38
(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)?
y equals 4x minus 22 (y=4x-22)
39
(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?
81 (square units)
40
(45 sec) Find the area of a right triangle that has a hypotenuse length of 12 and a leg length of 8.
16 radical 5 (square units)
41
(30 sec) Simplify the following: cosine squared of 3 pi over 4, plus, sine of 5 pi over 6.
1
42
(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?
48 and 56
43
(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?
40 (units squared)
44
(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.
Must have all three:
x = 5, x = -1, y = 0
45
(30 sec) Simplify: tangent theta times sine theta divided by secant theta.
sine squared theta
46
(30 sec) Each interior angle of a regular polygon measures 160 degrees. How many sides does the polygon have?
18
47
(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?
pi over 30
48
(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?
4x squared, plus 28x plus 49
49
(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?
$2880
50
(45 sec) Find the point(s) of inflection of f of x equals x cubed, minus 3x squared, minus 36x plus 5.
1 comma -33
(1, -33)
51
(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?
42 (degrees)
52
(30 sec) Give the geometric mean of 6 and 96.
24
53
(45 sec) Express the product of tangent x times cosecant x as a single trigonometric function.
secant x (or 1 over cosine x)
54
(30 sec) Solve the following equation: four times x to the two-thirds power minus 6 equals ten.
8 and -8 (need both answers) OR plus or minus 8
55
(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?
1536 (papers)
56
(45 sec) What are the solution(s) for 4x cubed plus 2x squared minus 2x equals 0?
-1, 0, 1/2 (Must have all three)
57
(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.
6 (feet) by 10 (feet)
58
(45 sec) Find the 10th term in the series 5, 9, 13, 17...
41
59
(30 sec) What is the radius of a sphere whose surface area and volume are numerically identical?
3
60
(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?
negative 9 divided by the quantity 5x minus 2 closed quantity OR negative 9 over 5x minus 2
61
(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?
20
62
(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?
15 (miles per hour)
63
(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.
13 comma 9 (13, 9)
64
(30 sec) Find the number of diagonals in a decagon.
35
65
(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.
12
66
(60 sec) What is the indefinite integral of 3x squared, minus, 4x, minus 5 cosine of 5x?
x cubed, minus, 2 x squared, minus sine 5x plus C
67
(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?
11 to 26
68
(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?
outlier
69
(45 sec) An isosceles trapezoid has a perimeter of 60. Its bases measure 12 and 28. What is the area of the trapezoid?
120 (square units)
70
(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?
900 (square feet)
71
(30 sec) What is the second derivative of 2x to the fourth, plus sine x, minus e to the x?
24x squared, minus sine x, minus e to the x
72
(30 sec) How many degrees are in 12.5% of a circle?
45 (degrees)
73
(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?
1/30 (1 to 30)
74
(30 sec) What is the log base 2 of the cube root of 4?
two-thirds (2/3)
75
(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?
70
76
(30 sec) What is the sum of the interior angles of a heptagon?
900
77
(30 sec) In terms of pi, convert 110 degrees to radians
11 pi over 18
78
(60 sec) What are the coordinates of the vertex of the parabola formed by the equation y equals 2x squared - 8x + 9?
2 comma 1 (2, 1)
79
(10 sec) What is the name given to two coplanar angles with a common side, a common vertex, and no common interior points?
Adjacent angles
80
(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?
-5 and 5
81
(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.
240x squared, plus 96x, plus 18
82
(30 sec) How many unique eight-letter patterns can be formed from the letters of the word parabola?
6720
83
(45 sec) What is the domain of f of x equals the square root of the quantity 2x plus 4?
x is greater than or equal to -2
84
(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?
y equals 2x minus 2
85
(45 sec) Three times one number minus a second is 8, and the sum of the numbers is 12. Find the numbers.
5 and 7
86
(30 sec) The diagonals of a rhombus have lengths of 16 and 30. Find the perimeter of the rhombus.
68
87
(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?
1.7
88
(30 sec) Find the second derivative of y equals x cubed plus sine of x.
6x minus sine of x
89
(30 sec) What is the sum of the positive factors of 42?
96
90
(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)?
21 (square units)
91
(45 sec) Find the volume of a right triangular prism with the base lengths 5, 12, and 13 and a height of 9.
270
92
(30 sec) Find the number of degrees through which the minute hand of a clock moves in 2 hours and 48 minutes
1008
93
(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?
2 comma 4
94
(30 sec) What is the product of 4 minus 5 eye (4-5i) and its conjugate?
41
95
(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.
1
96
(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.
20 (degrees), 50 (degrees), 110 (degrees)
97
(60 sec) In slope-intercept form, find the equation of the line that goes through the points (-3 comma 5), and (4 comma -2).
y equals negative x plus 2
(y = -x + 2)
98
(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.
28, 28, 37
99
(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.
150 (revolutions per minute)
100
(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?
50 by 70
101
(10 sec) What branch of mathematics deals with such concepts as mode, standard deviation, and z-scores?
Statistics
102
(30 sec) What must be added to the expression x squared minus 14x to make it a perfect square trinomial?
49
103
(30 s) What is the sum of the roots, in simplest fractional form, for the equation 7 - 13x - 2x squared = 0? (7 - 13x -2x^2 = 0)
-13/2 or -6 1/2
104
(45 s) Find the center of the circle given by the equation x squared plus y squared minus 14 x plus 10 y equals 9. (x^2 + y^2 - 14x + 10y = 9)
(7,-5)
105
(30 s) Find the limit, as x approaches infinity, of f of x = the quantity 3x - 9, close quantity, divided by the quantity x squared - 7, close quantity. (3x - 9)/(x^2 - 7)
0
106
(30 seconds) What is the largest area, in square feet, that can be fenced with 100 feet of fencing, assuming straight sides?
625 (square feet)
107
(45 seconds) In terms of pi, what is the circumference of a circle given by the equation, the quantity x minus 3, close quantity squared, plus the quantity y minus 5, close quantity squared, equals 75? ((x-3)^2 + (y-5)^2 = 75)
10 radical 3 pi, or 10pi radical 3, or 10pi times the square root of 3
108
(30 s) In feet, find the arc length of a circle with a diameter of 16 feet, bounded by an angle measuring 8 radians.
64 (feet)
109
(30 s) If the area of a circle is 72 square inches, what is the area of the sector, in square inches, created by a 60 degree central angle inside the circle?
12 (square inches)
110
(30 s) Solve the following, and give all solutions: 3 times the absolute value of the quantity x plus 5, close quantity, equals 12.
-9 and -1 (must have both)
111
(60 s) The weights of adult Newfoundland dogs have approximately a normal distribution, with a mean of 140 lbs. and a standard deviation of 20 lbs. Suppose that a Newfoundland dog is considered overweight if it weighs more than 180 lbs. To the nearest whole percent, what percentage of these dogs are overweight?
2%
112
(30 s) How many times greater is the volume of a sphere if the diameter of the sphere is doubled?
8 (times greater)
113
(45 s) What is the volume, in cubic units, of the smallest cube that can contain a sphere whose volume is 288 pi cubic units?
1728 (cubic units)
114
(60 s) Write the equation of the tangent line, in slope intercept form, of y = x squared - 10 x, at x = 1. (f(x) = x^2 - 10x)
y= -8x - 1 (y equals negative 8 x minus 1)
115
(90 s) Solve the equation cosine squared theta, minus one-half cosine theta, equals zero, if theta is an angle between 0 and 360 degrees, inclusive.
60 (degrees), 90 (degrees), 270 (degrees), 300 (degrees) (Must have all 4)
116
(10 s) What is name of the point of concurrency of the 3 altitudes of a triangle?
Orthocenter
117
(60 s) Factor completely: 2 x cubed plus 6 x squared minus 8x - 24. (2x^3 + 6x^2 - 8x - 24)
2 times the quantity x plus 3, times the quantity x plus 2, times the quantity x minus 2. (in any order, but must have all 3 quantities) [2(x+3)(x+2)(x-2)]
118
Give the fifth term of the geometric sequence if the first term is negative 5, and the common ratio is negative 3.
-405
119
(60 s) Find the second derivative of the following: 4 x to the fifth, plus 3 x cubed, minus the cosine of x, plus 1 over x. (4x^5 + 3x^3 – cosx + 1/x)
80 x cubed/(to the third), plus 18 x squared/(to the second), plus (the) cosine of x, plus 2 over/(divided by) x cubed/(to the third) [(80x^3 + 18x + cosx + 2/x^3)]
120
(30 s) What is the volume, in cubic units, of a regular square pyramid with base side length of 6 and height of 7?
84 (cubic units)
121
(45 s) A class had a collection of nickels and quarters that totaled 18 coins, and had a value of $2.70. How many were nickels and how many were quarters?
9 nickels and 9 quarters
122
(30 s) When rolling a standard 20 sided dice, what are the odds that a prime number will be rolled?
2:3
123
(45 s) Find the value of x for a pair of lines that are cut by a transversal, forming a pair of alternate interior angles that measure 85 degrees and 3x - 17 degrees, if the lines are parallel.
(x =) 34
124
(45 s) The radius of a right cylinder is 8. What is the height, if the total surface area is 256 pi?
8
125
(30 s) If f of x equals 2 x cubed, and g of x equals 2 x minus 25, what is the value of g of f of 5? (F(x)= 2x^3 and g(x) = 2x-25)
475
126
(45 s) If a basketball team scores 339 points in 7 games, and gives up 185 points in 7 games, to the nearest whole number, what is their average margin of victory?
22 (points)
127
(10 s) What name is given to the non-regular, equilateral parallelogram?
Rhombus (do not accept square)
128
(90 s) Suppose a new sports car is worth $24,000. It depreciates by one tenth of its value each year. To the nearest dollar, find the value of the car after 3 years.
$17,496
129
(30 s) Simplify the expression: "radical three, plus radical 27, minus radical 243".
negative 5 radical three OR negative 5 times the square root of three OR negative 5 times radical 3
130
(45 s) The locations of three water pumping stations form a triangle on a map. The distance from station A to station B is 681. The distance from station B to station C is 594. Between what two numbers must the distance from station A to station C be?
87 and 1275
131
(30 s) What is the limit, as x approaches 4, of the quantity x minus 4, close quantity, divided by the quantity negative 2 plus the square root of x, close quantity?
4
132
(45 s) The owner of a store displays a large jar of nickels and dimes, and offers the value of the coins to the person who guesses how many dimes there are. If there are 1,130 coins, and they are worth $100, how many dimes are there?
870
133
(45 s) What are the dimensions, in inches, of a 4 by 6 inch photo that is reduced by 25% and then enlarged by 150%?
4.5 (inches) by 6.75 (inches)
134
(45) How many knife slices are required to cut a 15 inch loaf of bread into slices that are all 3/4 inch wide?
19
135
(30 s) What is the vertex of the following function: f of x equals 4 times the absolute value of the quantity x minus 2, close quantity, plus 3?
(2, 3)
136
(90 s) An isosceles trapezoid has one base of 23, and a height of 8. If the area of the trapezoid is 136, what is its perimeter?
54
137
(30 s) What is the domain of the following rational function: f of x equals the quantity 3x plus 7, close quantity, divided by the quantity x squared minus 7x plus 10, close quantity? ((3x+7)/(x^2-7x+10))
(x = ) all real numbers except 5 and 2, OR x cannot equal 5 and 2
138
(10 s) In what quadrant is tangent negative and cosine positive?
4
139
(30 s) The half-life of Carbon-14 is 5,730 years. How old, in years, is a fossil containing 1/8 of the original amount of Carbon-14?
17,190 (years)
140
(30 s) A triangle has angles measuring x + 35, 4x + 20, and x + 65, each in degrees. What is the value of x, in degrees?
10
141
(90 s) Solve the following system of 3 equations with 3 variables. Give your answer as an ordered triple:
3x - 2y + 4z = 5,
6x - 3y - 2z = 1,
-2x + 2y + z = 1
(1, 1, 1)
142
(45 s) An online bookseller charges $3 per order plus $1 per book for shipping. John places an order for four books that have the same price. The total cost of his order is $30. What is the price, in dollars, of each book?
$5.75
143
(30 s) In circle A with a radius of 3, angle CAB equals 70 degrees. What is the exact area, in terms of pi, of sector CAB?
(7/4)pi or 7pi over 4
144
(45 s) Convert eight-pi over fifteen radians into degrees.
96 (degrees)
145
(30 s) Find the determinant of this two by two matrix:
Row 1 contains elements 6 and 4
Row 2 contains elements 9 and 3
-18
146
(Time 45)
Simplify the following:
7 log base 3 of a, plus log base 3 of b, minus 2 log base 3 of 8c.
log base 3 of the quantity a to the 7th times b over 64c squared, close quantity.
147
(30 s) A plastering contractor charges $3 per square foot. What is the cost of plastering 57 feet of wall in a house with an 8-foot ceiling?
$1368
148
(Time 30)
What is the limit as x approaches infinity of the quantity 3 x square plus 4 x divided by the quantity 2x squared plus 5?
3/2 (accept 1.5 or 1 1/2)
149
(45 s) Simplify the following: the tangent of 360 degrees, plus the sine of 360 degrees, minus the cosine of 360 degrees.
-1
150
(30 s) What is the area, in square meters, of a square with a diagonal of 4 meters?
8 (square meters)
151
(45 s) Factor the following polynomial completely: 8 a to the 6th minus 27 b cubed. (8a^6 - 27b^3)
the quantity 2 a squared minus 3 b, close quantity, times the quantity 4 a to the 4th plus 6 a squared (times) b plus 9 b squared, close quantity. [(2a^2-3b)(4a^4+6a^2b+9b^2) - can be in any order, as long as in the correct groupings in quantities]
152
(30 s) What is the domain of the function f(x)=2log2(x-3)? (Read as 2 times the log, base 2, of the quantity x minus 3)
x>3 (x is greater than 3)
153
(Time 30)
Bill Smith has 25 red socks and 30 white socks in a drawer. Since it is dark, he can't tell them apart. How many socks must he take from the drawer to make sure he has a pair of red socks?
32 socks
154
(60 s) A particle moves back and forth along a horizontal line with velocity given by the equation v of t equals 2t + 5. At time t = 0 seconds, the particle is 15 units right of the origin. How far right of the origin, in units, is the particle at time t = 3 seconds?
39 (units)
155
(45s)
Simplify the expression sine of x times the quantity tangent of x plus cotangent of x, close quantity, to a basic trigonometric function.
secant x
156
(30 s) Find k, given that the point 2 comma k (2,k) is equidistant from the point 3 comma 7 (3,7) and 9 comma 1 (9,1).
(k =) 0 (zero)
157
(45s)
Laura works at the "Sweater Barn" on commission. She earns 12% on her sales up to $1,000 and 15% on additional sales over $1,000. How much did Laura earn the week she sold $2,500 worth of merchandise?
$345
158
(60 s) When a parabola represented by the equation y - 2x^2 = 8x + 5 is translated 3 units to the left and 2 units up, what point is the vertex of the new parabola?
(-5, -1)
159
(30s)
If a right circular cylinder has a height of 4 inches and a diameter of 1 1/2 feet, what is the exact circumference of its base in inches?
18 pi (inches)
160
(30 s) How many diagonals does an octagon have?
20
161
(45 s) Identify all vertical and horizontal asymptotes of the graph of the function f(x) = (2x^2 - 5x - 12)/(x^2 - 16). (Read: The quantity 2 x squared minus 5x minus 12, close quantity, divided by the quantity x squared minus 16, close quantity.)
x = -4 (vertical) and y = 2 (horizonal)
162
(30s)
If the sine of an angle is 3/5 and located in the second quadrant, what is the secant of the angle?
-5/4
163
(45 s) Find the exact circumference, in terms of pi, for a circle with an inscribed isosceles right triangle having leg length of 4 radical 2.
8 pi
164
(45 s) Evaluate the definite integral, from -1 to 1, of the function x squared minus 2 dx.
-10 over 3 (-10/3)
165
What is the mathematical name for a straight line that connects two nonadjacent vertices of a polygon?
Diagonal
166
(45 s) What are the coordinates of both the vertices and co-vertices of the following ellipse: 16x^2 + 25y^2 = 400? (read as 16 x squared + 25 y squared = 400.)
(5,0), (-5,0), (0,4), and (0,-4) (Must have all 4, but don't need to identify which are vertices and which are co-vertices)
167
(90s)
What is the length of the major axis on the graph of 64 x squared plus 100 y squared equals 6400?
twenty (20)
168
(45 s) Simplify the following expression: The cotangent squared of x times the secant squared of x times the sine of x.
Cosecant of x (csc x) (do not accept 1/sin x)
169
(60s)
Find all the zeroes of the function: y = 2x cubed + x squared – 18x – 9.
(x=)-3, 3, 1/2 (any order)
170
(60 s) Joe's test scores were 70, 80, and 90. What was his weighted average if the tests were weighted 2, 3, and 5, respectively?
83
171
(30s)
A holding pen for cattle must be square, and have a diagonal length of 80 meters. Find the exact length of each side of the pen.
40 square root of 2 meters
172
(10 s) What type of lines do not intersect and are not coplanar?
Skew
173
(30s)
The sum of the digits of a two-digit number is 10. If the digits are reversed, the new number is 36 less than the original number. Find the original number.
73
174
(10 s) What is the term for a set of points that lie in the same plane?
Coplanar
175
(45 s) You want to juggle eggs for a living. Over five days, you break 200 eggs. Each day you break a dozen more eggs than the day before. How many eggs did you break each day?
16, 28, 40, 52, 64
176
(30s)
Two angles are adjacent and form an angle of 120 degrees. The larger angle is 20 degrees less than three times the smaller. Find the measure of both angles.
35 and 85 (degrees)
177
(60 s) Find the period, amplitude, phase shift, and vertical shift for the function f(x) = -4 + 3sin2x. (Read: negative 4 plus 3 sine 2x)
Amplitude = 3, period = pi, phase shift = 0, and vertical shift: 4 units down (must have all 4 parts with identifying characteristics)
178
178
(60s)
Find the slope of the line tangent to y equals the square root of the quantity x squared plus 2x plus 8, at the point (2,4).
three fourths, or 3 over 4, or 3/4
179
Solve the following equation for x:
log (base 4) of (5x-1) = 3
(x =) 13
