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WorksheetsmEEth 2017
Total questions: 100
Worksheet time: 50mins
It Rita can run around the block 5 times in 20 minutes. how many times can she run around the block in one hour?
10
50
15
100
Determine if the sequence in sin (u/n) is convergent or divergent. Find its limit if it is convergent
convergent, π/4
divergent
convergent, π/2
convergent, π
Evaluate the double integral dx dy / (x - y), with interior limits 2y to 3y and outer limits from 0 to 2.
ln 4
ln 2
ln
ln 3
A snack machine accepts only 5-centavo coins. Chocolate bars cost 25c each, packages of peanuts cost of 75c and a can of cola costs 50c. How many 5-centavo coins are needed to buy 2 chocolate bars, one pack of peanuts and a can of soda?
30
32
35
6
Find the equation of the circle which passes through the vertex and the endpoints of the latus rectum of the parabola y2 = 8x.
x2 + y2 + 10x = 0
x2 + y2 - 10x + 2y + 3 = 0
x2 + y2 - 10x = 0
x2 + y2 + 2x - 10y - 1 = 0
Express -3- 4i in polar form.
(square root of 5)^e-i arctan 2
square root of 2)^e -- i arctan square root of 5
(square root of 5) e - i^(π + arctan 4/3)
5 ei^(π + arctan 4/3)
Find the equation of the normal line to x2 + y2 at the point (2, 1)
4x - 3y = 0
x - 2y = 0
x + y = 0
x - y = 0
Find the value of x for which f(x) = cot 2x is discontinuous.
x = 3/2
x = 0
x = π/2
x = 0, π
What is the ratio of the sides of a triangle if the product of the sines of its angle is a maximum?
1 : 2 : 2
1 : 3 : 3
1 : 1 : 2
1 : 1 : 1
A pendulum 1 m long oscillates through an angle of 10o. Find the distance through which the end of the pendulum swings in going from one extreme position to the other.
π m
2π m
π/8 m
π/18 m
If y = arctan (In x), find y' when x = 1/e
e / 2
e / 3
e
e / 4
Hotels, like airlines, often overbook, relying on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservation will not be used. If 4 reservations are made, what is the probability fewer than two will cancel?
0.8192
0.3825
0.7241
0.5211
Find the area bounded by the parabolas
x2 - 2x + 2y + 5 = 0 and x2 - 2x + y + 1 = 0.
14
14 / 13
16
16 / 3
Find the general solution of y' = y sec x
y = C sec2x tan x
y = C (sec x + tan x)
y = C sec x tan x
y = C sec x
A company manufactures industrial laminates (thin nylon-based sheets) of thickness 002 tolerance of 0.004 in. Solve the inequality involving absolute values that describes the rand thickness for the laminate.
0.017 ≤ 𝑥 ≤ 0.024
0.014 ≤ 𝑥 ≤ 0.022
0.017 ≤ 𝑥 ≤ 0.025
0.016 ≤ 𝑥 ≤ 0.023
Determine all the values of (1 + i)i
cos (2sq. root of 2kπ) + i sin (2sq. root of 2 kπ)
cos (1/2 ln 2) + i sin (1/2 ln 2)
e^-π/4 + 2lπ (cos (1/2 ln2) + i sin (1/2 ln2))
e^-π/4 + 2kπ
Judy's English quiz scores are 56, 93, 72, 99, and 87, What is the median of her quizzes?
87
56
72
85
Find the equation of the line passing 3 units from the origin and parallel to 3x + 4y – 10 = 0.
3x + 4y -15 = 0
4x + 3y + 1 = 0
x-3y + 15 = 0
3x + 4y – 5 = 0
Which ratio best express the following: five hours is what percent of a day?
5/24 = x/100
5/24 = 24/x
5/100 = x/24
x/100 = 24/5
What is the graph of the curve whose equation is
5x2 + 5y2– 5x – 10y - 33 = 0
parabola
ellipse
hyperbola
circle
if a school buys three computers a, b, and c pesos each, gets a discount of 90%, which expression would determine the average price paid by the school?
(a + b + c) 0.9/3
(a + b + c) /3
(a + b + c) /0.9
(a + b + c) 0.9
Find the equation of the family of orthogonal trajectories of the system of parabolas y2 = 2x + C.
y = Ce^2x
y = Ce^-2x
y = Ce^x
y = Ce^-x
A laboratory keeps two acid solutions on hand. One is 20% acid and the other is 35% acid. How many liters of distilled water should be added to a liter of 35% acid solution in order to dilute it to a 20% acid solution?
0.45
0.75
0.25
0.57
Solve xy’ (2y - 1) = y (1 - x).
ln xy = x - 2y + C
ln xy = 2y – x + C
ln xy = x + 2y + C
In xy = 2(x - y) + C
in an arithmetic series, the terms of the series are equally spread out. For example, in 1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic, series is 3. The last term is 136, and the sum is 1,390. what are the first 3 terms?
3, 36 (1/3), 70
3, 10, 17
3, 23, 43
3, 69 (1/2), 138
Find the equation of the circle tangent to
4x-3y + 12 = 0 at (-3,0) and tangent also to
3x + 4y – 18 = 0 at (4,1).
x2 + y2 + 4x - 3y + 6 = 0
x2 + y2 + x - 2y + 3 = 0
x2 + y2 + x - y + 5 = 0
x2 + y2 - 2x + 6y - 15 = 0
Joseph gave 1/4 of his candies to Joy and Joy gave 1/5 of what she got to Tim. if Tim received 2 candies, how many candies did Joseph have originally?
30
20
50
40
A line that is perpendicular to the y-axis has a slope equal to ______________.
one
infinity
indeterminate
zero
What is the value of x if logx 1296 = 4?
3
6
5
4
It represents the distance of a point from y-axis.
coordinate
ordinate
abscissa
polar distance
What is the next term in the geometric sequence 16, -4,1, -/4, ...?
1 / 16
1 / 8
1 / 8
0
A steel girder 8 m long is moved on rollers along a walkway 4 m wide and into a corridor perpendicular to the walkway. How wide must the corridor be to successfully move the girder?
1.8 m
18 m
10 m
8 m
Find the centroid of the solid generated by revolving about x = 0 the first quadrant arc x2 + y2 = a2, the fourth quadrant arc of x2 - y2 = a2, the fourth quadrant arc of 2x – y = 2a and x = 0.
(0, 2/3)
(0, -1/3)
(0, 1/3)
(0, -2/3)
Jeff burns 500 calories per hour bicycling. How long will he have to bike to burn 750 calories?
1.5 hours
2 hours
0.5 hours
3 hours
Evaluate ∫ 𝑑𝑥/ (𝑥 + 2) from x = -10 to x = -6
ln (1/2)
ln 1
ln 2
2 ln 2
Find all the real solutions to the logarithmic equation ln x + ln 2 = 3
e^½
e^2
e^3/2
e
On a particular morning, the temperature went up 1 degree every 2 hours. If the temperature was 53 degrees at 5 AM. at, what time was it 57 degrees?
12 P.M
8 A.M.
1 P.M.
7 A.M.
Evaluate lim𝑥→2 (𝑥2−4) /(𝑥−2)
8
4
0
16
Aubrey measured the width of her dining room in inches. It is 150 inches. How many feet wide is her dining room?
10.5 ft
21.5 ft
12.5 ft
9.5 ft9.5 ft
Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards.
2.5 mils
1 mil
4 mils
2.04 mils
Find x. arctan x + arctan (1/3) = π/4
1/4
1/5
1/2
1/3
Assuming that the soap bubble retains its spherical shape as it expands, how fast is its radius increasing when its radius is 2 in, if air is blown into it at the rate of 4 in^3/sec?
1/π in/sec
3/2π in/sec
1/4π in/sec
2/3π in/sec
Approximately how many liters of water will a 10- gallon container hold?
42
32
9
38
If csc2θ = x2 + 1, what is cot2θ?
x
1 + x
x^2
1 - x^2
How many ancestors does a set of triplets have in the eleven generations before them? Assume there are no duplicates.
4085
4005
4009
4095
A point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing is known as
inflection point
maximum point
minimal point
point of tangency
A cone shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a rate of 0.2 cm/hr, while the length is increasing at a rate of 0.8 cm/hr. If the icicle is currently 4 cm in radius and 20 cm long, is the volume of the icicle increasing or decreasing, and at what rate?
decreasing at 20 cu. сm/hr
increasing at 24 cu. сm/hr
decreasing at 24 cu. сm/hr
increasing at 20 cu. сm/hr
Find the equation of the normal to x2 + y2 = 1 at the point (2, 1)
x – y =0
x = 2y
y = 2x
x + y = 1
Marvin helps his teachers plan a field trip. There are 125 persons to the field trip and each school bus holds 48 persons. What is the minimum number of school buses is needed to reserve for the trip?
5
4
3
2
The drivers at F and M trucking must report the mileage on their vehicle each week. The mileage reading of Ed's vehicle was 20,907 at the beginning of one week, 21,053 at the end of the same week. What is the total number of miles driven by Ed that week?
145 miles
1046 miles
146 miles
46 miles
Find the area bounded by x2 - 2x + 2y + 5 = 0 and x2 - 2x + y + 1 = 0.
14
16 / 3
16
14 / 3
________________ represents the distance of a point from the y-axis.
abscissa
coordinate
polar distance
ordinate
Give one indicated root of (-16i)1/2
2 cis 330°
2 cis 165°
2 cis 167°
2 cis 67.5°
From a ship sailing due east a light house was seen to bear N 45° E. After sailing 5 km, the lighthouse as a bearing of N 69° W. How far was the lighthouse from both points of observation?
3.87 km
3.00 km
0.87 km
3.33 km
Each of the question on a quiz is a five-part multiple choice question with exactly one correct answer. A student, totally unprepared for the quiz, guesses on each of 15 questions. If at least 11 questions must be answered correctly to pass the quiz, what is the chance the student passes?
0.10
0.20
0.50
0
Find the volume generated when the area bounded by the curve y = cosh x and the x-axis from x = 0 to x = 1 is revolved about the x-axis.
2.42
1.42
4.42
3.42
Bobby is 2 years as twice as old as Ellen. The sum of twice Bobby’s age and three times Ellen’s age is 56. How old is Ellen?
10
18
20
12
Water is running out of a conical funnel at a rate of 1 cu. in / sec If the radius of the base of the funnel is 4 in and the altitude is 8 in. find the rate at which the water level is dropping when it is 2 in from the top.
-1/9π in/sec
-1/2π in/sec
-1/π in/sec
-2/π in/sec
What curve is described by the equation 4x2 - y2 +8x + 4y = 15?
Ellipse
Parabola
Hyperbola
Circle
Carbon is a radioactive form of carbon that is found in all living plants and animals. After a plant and animal dies, the carbon 14 disintegrates Scientists determine the age of the remains by comparing its carbon 14 with the amount found in living plants and animals and follows exponential growth pattern. Charcoal from an ancient fire pit Java had 1/4 the amount of carbon 14 found in a living sample of wood with the same size Estimate the age of the charcoal.
11,350 years
11,500 years
11,280 years
11,200 years
A tangent to the conic is a line which ________________________.
passes inside a conic
touches the conic at only one point
is parallel to the normal
touches the normal
According to Newton's Law of Cooling the rate at which a substance cools in air are directly proportional to the difference between the temperature of the substance and that of air. If the temperature of the air is 30° and the substance cools from 100° to 70° in 15 minutes, how long will it take to cool 100° to 50°?
45.30 min
33.59 min
35.39 min
43.50 min
Find the maximum area of a rectangle which can be inscribed in an ellipse having the equation x2 + 4y2 = 4.
4
3
2
5
A square has a side 5 cm shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square
15 , 6
15 , 5
10 , 5
10 , 6
Find the approximate increase in the volume of the sphere of the radius increases from 2 to 2.05 in one second
5.51
2.12
5.55
2.51
A car consumes 16 gallons of gasoline to travel 448 miles. How many miles/gallons is the cars consumption?
26
24
22
28
A pebble dropped into a lake creates an expanding circular ripple. If the radius of the ripple is increasing at the rate of 2 in/sec, at what rate is its area increasing when its radius is 10 in.?
12.56 sq. in/sec
125.66 sq. in/sec
62.33 sq. in/sec
253.54 sq. in/sec
If sinθ = a and cos2θ = b then what is the value of sin2θ- 2cosθ?
I. a2 + 2 square root of b
II. a2 - 2 square root of b
III. b2 + 2 square root of a
IV. b2 - 2 square root of a
I and II only
III only
III and IV only
I only
Find the domain of the following function: f(x) = 3x, -6 ≤ 𝑥 ≤ 8.
(-6, 8)
[-18, 24]
(-18, 24)
[-6, 8]
Three circles of radii 3, 4, and 5 inches, respectively are tangent to each other externally. Find the largest angle of a triangle formed by joining the centers.
75.1°
72.6°
73.3°
73.4°
If the general equation of the conic is
Ax2 + Bxy + Cy2 + DX + Ey + F = 0. If B2- 4AC > 0,
the equation describes a __________
ellipse
hyperbola
parabola
circle
Determine the equation that expresses that G is proportional to k and inversely proportional to C and z. Symbols a, b and care constants.
G = ck / GG
G = a / bc
G = ck / zc
G = bC / zk
Bob notices that the ratio of boys to the total students in his class is 3:4. If there are 28 students in his class, how many of them are boys?
24
21
7
14
Evaluate ∫ (sin 5x + cos3x) dx from x = 0 to x = π/2
0.0347
0.0213
0.0123
0.0417
Solve for x in the equation:
arctan 2x + arctan x = 7/4.
0.182
0.218
0.821
0.281
Find the vertex of the parabola x2 = 8y
(2, 4)
(0,0)
(-2, 0)
(0,8)
Find the equation of the line which is perpendicular to the line 3x – 2y - 5 = 0 and which passes through the point of intersection of 4x - y - 5 = 0 and x - y - 5 = 0.
2x - 3y + 2 = 0
2x – 3y - 15 = 0
2x + 3y + 15 = 0
2x + 3y - 2 = 0
Which of the following linear equations has a negative slope?
y = 4x - 5
-5x + y = 1
6y + x =7
6 = y – x
Mrs. Farrell's class has 26 students. Only 21 were present on Monday. How many were absent?
5
15
16
4
A chicken farmer has 750 eggs. 4% of the eggs are cracked, 5% of the remainder are found to be defective. How many eggs could be sold if only eggs without cracks and defects are sold?
483
508
458
684
In the polar coordinate system, the distance from a point to the pole is _____________.
polar angle
radius vector
y-coordinate
x-coordinate
x2 - y2 = 16 is the equation of a:
ellipse
hyperbola
circle
parabola
Find the volume (in cubic units) generated by x2 + y2 + 6x + 4y + 12 = 0, about the y-axis.
47.23
59.22
62.11
39.48
Solve the equation cos2A = 1 – cos2A
45 , 315
45 , 225
45 , 225
45 , 225
What is the general solution of
(D4 – 1) y(t) = 0 ?
y = C1et+C2e-t+C3cost+C4sint
y = C1et+C2e-t+C3tet+C4te-t
y = C1et+C2e-t
y = C1tet+C2te-t
What percentage of the volume of a cone is the maximum right circular cylinder that can be inscribed in it?
24 percent
34 percent
44 percent
54 percent
If e2x – 3ex + 2 = 0, find x.
ln 2
ln 4
ln 3
no solution
On a certain day, the nurses at a hospital worked the following number of hours: Nurse Howard worked 8 hours; Nurse Pease worked 10 hours; Nurse Campbell worked 9 hours; Nurse Grace worked 8 hours; Nurse McCarthy worked 7 hours; and Nurse Murphy worked 12 hours. What is the average number of hours worked per nurse on this day?
7
8
9
10
If Joy is 10% taller than Joseph, and Joseph is 10% taller than Tom. How many percent is Joy taller than tom?
18 percent
20 percent
21 percent
23 percent
An Army food supply truck can carry 3 tons. A breakfast ration weighs 12 ounces, and the other two daily meals weigh 18 ounces each. Assuming each soldier gets 3 meals per day, on a ten-day trip, how many soldiers can be supplied by one truck?
100 soldiers
150 soldiers
200 soldiers
320 soldiers
Find the area enclosed in the second and third quadrants by the curve x = t2 – 1, y = 5t3 (t2 – 1).
8 / 5
8 / 7
8 / 3
18 / 5
From past experience, it is known 90% of one-year old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Find the probability that 3 children did not recognize their mother's voice.
0.677
0.323
0.729
0.271
Find the area bounded by the parabola sqrt. of x + sqrt. of y = sqrt. of a, and the line x + y =a.
a2
a2/2
a2/4
a2/3
What is the integral of cos x esinx dx?
e^cosx + C
e^sinx + C
e^-cosx + C
e^-sinx + C
The geometric mean and arithmetic mean of numbers are 8 and 10 respectively. What is the harmonic mean?
7.5
5.7
6.4
4.6
In how many ways can four coins be tossed once?
4
16
32
8
A statue 3 m high is standing on a base 4 m high. If an observer’s eye is 1.5 m above the ground, how far should he stand from the base in order that the angle subtended by the statue is a maximum?
3.41 m
3.51 m
3.71 m
4.41 m
Find the equation of the normal line to x + y at point (2, 1).
4x – 3y = 0
x – 2y = 0
x + y = 0
x – y = 0
Find the area of a triangle having vertices
-4 - i, 1 + 2i, 4 – 3i.
7
17
10
107
Ramil, bought 400 hotdogs for the school picnic. If they were contained in packages of 8 hotdogs, how many total packages did he buy?
50
5
20
10
