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WorksheetsmEEth 2019
Total questions: 94
Worksheet time: 47mins
Find the parametric equations for the line through the point (1,7,2) that is parallel to the plane X+Y+Z = 10 and perpendicular to the line x = 3 + t, y = -18 - t, Z = 5t.
x = 6t - 1
y = 4t -7
z = -2t - 2
x = 4t + 1
y = -6t + 7
z = -2t + 2
x = 6t + 1
y = -4t + 7
z = -2t + 2
x = 4t + 1
y = -6t
z = 2t + 2
It represents the distance of a point from the y-axis.
Ordinate
abscissa
Coordinate
polar distance
The locus of a point which moves so that its distance from a fixed point and a fixed line is always equal
ellipse
parabola
circle
hyperbola
Determine the equation that expresses the statement. F is directly proportional to y Symbols a, b, c and d are constants
F = a
F = a • y
F = b
F = cy^3 + a
If a quiz consists of four true-false questions, and a student guesses at each answer, what is the probability the student answer exactly half of the questions correctly?
0.5000
0.2500
0.1536
0.7521
Evaluate lim n->∞
| (n2+3i) (n – i) | / | ln^3 – 3n + 4 - i |
1
0
i / 2
- i / 2
Find the equation of the circle with center at the origin and passes through (-3,4).
x2 + y2 = 36
X2 + y2 = 25
x2 + y2 = 9
x2 + y2 = 16
Find the area bounded by r = 2 / (1 + cosθ) and cosθ = 0.
1/3
2/3
5/3
8/3
If sin θ = a and cos2 = b then what is the value of sin2 θ - 2 cos θ?
I. a + 2 square root of b
II. a - 2 square root of b
III. b + 2 square root of a
IV. b? - 2 square root of a
I only
I and II only
III and IV only
III only
Find an equation of the parabola with vertex t (-1, -2) latus rectum 12, opens downward
x2 + 12x + 12y - 25 = 0
x2 + 12x2y + 22 = 0
x2 - 2x + y – 23 = 0
x2 + 2x + 12y + 25 = 0
A man is driving a car at the rate of 30kn/hour towards the foot of monument 6m high. A what rate is he approaching the top when he is 36m from the foot of the monument?
-52.80 km/hr
10.55 km/hr
-29.59 km/hr
12.52 km/hr
A cross-section of a trough is a semi-ellipse with width at the top 18 in. and depth 12 in. The trough is filled with water to a depth of 8 in. Find the width of the surface of the water.
6 square root of 5 in
square root of 5 in
6 in
5 square root of 6 in
A secondary school is contracting its alumni asking for dominations to help put up new computer laboratory. Past records show that 80% of the alumni will make a contribution of of at least 50.00. A random sample of 20 alumni is selected. What is the probability that exactly 15 alumni will make a donation of at least P50.00?
0.576
0.167
0.174
0.204
Determine the differential equation of the family of lines passing through (h,k).
(y-h) + (y-k) = dy/dx
(x-h)dx - (y-k)dy = 0
(x+h)dx - (y-k)dy = 0
(y-k)dx - (x-h)dy = 0
Find two complex numbers whose sum is 4 and whose product is 8.
1 ± 2i
2 ± i
1 ± i
2 ± 2i
If 3x2 is multiplied by the quantity 2x^3y raised to the 4th power, what would this expression simplify to? A. 6x^9y to the 4th power
6x^9y to the 4th power
48x^14y to the 4th power
6x^14y to the 4th power
1296x^16y to the 4th power
A point is chosen at random inside a circle having a diameter of 8 inches. What is the probability that the point is at least 1.5 In away from the center of the circle?
55 / 64
5/8
5/ 64
12/45
In an ellipse a chord which contains a focus and is in a line perpendicular to the major axis is a:
conjugate axis
latus rectum
focal width
minor axis
Find the position value of c such that the area of the region bounded by the parabola y = x2 – c2 and y = c2 -x2 is 576
13
5
8
6
Obtain Lo-1 {(1/(s^2+1)^2 }
½(sint -t cost)
-½(sint -t cost)
½(sint + t cost)
–½(sint - t cost)
If Jim and Jerry work together they can finish a job in 4 hours. It Working alone takes Jim 10 hours to finish the job, how many hours would it take Jerry to do the job alone?
16
6.0
6.7
5.6
A line through (0,0) intersects y=x2 at a point(a,a2). The area of the upper region bounded above by the line and below by the curve is 27. Find a.
2 cube root of 6
cube root of 6
3 cube root of 6
cube root of 3
Simplify i^(39)
- i
1
- 1
i
If a rock is dropped, its distance below the starting point at the end of t sec is given by s=16 t square, where s is in ft. Find the rate of change of distance after 1.5 minutes.
288 Ft/sec
281 ft/sec
2,880 ft/sec
800 ft/sec
Find the equation of a line with 3 slope and y-intercept -2
y = 2x + 3
y = 2x - 3
y = -3x + 2
y = 3x - 2
Three randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the three students ‘drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN NNP, NNN.
Assuming each possible combination is equally likely. What is the probability that all three students get positive results?
1 / 2
1 / 3
3 / 4
1 / 8
Find the area of the first octant part of the plane x/a + y/b + z/c = 1, where a, b and c are positive. A. ½ Square root of (a2b2+b2c2+a2c2)
½ Square root of (a2b2+b2c2+a2c2)
a + b + c
Square root of (a + b + c)
Square root of (a2 + b2 + c2)
Find the volume generated by revolving the area bounded by y2 = 12x and x = 3 about the line x = 3.
131
191
181
151
Joey will be x years old y years from now. How old is she now?
y - x
x
x - y
y
A rectangle with sides parallel to the coordinate axes has one vertex at the origin, one on the positive x-axis and its fourth vertex in the first quadrant on the line with equation 2x + y = 100. What is the maximum possible area of rectangle?
3520
1250
1908
2250
Find the equation of the line passing 3 units from the origin and parallel to 3x + 4y - 10 = 0.
3x + 4y - 5 = 0
4x + 3y + 1 = 0
x - 3y + 15 = 0
3x + 4y - 15 = 0
Find the volume generated by revolving the area bounded by
y2 = 12x and x = 3 about the line x = 3.
191
181
151
131
Patrick has a rectangular patio whose length is 5m less than the diagonal and a width that is 7m less than the diagonal. If the area of his patio is 195 m2, what is the length of the diagonal?
20 m
10 m
16 m
8 m
Find | u x v | correct to three decimal places where |u| = 9, |v| = 3. Lθ = 85 deg.
2.989
31.897
2.353
26.897
If 1 is added to the difference when 10x is subtracted from-18x, the result is 57. What is the value of x?
7
2
- 2
- 7
Joseph gave ¼ of his candies to Joy and Joy gave 1/5 of what she got to Tim. It Tim received 2 candies, how many candies did Joseph have originally?
20
30
40
50
From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their mother's voice. Find the mean or X.
20
2
4
1
Find all values of z for which e^3z = 1
kπi
2kπ/3
1/3 kπi
1/8 ni + ½ kπi
In the vicinity of a bonfire, the temperature T in deg C at a distance of x meters from the center of the fire was given by:
T = 762,500
. ----------
. x2 + 300
At what range of distances from the fire's center was the temperature less than 500 deg C?
More than 45 meters
More than 30 meters
More than 35 meter
More than 20 meters
During his major league career, Hank Aaron hit 38 more home runs than Babe Ruth hit during his career. Together they hit 1,524 home runs. How many home runs did Babe Ruth hit?
781 home runs
800 home runs
743 home runs
762 home runs
if SinA = 4/5 and SinB = 7/25, what is sin (A + B) If A is in the 3rd quadrant and is in the 2nd quadrant.
- 3/5
3/5
2/5
4/5
Three randomly chosen senior high school students were administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the the three students.
Drug test evaluation as PPP, PPN, PNP, NPP, PAN, NPN, NNP, NNN.
Assuming each possible combination is equally likely, what is the probability at least one student gets negative result?
4 / 8
2 / 7
7 / 8
3 / 7
A bag contains 3 red, 6 blue, 5 purple and 2 orange marbles. One marble is selected at random. What is the probability that the marble in blue?
3 / 8
3 / 16
3 / 5
4 / 13
z varies directly as x and inversely as y2. If x =1 and y = 2. Find z When x=3 and y = 4.
1.5
3.5
2.5
3
Which of these is equal to 6 (x-3)?
x^6 – 3^6
6x + 3
6x - 18
6x - 3
If z = 6 e^πi/3 evaluate e^iz.
e^3i sq root of 3
e^-3i sq root of 3
e^ sq root of 3
e^- sq root of 3
After paying a commission of 7% of the sale price to his broker, Tess receives P103,000 for his car. How much was the car sold?
P110,753
P110,000
P110,420
P95,790
What is the maximum rectangular area that can be fenced in 20ft using two perpendicular corner sides of an existing wall
310 ft2
250 ft2
100 ft2
120 ft2
Find the area enclosed by the lemniscate of Bernoulli r2 = a2 cos2θ.
a2 / 2
a2 / 4
a2
a2 / 3
A hand soap manufacturer introduced a new liquid lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help Judge the success of the new product. The survey showed 40% of the consumers had seen an advertisement for the new soap, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. If a randomly selected consumer has seen an advertisement for the new soap, what is the probability that this consumer has tried the new soap?
72%
25%
40%
37.5%
Which of the following is equal to n-4 . n4?
1
n
- 16 n
0
Evaluate ∫ √ (1 - cosx) dx.
2 √2 cos x + C
-2 √2 cos x/2 + C
-2 √2 COS X + C
2 √2 cos x/2 + C
It the graph of y = f(x) is transformed into the graph of 2y - 6 = -4 f(x-3), point (a, b) on the graph of y = f(X) becomes point (A, B) where A and B are expressed as:
A = a + 4
B = 2b + 3
A = a + 6
B = 2b + 6
A = a + 3
B = - 2b + 3
A = a + 2
B = 2b - 3
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 all 20 children recognize their mother's voice
0.222
0.500
1.000
0.122
Find the radius of curvature of the parabola y2 – 4x =0 at the point (4,4).
22.36
20.36
25.36
27.36
Find the differential equation of the family of lines passing through the origin.
xdx + ydy = 0
xdy – ydx = 0
ydx + xdy = 0
ydx – xdy = 0
Find all real solutions to the logarithmic equation ln (x2 - 1) - ln (x - 1) = ln (4).
0
3
5
1 / 2
Gabby cuts a piece of rope into three pieces. One piece in 5 inches long. one piece is 4 inches long, and one piece is 3 inches long. The longest piece of rope is approximately what percent of the original length before the rope was cut?
55 %
42 %
33 %
50 %
What is the result when 6ab + 3b is subtracted from -6ab-3b?
12ab + 6b
- 12ab - 6b
18ab
0
Find the area bounded by y = x^3, the x-axis and the lines X = -2 and x =1.
0.43
2.45
1.25
4.25
The table shows the number CD players sold in a small electronics store in the years 1989-1999 as follows:
What was the average rate of change of sales between 1989 and 1997
15 CD players/year
150 CD players/year
70 CD players/year
695 CD players/year
A man is driving a car at the rate of 30 km/hr towards the foot of monument 6m high. At what rate is he approaching the top when he is 36m from the foot of the monument?
12.52 km/h
-52.80 km/hr
10.55 km/hr
-29.59 km/h
Find the vertex of the parabola x2 = 8y.
(2,4)
(0,5)
(0,0)
(-2,0)
A and B working together can do a Job in 5 days. B and C together can do the same in 4 days A and C in 2.5 days. In how many days can all of them finish the job working together?
1.07
2.80
2.03
3.10
Which of the following is a disadvantage of using the sample range to measures of spread or dispersion?
It produces very small spreads.
The largest of the smallest observation (or both) may be a mistake or an outlier.
The sample range is not measured in the same units as the data.
It produces spreads that are too large.
Obtain L {t^n}
n! / s^n – 1
n! /s^n
(n+1)! /s^(n+1)
n! / s^(n+1)
Jenny flipped a coin three times and got heads each time. What is the probability that she gets heads on the fourth flip?
1
0
1/16
1/2
Oscar sold 2 glasses of milk for every 5 sodas he sold. If he sold 10 glasses of milk, how many sodas did he sel112
45
20
25
10
How many positive real roots are there in the polynomial x^4 - 4x^3 + 7x2 - 6x - 18 = 0.
1 or 2
3 or 1
3 or 0
1 or 0
The square of a number added to 25 equals 10 times the number. What is the number?
- 5
- 10
5
10
Evaluate lim (1 + 2x) ^ (1 + 2x)/x
1
e
0
e2
A man on a wharf 3.60 m above sea level is pulling a rope tied to a raft at the rate of 0.60 m/sec. How fast is the raft approaching the wharf when there are 6m of rope out?
-0.22 m/sec
-1.75 m/sec
-0.12 m/sec
-0.75 m/sec
From a stationary point directly in front of the center of the bull’s-eye, Kim aims two Arrows at the bull's eye. The first arrow nicks one point on the edge of the bull’s-eye the second strikes the center of the bull's eye. Kim knows the second arrow traveled 20 meters since she knows how far she is from the target. If the bu11's-eye is 4 meters wide, how far did the first arrow travel? Assume the arrows traveled in straight-line paths and the bull’s-eye is circular.
19.9 m
24.0 m
20.1 m
22.5 m
A voltage v = 150 + j180 is applied across an Impedance and the current flowing is found to be I = 5 -j4. Determine the resistance.
0.75 ohms
0.77 ohms
0.78 ohms
0.76 ohms
Determine the equation that express G is proportional to k and inversely proportional to C and z. Symbols a, b and c are constants.
G = ck/zC
G = a/bc
G = bc/zk
G = ck/GG
Determine the equation of the line passing through the points (1, 17) and (13,4).
13x - 12y - 217 = 0
13x - 12y + 217 = 0
13x + 12y - 217 = 0
13x + 12y + 217 = 0
Describe the locus represented by |z – i| = 2
hyperbola
circle
parabola
ellipse
Two hundred single-sport athletes were crossclassified according to gender as follows:
. Swimmer Runner Cyclist
Male 25 60 25
Female 20 50 20
What is the probability that the athlete is male or a swimmer or both?
0.550
0.450
0.230
0.005
Solve the equation (x2y - 2) + (x + 2xy – 5) i = 0.
x = 1, y = 2
x = 3, y = 4
x = ½, y = 3
x = 4, y = -½
Find two numbers whose sum is 50 and with the largest possible product.
25 , 25
23 , 25
22 , 23
20 , 30
If dy = x2dx; what is the equation of y in terms of x if the curve passes though (1, 1)?
x^ (3) + 3y2 + 2 = 0
x^ (3) - 3y + 2 = 0
x - 3y + 3 = 0
2y + x3 + 2 = 0
A car rental company offers two plans for renting a car:
Plan A: $30 / day and $ 0.20/ mile
Plan B: $ 55 / day with free unlimited mileage
For what range of miles will plan B save a customer’s money?
More than 125 miles
Less than 250 miles
More than 170 miles
Less than 170 miles
Find the value of x for which f(x) = x2 + 5x +2 is minimum
5 / 2
2
- 2
- 5 / 2
In order to pas certain exam candidates must answer correctly 70% of the test questions, if there are 70 questions on the exam, how many questions must be answered correctly in order to pass?
52
60
56
49
A group consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses then 51% of the group members will be nurses. Find the value of n.
100
110
80
55
While bowling in a tournament, Jake and his friends had the following scores:
Jake 189
Charles and Max each scored 120
Terry 95
What was the total score for Jake and his friends at the tournament?
524
526
404
504
Find the height of a tree if the angle of elevation of its top changes from 20° to 40° as the observer advances 23 meters toward the base.
16.79 m
14.79 m
13.78 m
15.78 m
A normal to a given plane is ______________.
oblique to the plane
parallel to the plane
perpendicular to the plane
lying in the plane
Find the equation of the normal to x2 + y2 = 1 at the point (2,1)
x + y = 1
x = 2y
y = 2x
x - y = 0
Evaluate ∫ x dx square root (x2 - 8x).
Square root of (x2 - 4x + 4) ln (x - 4 + sq root (x2 + 8x) + C
Square root of (x2 - 4x + 2) ln (x - 4 + sq root (x2 – 8x) + C
Square root of (x2 - 8x + 4) ln (X – 4 + sq root (x2 – 8x) + C
Square root of (x2 - 2x - 4) ln (X – 4 + sq root (x2 – 2x) + C
The plane rectangular coordinate system is divided into four parts which are known as _________.
octants
quadrants
coordinates
axis
What curve is described by the equation 4x2 - y2 + 8x + 4y = 15?
hyperbola
circle
parabola
ellipse
From a recent study. 90% of one-year-old children can distinguish their mother's voice from that of a similar sounding female. A random sample of 20 oneyear-olds are given this voice recognition test. Find the probability that all the 20 one-year-olds recognize their mother’s voice
0.122
0.001
0.522
1.000
What is the length of the latus rectum of the parabola y = 4px2?
p
- 4p
2p
4p
