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WorksheetsMEETH 2021 Sept
Total questions: 89
Worksheet time: 45mins
At the city park, 32% of the trees are oaks, if there are 400 trees in the park, how many trees are NOT oak .
278
312
272
128
It is estimated that the annual cost of driving a certain new car is given by the formula: C = 0.25 m + 1,600 where m represents the number of miles driven per year and C is the cost in dollars. Jane purchases such a car and determines between $5,350 and $5,600 for next year's driving cost. What is the corresponding range of miles that she can drive her new car?
Between 13,000 mi and 18,000 mi
More than 16,000 mi
Between 15,000 mi and 16,000
Between 13,000 mi and 16,000
At exactly what time after 5 o'clock will the hour hand and the minute hand be perpendicular for the first time?
5:15 and 25 seconds
5:10 and 54 seconds
5:20 and 14 seconds
5:05 and 34 seconds
Find the equation of the line passing through the intersection of x - y = 0 and 3x - 2y = 2 cutting from the first quadrant a triangle whose area is 9.
x + y + 1 = 0
2x + y - 2 = 0
3x + y – 3 = 0
x + 2y - 6 = 0
A ball bounces 2/3 of the altitude from which it falls. is dropped from a height of 18 ft., how far will it travel before coming to rest?
99 ft
90 ft
19 ft
9 ft
Determine the correct equation for the line with a slope of 7 and y-intercept of -4.
y = -1/7x – 4
y = 7x – 4
y = 7x + 4
y = -7x + 4
Evaluate
-12 + 6i
- 1/4
-(4/3) - 4i
Sqr. root of 2 (1+i)/2
Find the area of the region enclosed by the triangle with vertices (1, 1), (3, 2) and (2, -4).
3/2
1/2
7/2
5/2
If a person throws away 3.5 lbs of trash daily, how much trash will the person throw away in one week?
31.5 lbs
40.2 lbs
24.5 lbs
24.0 lbs
The current I following in an RL circuit is given by I = (E/R) (1 - eRt/L), where E is the voltage applied to the circuit, R is the resistance and L is the inductance. Express I in terms of E and R when t = L/R.
0.632 (E/R)
0.435 (E/R)
0.548 (E/R)
0.388 (E/R)
The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. Find the width of the rectangle.
15 inches
14.5 inches
37.5 inches
13.5 inches
The area of a square whose sides measures 4 units is added to the difference of 11 and 9 divided by 2. What is the total value?
5
9
16
17
A normal to a given plane is
perpendicular to the plane
parallel to the plane
lying in the plane
oblique to the plane
Solve the equation 5z” + 2z + 10 = 0
1 - i , 1 - 2i
1 + i , 1 - 2i
1 + i , 1 - 2i
( -1 7i ) / 5
The equation x” + Bx + y” + Cy + D = 0 is:
hyperbola
ellipse
circle
parabola
The sum of the distances from the two foci to any point in what curve is constant?
hyperbola
parabola
any conic
ellipse
When the energy/hour required in driving a boat varies as the cube of the velocity, find the most economical rate/hour when going against the rest current of 4kph.
5 kph
12 kph
8 kph
6 kph
The towns are located near the straight shore of the lake. Their nearest distances to the point in the shore are 1km and 2 km respectively, and these points on the shore are 6 km apart. Where should the finished fish port be located to maximize the total amount of paving necessary to build a straight road from each town to the pier?
12 km from the point on the shore nearest the first town
12 km from the point on the shore nearest the other town
2 km from the point on the shore nearest the first town
2 km from the point on the shore nearest the other town
If the coefficient ao of a Fourier series of a periodic function is zero, it means that the function has
Odd-quarter wave symmetry
Even-quarter wave symmetry
Odd symmetry
Odd symmetry or even-quarter wave symmetry or oddquarter wave symmetry
Find the vertex of the parabola x” = 4y.
(4,0)
(0,0)
(0,4)
(-4,0)
A movie is scheduled for 2 hours. The theater advertisements are 3.8 long. There are two previous ones: 4.6 min and 2.9 min long. The rest of the time is devoted to the feature. How long is the feature film?
94.3 min
97.5 min
108.7 min
118.9 min
What is the smallest positive value for x where y = sin 2x reaches i maximum?
pi / 4
pi
3(pi)/2
2pi
Find solution to the system of equations x - 2y = 5 and 2x + 5y = 1.
(3, -1)
(-1, -3)
(3, 1)
(1, 3)
Solve the differential equation y" - 4 y' + 3y - sin x.
y(x) = C1 e^3x + C2 e^x + 1/5 cos x + 1/10 sin x
y(x) = Cl e^3x + C2 e^x sin x
y(x) = C1 sin 3x + C2 x + cos 3x
y(x) = C1 sin x + C2 x + 1/10 sin x
Mon and Mila can restock an aisle at the supermarket in 1 hour working together. Working alone, Mon can restock an aisle in 1.5 hours and Mila in 2 hours. If they work together in 2 hours, how many aisles will they have completed?
5.11
4.33
4.50
3.50
Find the equation of the normal line to x” + y” = 1 at the point (2, 1).
y = 2x
x - y = 0
x = 2y
x + y = 1
A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least P50. A random sample of 20 alumni is selected. What is the probability that less than 17 alumni will make a contribution of at least P50?
0.589
0.301
0.200
0.421
What is 20 % of 96?
19.20
0.09
0.92
1.92
What conic section is described by the equation 4x” – “y” + 8x + 4y - 15?
ellipse
hyperbola
parabola
circle
Given: sin A = -4/5, A in Quadrant III cot B = 4.5, B in Quadrant III Evaluate sin (A + B).
5 / 19 square root of 17
19 / 5 square root of 17
square root of 17
-1/ square root of 17
Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486.
540
748
984
844
Find the centroid of a semi-circular region of radius a.
a / 2pi
4a / 3pi
3a / 4pi
a / pi
From the top of a building 100 m high, the angles of depression of two cars due east of the observer are 32 degrees 25' and 58 degrees 33' respectively. Find the distance between the cars.
106.00 m
96.30 m
9.63 m
63.91 m
A line segment is a side of a square and also the hypotenuse of an isosceles right triangle. What is the ratio of the area of the square to the area of the triangle?
2 : 1
4 : 1
1 : 1
3 : 2
Sam scored 96% on his first Calculus quiz, 74% on his second and 85% on his third. What is his quiz average?
85%
75%
96%
95%
The time a student spends learning computer software package is normally distributed with a mean of 8 hours and standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends less than 6 hours earing a software package?
1
0.15
0.21
0.09
A man is running around circular track 200 m circumference. An observer uses a stopwatch to time each lap, obtaining the data as follows: What is the man’s average speed between 68 and 168 sec?
3 m/sec
8 m/sec
1.82 m/sec
4 m/sec
Jonas is 5 ft 11 in tall and Pedro is 6 ft 5 in tall. How much taller is Pedro than Jonas?
1 ft
6 in
7 in
1 ft 7 in
Sand is being poured into a conical pile in such a way that height is always 1/3 of the radius. At what rate sand is being added to the pile when it is 4 ft high if the height is increasing at 2 in/min.
30,288.13 in/min
53,288.13 in/min
100,132.88 in/min
130,288.13 in/min
Jun rows his banca across a river at 4 km/hr. How long will it take Jun to cross the river?
34.25 min
0.25 min
43.22 min
3.75 min
What percentage of 18,000 is 234?
1.3 %
1,300 %
130 %
13 %
Michael walks to school. He leaves each morning, at 7:32 A.M. and arrives at school 15 minutes later. If he travels at a steady rate of 4.5 miles/hr, what is the distance between his home and school?
1.8 miles
1.5 miles
1.9 miles
1.1 miles
For the 2 functions, f(x) and g(x), tables of values are shown below. What is the value of g[f(2)]?
- 1
- 5
- 3
2
Daniel has one more Algebra exam to take before computing the average of his grades. His Algebra scores so far are 93, 54, 94, 36, 97. What must be his score on this last exam so he can maintain his present average? typo : 54 = 94 , 36 = 96
94
95
92
97
Evaluate
infinity
e'' / pi
e^(2pi)
e
Evaluate sin [Arccos (-2/3)].
Square root of 3
Square root of 5
(1/3) Square root of 5
(1/5) Square root of 3
Find the area of the square whose side is a^2 b^3.
a^2 b^3
a^2 b^6
a^4 b^3
a^4 b^6
If 1 cm = 0.39 in, about how many cm are there in 0.75 in?
0.52
1.75
0.29
1.92
The value of a computer is depreciated over 5 years for tax purposes. That is, at end of 5 years, the computer is worth 0. If a business paid $21,000 for a computer, how much will it have depreciated after 2 years?
$ 4,200
$ 8,400
$ 10,500
$ 8,200
Solve [y - square root of (x” + y”)] dx + x dy = 0.
typo : - xdy = 0
Square root of (x” + y” + y) = C
Square root of (x” + y”) + y = C
Square root of (x” – y”) + y = C
Square root of (x + y) + y = C
Four is added to the quantity two minus the sum of negative seven and six. This answer is then multiplied by three. What is the result?
57
21
15
- 21
From a sample size of 100, the following descriptive measures were calculated: median = 23; mean = 20; standard deviation = 5; range = 35. Seventy-five sample values are between 5 and 35. If you knew the sample mean, median, and standard deviation were correct, which of the following conclusions might you draw?
The number of sample values between 10 and 30 was miscounted
The range must have been calculated incorrectly because it should not be seven times the standard deviation's value.
The number of sample values between 5 and 35 have been miscounted because all 100 values must be in this interval.
The distribution is skewed to the right because the median exceeds the mean.
What is the maximum rectangular area that can be fenced in 20 ft. using two perpendicular corner sides of an existing wall?
310 square ft
120 square ft
100 square ft
250 square ft
Which of the following is not a multiple of 11?
Typo : 121 = 122
221
122
759
1111
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. How many questions should the student expect to answer correctly?
2
13
5
3
If log2=a, log3=b, log5=c, then log (7.5) = _______.
c/(a+b)
ab/c
c/ab
b + c - a
A high school band teacher has a record of each student's attendance. The result is listed below in days each student has been absent?
3, 4 , 7, 2, 2, 1, 0, 0, 1, 0, 3, 3, 2, 1, 6, 0, 1,
0, 1, 1 , 1, 5, 3, 1, 1, 0, 0, 2, 1, 2, 1, 0, 0, 4,
What proportion of students have been absent less than 5 days?
0.06
0.60
0.90
0.09
Manuelita had 35 stuffed animals. Her grandmother gave fifteen of them to her. What percentage of the stuffed animals did her grandmother give her?
typo : 35 = 75
15 %
20 %
10 %
25 %
What is the conic section where eccentricity is less than 1?
circle
ellipse
parabola
line
Which of the following equations is an EXACT differential equation?
x dx + (3x - 2y) dy = 0
(2xy + x) dx + (x” + y) dy = 0
y” dx + (2x - 3y) dy = 0
(x” + 1) dx - xy dy = 0
Evaluate
0
1
none
infinity
When a metallic ball bearing is placed inside a cylindrical container of radius 2 cm, the height of the water inside the container increases by 0.6 cm. What is the radius of the ball bearing?
2.2 cm
0.6 cm
1.8 cm
1.2 cm
If y = 2x + sin 2x, find x when y' = 0.
3pi /2
2pi / 3
pi / 2
pi / 3
Larry finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower?
73.61 m
53.61 m
83.61 m
63.61 m
After the price of gasoline went up by 10%, a consumer reduced his consumption by the same percent. By what percent would his gasoline bill be changed?
1 %
10 %
11 %
0.1 %
What is the ratio of the sides of a triangle if the product of the sines of its angles is a maximum?
1 : 2 : 2
1 : 1 : 2
1 : 1 : 1
1 : 3 : 3
Find the maximum value of 3^sin 3x.
1 / 3
infinity
1
3
The square of a number added to 25 equals 10 times the number. What is the number?
- 5
5
- 10
10
Compute log (3 - 2i).
0.5570 - 0.2554i
1.6575 + 0.8544i
0.2575 - 0.3545i
0.7580 + 0.7580i
The product of the sines of the angles of a triangle is a maximum. What is the ratio of its sides?
1 : 2 : 2
1 : 1 : 1
1 : 2 : 1
1 : 1 : 3
The dimensions of a rectangular prism can be expressed as x + 1, x – 2, and x + 4. In terms of x, what is the volume of the prism?
x^3 + 5x - 2x + 8
x^3 + 3x - 6x – 8
x^3 + 3x + 6x - 8
x^3 - 5x + 2x + 8
A shirt that regularly costs $ 340 is marked down 15%. What is the sale price of the shirt?
$ 289.00
$ 338.50
$ 295.00
$ 190.00
The temperature at 6 PM was 31½F. By midnight it had dropped 40½F. What was the temperature at midnight?
- 9½F
0½F
- 11½F
2½F
Find the volume generated by revolving the circle x” + y” + 6x + 4y + 12 = 0 about the y-axis.
22.58
55.28
65.55
59.22
The line passing through the focus and perpendicular to the directrix of a parabola is called ____________.
latus rectum
axis
secant line
tangent line
The tangent of an angle of a right triangle is 0.75. What is the cosecant of the angle?
1.333
1.414
1.732
1.667
What type of conic is x” - 4y + 3x + 5 = 0?
hyperbola
parabola
circle
ellipse
A 20 ft light post casts a shadow 25 ft long. At the same time, a building nearby casts a shadow 50 ft long. How tall is the building?
62 ft
94 ft
40 ft
10 ft
Liza thought she had the exact money to buy 10 chocolate bars. However, the price per bar had increased by 50 centavos. Consequently, she was able to buy only 8 bars and had P2 left. How much money did Liza have?
80
40
60
30
What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis?
2y dx == x dy = 0
x dy + y dx = 0
2x dx - y dy = 0
dy/dx - x = 0
A periodic function has zero average value over a cycle and its Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function?
even quarter-wave
odd
odd quarter-wave
even
Parcel charges of a courier company are follows: P40 for the first 2 kilograms P15 for each of the succeeding kilogram weight of parcels. With these rates, what amount would be charged on a parcel weighing 30 kg?
P660
P450
P460
P650
Evaluate ∫ ln x dx from 1 to e.
0
1
2
3
A chord of a circle of a diameter 10 ft is decreasing in length 1 ft/min. Find the rate of change of the smaller are subtended by the chord when the chord is 8 ft. long.
3/5 ft/min
5/3 ft/min
3 ft/min
5 ft/min
Hotels, like airlines, often overbook, counting on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservations will not be used if four reservations are made, what is the chance fewer than two will cancel?
0.3825
0.7241
0.5211
0.8192
Find the area bounded by y” = 4x and x” = 4y. of the square in simplified form?
5.33
0.33
8.33
2.33
If the side of a square can be expressed as a a^2bcube, what is the area of the square in simplified form?
a^2b to the 6th power
a^4b to the 6th power
a^4b to the 5th power
a^2b to the 5th power
If one-inch equals 2.54 centimeters, how many inches are there in 20.32 centimeters?
7.2
10.2
9
8
Find the area of the polygon with vertices at: 2+3i, 3+i, -2-4i, -4-i, -1+2i.
47
35/2
25
47/2
