WorksheetsMath 1-1
Total questions: 50
Worksheet time: 25mins
The area bounded by the curve y = 12x and the line x = 3 is revolved about the line x = 3. What is the volume generated?
186
179
181
184
A and B can do a piece of work in 3 days, B and C in 4 days, while A and C in 2.5 days. In how many days can all of them do the work together?
3.17
1.02
3.83
2.03
60% of 390?
234
190
180
134
What is |u × v| if |u| = 9, |v| = 3 and θ = 85°?
26.897
2.353
308.611
56.45
Joseph is X years old y years from now. His age now is?
x
y
x - y
y - x
Determine the differential equation of the family of lines passing through (h, k).
(y - k) dx - (x - h) dy = 0
(y - h) + (y - k) dy/dx
(x - h) dx - (y - k) dy = 0
(x + h) dx - (y - k) dy = 0
A normal to a given plane is:
perpendicular to the plane
lying on the plane
parallel to the plane
oblique to the plane
What is the area bounded by the curve y = x³, the x-axis and the line x = -2 and x = 1?
5.24
5.42
4.25
2.45
Find all values of z for which e^z = 1.
2kπi
3kπi
(1/8)πi + (1/2)kπi
(1/2)kπi
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 is 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 of X.
1
3
1/2
2
Jennifer flipped a coin three times and got heads each time. What is the probability that she gets heads on the next flip?
1
1/16
1/2
0
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 chosen is blue?
4/13
3/8
3/16
3/5
Describe the locus represented by |z - i| = 2.
Circle
Ellipse
Hyperbola
Parabola
The plane rectangular coordinate system is divided into four parts which are known as:
Octants
Quadrants
Axis
Coordinates
A cross-section of a trough is a semi-ellipse with width at the top 18 cm and depth 12 cm. The trough is filled with water to a depth of 8 cm. Find the width at a surface of the water.
5(sqrt. of 2) cm
12(sqrt. of 2) cm
7(sqrt. of 2) cm
6(sqrt. of 2) cm
A fencing is limited to 20 ft length. What is the maximum rectangular area that can be fenced in using perpendicular corner sides of an existing wall?
120
100
140
190
A man on a wharf (pier) is pulling a rope tied to a raft at a time rate of 0.60 m/sec. If the hands of the man pulling the rope are 3.66 m above the level of the water, how fast is the raft approaching the wharf if there are 6.10 m of rope out?
-0.75 m/sec
-0.35 m/sec
-0.45 m/sec
-0.65 m/sec
Jeremy ate 9 ounces of a 16-ounce carton of ice cream. What percentage of the carton did he eat?
56.25%
17.25%
19.50%
18.75%
The value of 5! is equal to
1
5
25
120
After paying a commission to his broker of 7% of the sale price, a seller receives $103,000 for his house. How much did the house sell for?
$99,790
$110,000
$110,420
$110,753
Evaluate lim (n²+3i)(n-i) / (in³-3n+4-i)
0
1
∞
1/2
Find the equation of a circle with center at the origin and passes through the point (-3,4)
x² + y² = 16
x² + y² = 25
x² + y² = 36
x² + y² = 9
Evaluate ∫ x dx / sqrt(x² - 8x)
sqrt(x² - 4x) + 4 ln |x + sqrt(x² - 8x) / 4| + C
sqrt(x² - 8x) + 4 ln |x - 4/4 + sqrt(x² - 8x) / 4| + C
sqrt(x² + 8x) + 4 ln |x + 4 + sqrt(x² + 8x) / 4| + C
sqrt(x² + 4x + 2) + 4 ln |x + 2 + sqrt(x² + 4x + 2) / 4| + C
If x varies directly as z and inversely as y², and y = 2 and z = 2 when x = 1, find the value of x when y = 4 and z = 1.
1/2
1/8
8
4
If sin θ = a and cos² θ = b then what is the value of sin² θ - 2 cos θ?
I. a² + 2 sqrt(b) II. b² + 2 sqrt(a) III. a² - 2 sqrt(b) IV. b² - 2 sqrt(a)
I and II only
III only
III and IV only
I only
How many terms are there in the expansion of (x + y)^7?
6
7
8
9
cos 1° x cos 2° x cos 3° x ... x cos 180° is equal to:
0
1
1/2
-1
The parabola defined by the equation 3y² + 4x = 0 opens
upward
downward
to the left
to the right
Find the work done in moving an object along a vector a = 3i + 4j if the force applied is b = 2i + j
8
9
10
12
Find the domain of the following function: f(x) = 3x, -6 ≤ x ≤ 8
(-6, 8)
[-18, 24]
(-18, 24)
[-6, 8]
What is the equation of the directrix of the parabola x² = 4(y - 2)?
x = -1
x = 1
y = 1
y = -1
Where is the center of the circle x² + y² - 10x - 4y + 196 = 0?
(2, -5)
(-2, 5)
(-5, 2)
(5, -2)
A periodic waveform possessing half-wave symmetry has no
even harmonics
odd harmonics
sine terms
cosine terms
Find the point along the line x = y = z that is equidistant from (3, 0, 5) and (1, -1, 4).
(1, 1, 1)
(2, 2, 2)
(3, 3, 3)
(4, 4, 4)
Find the slope of the line through the points (-2, 5) and (7, 1).
4/9
-4/9
9/4
-9/4
f(x) = 1/(x -2), (fg)(1) = 6 and g(1) = -1, then g(1) = ?
-7
5
-5
7
Evaluate the inverse Laplace transform of 6 over (s^2 +4).
3 sin 2t
cos 2t
3 sinh 2t
3 cosh 2t
A particle moves from left to right along the parabola y = x^2 with constant speed 5. Find the magnitude of the normal components of the acceleration.
3(sqrt. of 5)
2(sqrt. of 5)
4(sqrt. of 5)
5
The velocity attained by an object falling freely a distance h feet from rest is given by v= sqrt. of (64.4h) ft/sec. Estimate the error in v due to an error of 0.5 ft when h is measured as 100 ft.
0.1 ft/sec
0.2 ft/sec
0.3 ft/sec
0.4 ft/sec
A tank contains 200 liters of fresh water. Brine containing 2 kg/liter of salt enters the tank at the rate of 4 liters per min and the mixture kept uniform by stirring, runs out at 3 liters per min. Find the amount of salt in the tank after 30 min.
196.99 kg
186.50 kg
312.69 kg
234.28 kg
The inner surface of a tank is in the form of a hemisphere of radius 3.0m with a diametral plane on top. Determine the total work done in pumping the water to the top of the tank. For water, w = 9.802 kN/cu. m.
632.50 kN-m
542.30 kN-m
623.50 kN-m
524.30 kN-m
A wheel 4ft in diameter is rotating at 80 r/min. Find the distance (in ft) traveled by a point on the rim in 1 s.
18.6
16.8
17.8
18.7
A gull flying parallel to the surface of the water drops a clam, which takes 3 sec to hit the water. How high in meters was the gull when it dropped the clam?
138
124
144
159
Find the 7th term of 0.5, 0.2, 0.125, ...
0.010
0.025
0.050
0.100
Find the inverse function of y = f(x) = 2x -6.
y = g(x) = 2x + 6
y = g(x) = 6x -2
y = g(x) = (x /2)+3
y = g(x) = x/2 -3
The base of an isosceles triangle is 20.4 and the base angles are 48°40'. Find the altitude of the triangle.
11.6
15.6
15.4
12.8
In a certain community of 1,200 people, 60% are literate. Of the males, 50% are literate, and of the females 70% are literate. What is the female population?
850
500
550
600
Equal-sized spheres are contained in a regular tetrahedron (with equilateral triangle for each face), such that along of the 6 sides of the tetrahedron, there are 4 spheres in line. How many total spheres are there?
14
20
22
18
The cross-sections of a certain trough are inverted isosceles triangles with height 6 ft and base 4 ft. Suppose the trough contains water to a depth of 3 ft. Find the total fluid force on one end.
187.2 lb
178.2 lb
192.4 lb
129.4 lb
A motorboat moves in the direction N 40 deg E for 3 h at 20 mi/h. How far north does it travel?
46 mi
39 mi
60 mi
58 mi
