WorksheetsMATH 5
Total questions: 50
Worksheet time: 4hrs 10mins
A number is 1 more than twice another. Their squares differ by 176. What is the
larger number?
9
7
15
16
The sides of a right triangle is in arithmetic progression whose common difference is 6
cm. Its area is:
216 sq. cm
234 sq. cm
212sq. cm
245sq. cm
In how many ways can a person choose 1 or more of 4 electrical appliances?
12
15
16
18
The probability that a certain man will be alive 25 years hence is 3/7, and the probability
that his wife will be alive 25 years hence is 4/5. Determine the probability that 25 years
hence, only the man will be alive.
23/35
33/35
13/35
3/35
Find the y – intercept of the line tangent to the parabola x = 2y2 at the point (2,1).
-7
7
3/2
½
. A growth curve is given by A = 10e2t. At what value of t is A = 100?
5.261
3.070
1.151
0.726
If the short leg of a right triangle is 5 units long and the long leg is 7 units long, find the
angle opposite the short leg, in degrees.
31.5
32.5
34.5
35.5
Express 2 sin2 𝜃 as a function of cos 2𝜃.
cos 2𝜃 – 1
cos 2𝜃 + 1
cos 2𝜃 + 1
1 - cos 2𝜃
The x – and y – axes are the asymptotes of a hyperbola that passes through the point
(2,2). Its equation is
x2 – y2 = 0
xy = 4
y2 – x2 = 0
x2 + y2 = 4
If the area of the equilateral triangle is 4(sqrt. of 3), find the perimeter.
16
12
14
18
Find the area bounded by the curve r = 8 cos 𝜃
50.27
12.27
8
67.02
. What is the length of the transverse axis of the hyperbola whose equation is 9y2 – 16x2 =
144?
6
9
8
7
Find the area bounded by x = 2y – y2 and the axis.
.4/3
5/3
6/3
7/3
Derek is purchasing lunch meat for the class picnic. There are 300 people attending the picnic. Derek expects that for every 10 people 11 sandwiches will be eaten and that 20 pounds of meat will make 90 sandwiches. How much lunch meat should Derek buy?
73 ^1/3 pounds
67^2/3pounds
110 pounds
330 sandwiches
A certain radioactive material has a half-life of 7 days. A test sample of this material has an initial mass of 400 kg. Which of the following would be the most appropriate unit to use when labeling the time axis of a graph of remaining material vs. time elapsed until 6.1 grams remain?
Hours
Days
Weeks
Years
Usain Bolt set a world record of 9.58 seconds for the 100 meter dash. White-tailed deer can run at 48 kilometers per hour for short periods. If Mr. Bolt and a white-tailed deer run a 100 meter dash at these speeds, who would win, and by how much?
Mr. Bolt wins by 3.75 seconds
Mr. Bolt wins by 2.08 seconds
Deer wins by 3.75 seconds
Deer wins by 2.08 seconds
After getting his wisdom teeth pulled, Matt was prescribed 60 mg of Codeine to be taken every 4 hours for 5 days. The pharmacy has 30 mg pills. How many pills should Matt receive when filling the prescription?
72
60
56
89
Evaluate the lim (x2 – 16)/(x – 4).
5
8
7
4
Evaluate the limit (x – 4)/(x2 – x – 12) as x approaches 4.
undefined
0
infinity
1/7
Find y” if y = au.
a^u ln a
u ln a
a^u/ln a
a ln u
If ln (ln y) + ln y = ln x, find y’.
x/(x – y)
x/(x + y)
y/(x + y)
y/(x – y)
Find the derivative of arc sec (2x)
1/[x√(4x2 – 1)]
2/[x√(4x2 – 1)]
1/[x√(1 – 4x2)]
2/[x√(1 – 4x2)]
Find the derivative of arc csc (3x).
-1/[x√(9x2 – 1)]
1/[3x√(9x2 – 1)]
3/[x√(1 – 9x2)]
-3/[x√(1 – 9x2)]
Find the derivative of 4 arc tan (2x).
4/(1 + x2)
-4/(1 + x2)
8/(1 + 4x2)
-8/(1 + 4x2)
Find the derivative of arc cos (2x).
-2/√(1 – 4x^2)
2/√(1 – 4x^2)
2/(1 + 4x^2)
2/√(2x^2 – 1)
Find the derivative of loga u with respect to x.
log u du/dx
u du/ln a
loga e/u
loga du/dx
Find y’ if y = arc sin (x)
√(1 – x^2)
1/√(1 – x^2)
1/(1 + x^2)
0
A cube has a volume of 1728 cu mm. If the allowable error in the edge of a cube is 0.04 mm, compute the allowable error in the volume of the cube.
17.28 cu mm
16.88 cu mm
-16.88 cu mm
-17.28 cu mm
If the volume of a sphere is 1000π/6 cu mm and the allowable error in the diameter of the sphere is 0.03 mm, compute the allowable error in the volume of a sphere.
-4.71 cu mm
4.71 cu mm
5.53 cu mm
-5.53 cu mm
If the area of a circle is 64π sq mm, compute the allowable error in the area of a circle if the allowable error in the radius is 0.02 mm.
1.01 sq mm
1.58 sq mm
2.32 sq mm
0.75 sq mm
Find the approximate increase by the use of differentials, in the volume of the sphere if the radius increases from 2 to 2.05.
2.51
67.3
13.12
34.67
If y = 3x2 – x + 1, find the point x at which dy/dx assume its mean value in the interval x = 2 and x = 4.
3
4
5
6
A surveying instrument is placed at a point 180 m from the base of a bldg on a level ground. The angle of elevation of the top of a bldg is 30 degrees as measured by the instrument. What would be error in the height of the bldg due to an error of 15 minutes in this measured angle by differential equation?
1.05 m
1.09 m
2.08 m
1.05 m
The expression for the horsepower of an engine is P = 0.4 n x2 where n is the number of cylinders and x is the bore of cylinders. Determine the power differential added when four cylinder car has the cylinders rebored from 3.25 cm to 3.265 cm
0.156 hp
0.16 hp
0.319 hp
0.180 hp
If y = x(3/2) what is the approximate change in y when x changes from 9 to 9.01?
0.045
0.405
450
45
What is the allowable error in measuring the edge of a cube that is intended to hold a cu m, if the error in the computed volume is not to exceed 0.03 cu m?
25
0.0025
0.003
3
The altitude of a right circular cylinder is twice the radius of the base. The altitude is measured as 12 cm. With a possible error of 0.005 cm, find the approximately error in the calculated volume of the cylinder.
0.188 cu cm
0.144 cu cm
0.104 cu cm
0.126 cu cm
The diameter of a circle is to be measured and its area computed. If the diameter can be measured with a maximum error of 0.001 cm and the area must be accurate to within 0.10 sq.cm. Find the largest diameter for which the process can be used.
64
67
76
78
An elliptical plot of garden has a semi-major axis of 6 m and a semi-minor axis of 4.8 meters. If these are increased by 0.15 m each, find by differential equations the increase in area of the garden in sq. m.
0.62π
1.62π
2.62π
2.26π
The function y = (x – 4)/(x + 2) is discontinuous at x equals?
-2
3
-6
8
Compute the equation of the horizontal asymptote of the curve y = (2x – 1)/(x + 2).
y = 2
y = 0
y – 1 = 0
y – 3 = 0
Compute the equation of the vertical asymptote of the curve y = (2x – 1)/(x + 2).
x + 2 = 0
x – 3 = 0
x + 3 = 0
x – 2 = 0
Evaluate the limit (ln sin x)/(ln tan x) as x approaches to 0.
1
2
3
4
Evaluate the limit (x + sin2x)/ (x – sin2x) as x approaches to 0.
2
-3
-5
4
Find the limit [sqrt(x + 9) – 3]/x as x approaches 0.
α
¼
0
½
Evaluate the limit of (x + 2)/(x – 2) as x approaches α
1
-1
-2
2
Evaluate the limit of 8x/(2x – 1) as x approaches α.
4
3
2
1
Evaluate the limit of (4 tan3 (x)/ 2sin(x) – x as x approaches 0.
1
0
2
α
Evaluate the limit of (1 – sec2 (x)/cos (x) – 1 as x approaches 0.
-2
2
3
-3
Evaluate the limit of (x2 – x – 6)/(x2 – 4x + 3) as x approaches 3.
3/2
3/5
0
5/2
