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WorksheetsFinal Examination in MATH 153 - Part 1 (Elements)
Total questions: 50
Worksheet time: 17mins
Name
Class
Date
1.
For a given function, it is found that f(t) = f(-t). What type of symmetry does f(t) have?
a)
odd symmetry
b)
even symmetry
c)
Rotational symmetry
d)
Quarter-wave symmetry
2.
Naperian logarithm have a base closest to which number?
a)
2.17
b)
2.72
c)
3.14
d)
10
3.
To find the angle of the triangle given only the lengths of the _____.
a)
the law of cosines
b)
the law of sines
c)
the law of tangents
d)
the inverse-square law
4.
What is the inverse natural function of the cosecant?
a)
secant
b)
sine
c)
cosine
d)
cotangent
5.
A statement of truth of which follows with little or no proof from a theorem.
a)
Axiom
b)
Hypothesis
c)
Corollary
d)
Conclusion
6.
A frequency curve which is composed of series of rectangles constructed with the steps as the base and the frequency as the height.
a)
Histogram
b)
Ogive
c)
Frequency of distribution
d)
Bar graph
7.
Convergent series is a sequence of decreasing number or when the succeeding term is _____ the preceding term.
a)
greater than
b)
equal to
c)
lesser than
d)
none of the above
8.
A and B are independent events. The probability that event A will occur is Pa and the probability that A and B will occur is Pab. From these two statements, what is the probability that event B will occur?
a)
Pa - Pb
b)
Pb - Pab
c)
Pa x Pb
d)
Pab/Pa
9.
In any square matrix, when the elements of any two rows are exactly the same, the determinant is _____.
a)
zero
b)
positive integer
c)
negative integer
d)
unity
10.
Is a sequence of terms whose reciprocals form an arithmetic progression?
a)
geometric progression
b)
harmonic progression
c)
algebraic progression
d)
ratio and proportion
11.
Binary number system is a system of notation for real number that uses the place method with 2 as the base, what is another name of binary number system?
a)
Binary digits
b)
Binumber system
c)
Dyadic number system
d)
Bits
12.
MCMXCIV is the roman numeral equivalent to _____.
a)
1974
b)
1984
c)
1994
d)
2994
13.
Terms that differs only in numeric coefficients are known as _____.
a)
unlike terms
b)
unequal terms
c)
like terms
d)
similar equations
14.
7 + 0i is?
a)
an irrational number
b)
real number
c)
imaginary number
d)
a variable
15.
If a two digit number has x for its unit digit and y for its tens digit, the number is represented as _____.
a)
x + y
b)
y - x
c)
10y + x
d)
10x - y
16.
The part of theorem which is assumed to be true.
a)
Corollary
b)
Hypothesis
c)
Postulate
d)
Conclusion
17.
Refers to the construction of drawing of lines and figures the possibility of which is admitted without proof.
a)
Corollary
b)
Theorem
c)
Postulate
d)
Hypothesis
18.
A proved proposition which is useful mainly as preliminary to the proof of a theorem.
a)
Lemma
b)
Hypothesis
c)
Postulate
d)
Corollary
19.
Many integrals may be evaluated by introducing a new variable of integration in place of the original variable, the two variables being connected by some suitable formulas. This process is called
a)
integration by parts
b)
integration by substitution
c)
partial derivatives
d)
the chain rule
20.
The variable inside the integral is called variable of integration or integration variable. It is sometimes referred to as
a)
calculus variable
b)
dummy variable
c)
limits variable
d)
limits range
21.
The value of x in trigonometric substitution with an integrand involving (a² – x²) is
a)
a sec θ
b)
a tan θ
c)
a cos θ
d)
a sin θ
22.
The area of the surface generated by rotating any plane curve about a certain axis in its plane is equal to the product of the length of the arc and the distance traveled by its centroid.
a)
Varignon’s theorem
b)
first proposition of Pappus
c)
method of section
d)
second proposition of Pappus
23.
The volume of any solid revolution is equal to the generating arc times the circumference of the circle described by the centroid of the area. This is known as
a)
first proposition of Pappus
b)
Cavalieri’s theorem
c)
second proposition of Pappus
d)
Simpson’s rule
24.
Newton was inspired by an apple. Pappus propositions were inspired by what fruits?
a)
apple and pear
b)
lemon and orange
c)
apple and lemon
d)
apple and banana
25.
When the ellipse is rotated about its shorter axis, the ellipsoid is
a)
paraboloid
b)
prolate
c)
spheroid
d)
oblate
26.
When the ellipse is rotated about its longer axis, the ellipsoid is
a)
paraboloid
b)
prolate
c)
spheroid
d)
oblate
27.
When a catenary (y = cosh x) is rotated about its axis of symmetry, it generates a solid called
a)
paraboloid
b)
conoid
c)
catenoid
d)
hyperboloid
28.
A solid of revolution of a parabola is known as
a)
paraboloid
b)
hyperboloid
c)
catenoid
d)
conoid
29.
A section of a surface of revolution is the section containing the axis of revolution.
a)
right
b)
central
c)
median
d)
meridian
30.
An infinite series in which successive terms are of the form of constant times successive integral power of the variable. It takes the form of a0 + a1x + a2x2 + a3x3 + …
a)
Fourier series
b)
Taylor’s series
c)
McClaurin series
d)
power series
31.
Who invented the symbol “∞” for infinity?
a)
John Stockton
b)
John Venn
c)
John Wallis
d)
John Napier
32.
Calculus was invented by
a)
Newton
b)
Leibnitz
c)
Gauss
d)
Newton and Leibnitz
33.
Varignon’s theorem is used to determine
a)
location of centroid
b)
moment of inertia
c)
mass moment of inertia
d)
moment of area
34.
If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the curve is
a)
a paraboloid
b)
a sinusoid
c)
a cissoid
d)
an exponential
35.
A function F(x) is called f(x) _____ of f(x) if F’(x) = f(x).
a)
explicit function
b)
derivative
c)
implicit function
d)
antiderivative
36.
Points of derivatives which do not exists (and so equals zero) are called .
a)
stationary points
b)
minimum points
c)
maximum points
d)
minimum and maximum points
37.
At the points of inflection where x = a,
a)
f”(a) ≠ 0
b)
f”(a) = 0
c)
f”(a) > 0
d)
f”(a) < 0
38.
At the minimum point, the slope of the tangent line is
a)
negative
b)
infinity
c)
positive
d)
zero
39.
What is the point where the second derivative is zero?
a)
maxima
b)
minima
c)
inflection point
d)
point of intersection
40.
The point on the curve where the second derivative of a function is equal to zero is called
a)
maxima
b)
minima
c)
point of inflection
d)
critical point
41.
The point on the curve where the first derivative of a function is zero and the second derivative is positive is called
a)
maxima
b)
minima
c)
point of inflection
d)
critical point
42.
Evaluate the integral tanh u du.
a)
ln sinh u + c
b)
ln cos h u + c
c)
cosh u + c
d)
coth u + c
43.
The derivative of a^u with respect to x is
a)
a^u ln a du/dx
b)
a^u ln u du/dx
c)
u^a ln a du/dx
d)
u^a ln u du/dx
44.
If y = tanhx, find dy/dx.
a)
sech^2 x
b)
-sech^2 x
c)
sech x tanh x
d)
-sech x tanh x
45.
The fields of mathematics which rest upon the fundamental concept of limits and was created by Newton and Leibnitz.
a)
Physics
b)
Calculus
c)
Boolean Algebra
d)
Quantum Mechanics
46.
The _____ of a relation is the set of second elements of the pair in the relation.
a)
domain
b)
range
c)
graph
d)
function
47.
A relation in which there is exactly one range element associated with each domain element.
a)
graph
b)
set
c)
formula
d)
function
48.
The _____ of a relation is the set of first elements of pairs in the relation.
a)
domain
b)
range
c)
graph
d)
function
49.
Any set of ordered pair is called a
a)
relation
b)
range
c)
domain
d)
graph
50.
Any pair of elements (x, y) having a first element x and a second element y is called
a)
range
b)
domain
c)
coordinates
d)
ordered pair
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