問題一覧
1
What are irrational numbers?
e, π, sqrt of 2
2
What are the equivalent values of i¹, i², i³, i⁴?
i, -1, -i, 1
3
Example of natural numbers
1, 2, 3, 4
4
Zero is included in whole numbers.
True
5
Numbers which can be expressed as a quotient of two numbers or a fraction.
rational numbers
6
The smallest natural number that have two natural numbers as a factor.
Least Common Multiple
7
The least common multiple of two or more denominators
Least Common Denominator
8
The largest number which is a factor of each of the given numbers.
Greatest Common Factor
9
The sum of roots X1+X2 is equal to
-B/A
10
The product of roots x1•x2 is equal to
C/A
11
If B²-4AC=0, the roots are
equal
12
B²-4AC>0, the roots are
real and unequal
13
B²-4AC<0, the roots are
imaginary
14
1 US gal is equal to
3.785 liters
15
1 liter is equal to
1.06 quarts
16
1 ton is equal to
2000 lbs
17
1 lb is equal to
16 oz
18
1 mile is equal to
5280 feet
19
All circles having the same center but with unequal radii are called
Concentric circles
20
The plane rectangular coordinate system is divided into four parts which are known as
quadrants
21
An angular unit equivalent to 1/400 of the circumference of a circle is called
Grad
22
1 is equal to
e^(2kπi)
23
cosh (jπ/4)
cos (π/4)
24
tan² (j0.78)
j tanh (0.78)²
25
Using power series expansion about 0, find cos x by differentiating from sin x.
1-(x²/2!)+(x⁴/4!)-(x⁶/6!)+...
26
Using power series expansion, find sinh x
x+(x³/3!)+(x⁵/5!)+(x⁷/7!)+...
27
Using power series expansion, find e^x
1+x+(x²/2!)+(x³/3!)+...
28
A periodic function has zero average value over a cycle and it's Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function?
even quarter
29
cosh (x), sinh (x), tanh (x) is equal to
cos (ix), -isin (ix), -itan (ix)
30
cosh (ix), sinh (ix), tanh (ix) is equal to
cos (x), isin (x), itan (x)
31
A line is perpendicular to the y-axis has a slope equal to:
zero
32
It represents the distance of a point from the y-axis
abscissa
33
The locus of a point which moves so that its distance from a fixed point and a fixed line is always equal is
parabola
34
A conic section whose eccentricity is equal to one (1) is known as:
parabola
35
The ____ of a parabola is the line which passes through the focus and is perpendicular to the directrix.
axis
36
The ____ of a parabola is the line which passes through the focus and is parallel to the directrix.
latus rectum
37
What curve is described by the equation y²+4y+x-1=0
parabola
38
What is the length of the latus rectum of the parabola y=4px²
4p
39
The locus of a point which moves so that the sum of its distances between two fixed points is constant is called
ellipse
40
A conic section whose eccentricity is less than one (1) is known as:
ellipse
41
What curve is described by the equation 4x²-y²+8x+4y=15
hyperbola
42
In conic section, if the eccentricity is greater than one (1), the locus is
hyperbola
43
If the general equation of the conic is Ax²+Bxy+Cy²+Dx+Ey+F=0. If B^2-4AC>0, the equation describes a
hyperbola
44
A point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing is known as
inflection point
45
In the equation y=-x²+x+1, where is the curve facing?
downward
46
A given function f (t) can be represented by a Fourier series if it
all of the above
47
In a Fourier series expansion of a periodic function, the coefficient a0 represents its
DC value
48
If in the Fourier series of a periodic function, the coefficient a0, is zero, it means that the function has
any of the above
49
The axis of the hyperbola through its foci is known as
transverse axis
50
Describe the locus represented by |z+2i|+|z-2i|=6
ellipse
51
The product of the slopes of any two straight lines is negative 1, one of the lines are said to be
perpendicular
52
A normal to a given plane is
perpendicular to the plane
53
In the polar coordinate system, the distance from a point to the pole is
radius vector
54
A periodic function f (t) is said to possess odd quarter-wave symmetry if
both (b) and (c).
55
If the average value of a periodic function over one period is zero and it consists of only odd harmonics then it must be possessing _____ symmetry.
half-wave
56
If in the Fourier series of a periodic function, the coefficient a0 = 0 and an = 0, then it must be having ____ symmetry.
either (a) or (b).
57
In the case of a periodic function possessing half-wave symmetry, which Fourier coefficient is zero?
a0
58
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
59
Which of the following periodic function possesses even symmetry?
cos 3t
60
If the Fourier coefficient bn, of a periodic function is zero, then it must possess ______ symmetry.
either (a) and (b).
61
A complex voltage waveform is given by V = 120 sin wt + 36(3wt + pi/2)+12 sin (5wt + pi). It has a time period of T seconds. The percentage fifth harmonic contents in the waveform is
10
62
In the waveform of V = 120 sin wt + 36(3wt + pi/2)+12 sin (5wt + pi), the phase displacement of the third harmonic represents a time interval of _____ seconds.
T/12
63
When the negative half-cycle of a complex waveform is reversed, it becomes identical to its positive half-cycle. This feature indicates that the complex waveform is composed of
both (a) and (b)
64
A periodic waveform possessing half-wave symmetry has no
even harmonics
65
The Fourier series of a wave form possessing .even quarter-wave symmetry has only
odd cosine terms
66
The Fourier series of a waveform possessing odd quarter-wave symmetry contains only
odd sine terms
67
Give example of non-integers
1/2, 0.10 , 3/5
68
Classify 1 (one) in number system
neither prime nor composite
69
Classify 2 in number system
prime and even
70
Classify zero in number system
whole number and not a natural number
71
Describe the property of (a+b)+c=c+(a+b)
Commutative
72
Which of the following refers to a three dimensional figure having a polygon as its base and triangles for the rest of its faces meeting at a point
pyramid
73
Which of the following refers to an angle having a measure greater than 90° but less than 180°
obtuse angle
74
Which of the following refers to a quadrilateral with opposite sides parallel and each pairs of opposite sides and angles is congruent
parallelogram
75
1 yard is equal to
36 inches
76
1 dime is equal to
10 centavos
77
1 cup is equal to
8 oz
78
orthogonal trajectories is equal to
perpendicular slope
79
the equation of a limacon is
r = a + b cos theta
80
find the area enclosed by the lemniscate of bernoulli r² = a² cos 2 theta
a²
81
The mathematical expression (1+I)^n is referred to
compound amount factor
82
what is the factor name for the formula (1+I)^-n
single payment present worth
83
when using net present worth calculations to compare two objects, which of the following could invalidate the calculation
evaluating over a different period of time
84
which of the following corresponds to the meaning of annuity
a series of uniform amounts over a period of time
85
what is a borrower of a particular loan almost always required to do during repayment?
repay the loan over over-agreed upon amount of time
86
an interest earning fund in which equal deposits are made at equal intervals of time for the purpose of gradually accumulating a specific sum of money required at some future date
sinking fund
87
what is the formula for a straight line depreciation rate?
100 percent-percent net savage value/ estimated service life
88
it is an amount which a willing buyer will pay to a willing seller for the property where each has equal advantage and is under no compulsion to buy or sell
market value
89
what is "work in process" classified as?
an asset
90
which of the following does not affect owner's equity?
license to start operation
91
what is another term for acid test ratio
quick ratio
92
the ability to convert assets to cash quickly is known as
liquidity
93
In an ellipse a chord which contains a focus and is in a line perpendicular to the major axis is a
latus rectum
94
what is the ratio of the sides of the triangle if the product of the sines of its angle is a maximum?
1:1:1
95
which of the following is a disadvantage of using the sample range to measure of spread or dispersion?
the largest or the smallest observation (or both) may be a mistake or an outlier