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Worksheets[Part 2] Midterm Exam in MATH 153 - 51-100
Total questions: 50
Worksheet time: 25mins
Name
Class
Date
1.
A _____ is an ancillary theorem whose results is not for the proof.
a)
postulate
b)
lemma
c)
hypothesis
d)
conclusion
2.
Statements that are accepted without discussion or proof are called axioms. The word “axiom” comes from the Greek “axioma” which means _____.
a)
worth
b)
correct
c)
true
d)
perfect
3.
In mathematical and other fields of logical reasoning, axioms are used as basis for the formulation of statements called _____.
a)
lemma
b)
hypothesis
c)
postulate
d)
theorem
4.
“The product of two or more number is the same in whatever order they are multiplied “. This refers to _____.
a)
Associative law of addition
b)
associative law of multiplication
c)
commutative law of multiplication
d)
distributive law of multiplication
5.
If a = b, then b can replace a in any equation. This illustrates what law of identity?
a)
Reflexive law
b)
Law of symmetry
c)
Transitive law
d)
Substitution law
6.
If a = a, then it illustrates what law of identity?
a)
reflexive law
b)
law of symmetry
c)
transitive law
d)
substitution law
7.
If a = b and b = c, then a = c this illustrates _____.
a)
reflexive law
b)
law of symmetry
c)
transitive law
d)
substitution law
8.
Any equation which, because of some mathematical process, has fewer roots than its original is sometimes called as _____.
a)
redundant equation
b)
literal equation
c)
linear equation
d)
defective equation
9.
An algebraic expression which can be represented as a quotient of two polynomials.
a)
Irrational algebraic equation
b)
Reduced algebraic expression
c)
Rational algebraic equation
d)
Complex algebraic equation
10.
A statement containing one or more variables and having the property that it becomes either true or false when the variables are given specific values from their domains.
a)
solution
b)
problem
c)
open sentence
d)
worded problem
11.
Any algebraic term is a/an _____ term in certain representing numbers if it consists of the products of possible integral powers of these numbers and a factor not containing them.
a)
integral
b)
rational
c)
irrational
d)
integral rational
12.
An equation in x and y which is not easily solved for y in terms of x is called _____.
a)
explicit
b)
implicit function
c)
discontinuity
d)
quadratic
13.
The number which are represented with letters.
a)
variables
b)
unknowns
c)
literal numbers
d)
terms
14.
Equations whose members are equal only for certain or possibly no value of the unknown.
a)
conditional equations
b)
inequalities
c)
unconditional equations
d)
temporary equations
15.
A common fraction with unity for numerator and a positive integer as denominator (i.e. 1/n).
a)
Ordinary fraction
b)
Unit fraction
c)
Common fraction
d)
Improper fraction
16.
If the absolute value of the numerator of a fraction is smaller than the denominator, it is called _____.
a)
proper fraction
b)
improper fraction
c)
Decimal fraction
d)
mixed number
17.
A number containg a non-terminating but repeating decimal is a/an _____.
a)
integer
b)
rational number
c)
natural number
d)
irrational number
18.
A positive integer which has no perfect-square factor greater than 1.
a)
Radical expression
b)
Square integer
c)
Square integer
d)
Square-free integer
19.
Numbers are used to describe a _____.
a)
magnitude
b)
position
c)
magnitude and position
d)
none of the above
20.
Are symbols or combinations of symbols which describe a number.
a)
Numerals
b)
Digits
c)
Terms
d)
Notations
21.
The complex number is in the form of a + bi. If a = 0, what do you call the resulting number?
a)
Absolute value of the complex number
b)
Pure imaginary number
c)
Argument
d)
Irrational number
22.
For a complex number a + bi, the real number √(a² +b²) is _____ of the complex number.
a)
absolute value
b)
magnitude
c)
modulus
d)
all of the above
23.
The _____ of two complex number is found by multiplying each term of the one by every term of the other.
a)
sum
b)
difference
c)
product
d)
quotient
24.
What is another name for amicable numbers?
a)
compatible numbers
b)
friendly numbers
c)
Fermats numbers
d)
Inconsistent numbers
25.
What is the smallest pair of friendly number?
a)
180 and 190
b)
200 and 120
c)
220 and 284
d)
220 and 264
26.
Prime numbers that appear in pair and differ by 2 (e.g. 3 and 5, 11 and 13 etc.) are called _____.
a)
Mersenne primes
b)
prime number theorem
c)
twin primes
d)
pseudo primes
27.
For a cubic equation, the discriminant is found to be greater than zero. The roots are _____.
a)
one real and two conjugate complex roots
b)
three distinct roots
c)
three real roots , which two are equal
d)
none of these
28.
What do you call an angle whose terminal side coincides with an axis?
a)
Reflex
b)
Quadrantal
c)
Right
d)
Co-terminal
29.
Are numbers which can be drawn as dots and arranged in triangular shape ( i.e. 1, 3, 6, 10, 15, 21…)
a)
Triangular number
b)
Square numbers
c)
Pentagonal numbers
d)
Tetrahedral numbers
30.
A figure numbers which can be drawn as dots and arranged in square shape ( i.e. 1, 4, 9, 16, 25…)
a)
Cubic numbers
b)
Square numbers
c)
Pyramid numbers
d)
Pentagon numbers
31.
A sequence of numbers where the number is equal to the sum of the two preceding numbers such as 1, 1, 2, 3, 5, 8, 13, 21… is called _____.
a)
Fermat’s numbers
b)
Fibonacci numbers
c)
Gaussian numbers
d)
Archimedean numbers
32.
What is the multiplicative inverse of the integer 5?
a)
1
b)
5
c)
-5
d)
1/5
33.
What is the additive identity element?
a)
0
b)
1
c)
-1
d)
infinity
34.
What is the multiplicative identity element?
a)
0
b)
1
c)
-1
d)
infinity
35.
The number 0 such that 0 + a = a for all a is called _____.
a)
additive inverse
b)
additive identity
c)
commutative law of addition
d)
associative law of addition
36.
The additive inverse of a complex number a + bi is _____.
a)
a - bi
b)
a + bi
c)
-a - bi
d)
-a + bi
37.
All real numbers have additive inverse, commonly called _____.
a)
reciprocals
b)
opposites
c)
addends
d)
equivalent
38.
All real numbers except zero have multiplicative inverses, commonly called _____.
a)
equivalent
b)
factors
c)
opposites
d)
reciprocals
39.
The number zero has no _____.
a)
multiplicative inverse
b)
additive inverse
c)
multiplicative identity
d)
additive identity
40.
What is the additive inverse of a + bi?
a)
bi
b)
-a - bi
c)
1/(a + bi)
d)
a -bi
41.
What is the multiplicative inverse of a + bi?
a)
0
b)
1
c)
- a -bi
d)
(a/a² - b²) - bi/(a² + b²)
42.
Which of the following is NOT a property of a binomial expansion of (x + y)ⁿ?
a)
power is decreasing
b)
power of y is increasing
c)
sum of exponents in each term = n
d)
number of terms = n - 1
43.
A triangular array numbers forming the coefficient of the expansion of a binomial is called _____.
a)
Egyptian triangle
b)
Golden triangle
c)
Pascal’s triangle
d)
Bermuda triangle
44.
The coefficient of the second term of the expansion of (x + y) n is always equal to _____.
a)
n
b)
n - 1
c)
n + 1
d)
n/2
45.
How is a number in the Pascal’s triangle obtained?
a)
by getting the product of the two numbers directly above it
b)
by getting the sum of the two numbers directly above it
c)
by getting the difference of the two numbers directly above it
d)
by getting the mean of the two numbers directly above it
46.
If the sign between the terms of the binomial is negative, its expansion will have signs which are _____.
a)
all positive
b)
all negative
c)
alternate starting with positive
d)
alternate starting with negative
47.
Indicate the false statement:
a)
the multiplicative identity is 1
b)
the product of a positive number and a negative number is negative
c)
ab = ba is the associative law for multiplication
d)
x² - y² = (x + y)(x - y)
48.
The absolute value of a non-zero number is _____.
a)
always zero
b)
always negative
c)
always positive
d)
sometimes zero and sometimes positive
49.
A line segment joining two points on a circle.
a)
sector
b)
chord
c)
arc
d)
tangent
50.
In the proportion of four quantities, the first and fourth terms are referred to as the _____.
a)
means
b)
extremes
c)
denominators
d)
numerators
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