WorksheetsMATH IN THE MODERN WORLD MIDTERM
Total questions: 50
Worksheet time: 25mins
Patterns are defined as regular, repeated, or recurring forms or designs.
Irregular
Random
Regular
Spontaneous
According to the module, what is the source of patterns in nature?
Accidental formations
External interventions
Connection and interaction of organisms and other natural objects
Geological chance
Which of the following is listed as an example of a pattern in nature that helps discover mathematical principles?
Human-built bridges
Seeds in a sunflower
Architectural blueprints
Computer programs
The patterns in nature play an important role and also give what to one’s eyes?
Utility
Structure
Aesthetic
Complexity
What is the term for patterns that are formed without external intervention?
Invoked organized patterns
Accidental patterns
Self-organized patterns
Conditional patterns
Which of the following is explicitly categorized in the module as an "invoked organized pattern" (formed with external intervention)?
Snowflakes
Snail’s shell
Honeycombs
Tiger’s stripes
What is the next number in the sequence: 1,3,5,7,9,___?
10
11
12
14
The sequence 1,3,5,7,9 is an example of an arithmetic progression with a common difference of:
1
2
3
4
The Introduction to Module 1 states that mathematics comes into play in both nature and what other field?
Technological advancements
Political systems
Human endeavors
Astronomical observations
If a pattern of dots in an N×N grid contains N+1 dots, how many dots will the 5×5 grid contain?
5 dots
6 dots
7 dots
8 dots
The module introduction states that Module 1 discusses patterns, the nature of mathematics, and which specific sequence?
Arithmetic Sequence
Geometric Sequence
Harmonic Sequence
Fibonacci sequence
If the first two terms of the Fibonacci sequence are F0=0 and F1=1, what is the fifth term, F4?
2
3
5
8
The underlying goal of studying patterns is to discover the underlying mathematical principles behind nature’s designs. This suggests that humans are hard wired to recognize what?
Logic
Patterns
Language
Calculation
What is the sequence 3,7,11,15,… an example of? (Based on the structure of Example 2)
Geometric progression
Quadratic sequence
Arithmetic progression
Fibonacci sequence
What would be the next term in the sequence 3,7,11,15,___?
17
18
19
20
Which of these concepts is defined as a repeated or recurring form or design?
Number
Pattern
Sequence
Regularity
The module states that mathematics helps predict the behavior of nature and which other element in the real world?
Physics
Statistics
Logic
Phenomena
What is a symbol that acts as a placeholder for expressions or quantities that can modify or change?
Constant
Statement
Variable
Operator
A statement that asserts that all elements in a set have the same property is called a/an:
Conditional Statement
Existential Statement
Universal Statement
Universal Conditional Statement
The statement "If b is a cat, then b is a mammal" is an example of a:
Universal Statement
Conditional Statement
Universal Existential Statement
Existential Universal Statement
Which type of statement contains a variant of the word "if-then"?
Universal Statements
Conditional Statements
Universal Existential Statements
Existential Universal Statements
Which type of statement contains some variation of the words "for all"?
Conditional Statements
Universal Statements
Existential Universal Statements
Universal Existential Statements
The statement "For all animals b, if b is a cat, then b is a mammal" is an example of a:
Conditional Statement
Existential Universal Statement
Universal Existential Statement
Universal Conditional Statement
Which statement type declares that a certain feature is true for all objects of a given type and declares something exists?
Universal Conditional Statement
Existential Universal Statement
Universal Existential Statement
Simple Universal Statement
The statement "Every real number has an additive inverse" is an illustration of a/an:
Universal Conditional Statement
Universal Existential Statement
Existential Universal Statement
Simple Conditional Statement
The statement "There is a positive integer that is less than or equal to every positive integer" is an illustration of a/an:
Universal Statement
Universal Conditional Statement
Universal Existential Statement
Existential Universal Statement
Which English term is used to represent the basic mathematical operation of division (/,÷)?
Sum
Product
Minus
Quotient
Which English term is equivalent to the equality relation (=)?
More than
Subtracted by
Multiplied with
Is the same as
The phrase "Five times a number" translates mathematically to:
5+x
5x
5÷x
x−5
The expression a2≥0 is a formal way of rewriting which statement?
Given any real number a, a is positive.
The square of any real number is nonnegative.
If a is positive, then a2 is positive.
There is a real number a such that a2 is nonnegative.
The English phrase "difference" refers to which mathematical operation?
Addition (+)
Multiplication (⋅)
Subtraction (−)
Division (/)
If a real number x is negative, then x2 is:
Negative
Zero
Positive
Cannot be determined
What kind of statement is this: "For all odd number x, there is a real number y such that y is a reciprocal for x."?
Conditional Statement
Universal Conditional Statement
Existential Universal Statement
Universal Existential Statement
Who is credited with introducing the use of the word "set" as a formal mathematical term in 1879?
Euclid
Aristotle
René Descartes
George Cantor
Intuitively, a set is defined as simply a:
Collection of numbers
System of rules
Collection of elements
List of ordered pairs
What is the meaning of the symbol "∈"?
Is a subset of
Is an element of
Is not an element of
Is a proper subset of
What is the meaning of the symbol "∈/"?
Is a subset of
Is an element of
Is not an element of
Is an empty set
Which notation is used to specify a set by writing all of its elements, such as {1,2,3}?
Set-builder notation
Interval notation
Set-roster notation
Exponential notation
How is the symbol "..." (ellipsis) interpreted when used in the set {1,2,3,...}?
It means the set is finite.
It means the elements are repeated.
It means "and so on" (indicating an infinite set).
It indicates that the elements are integers only.
The set {x∈S∣P(x)} is a representation of which notation?
Set-roster notation
Set-builder notation
Cartesian product notation
Relation notation
How many elements are in the set {5,{5}}?
One (5)
Two (5 and the set {5})
Three (5, the set {5}, and {5} itself)
Four (5, 5, {5}, {5})
What is the correct way to compare {2} and 2?
{2}=2
{2}∈2
{2}≠2
{2}⊂2
What is the meaning of the symbol "⊆"?
Is a proper subset of
Is an element of
Is a subset of
Is a superset of
For A to be a Proper Subset of B (A⊂B), which condition must be met?
Every element of A is an element of B, and A is equal to B.
Every element of B is an element of A.
Every element of A is an element of B, and there is at least one element in B not included in A.
A and B have no elements in common.
Given X={3,4,5} and Y={5,3,4}, how are X and Y related?
X is a proper subset of Y.
Y is a proper subset of X.
X and Y are disjoint.
X and Y represent the same set (X=Y).
The Cartesian product of sets A and B, denoted A×B, is the set of all:
Elements common to A and B.
Ordered pairs (a,b) where a∈A and b∈B.
Unordered pairs {a,b} where a∈A and b∈B.
Functions from A to B.
If A={2,3,4} and B={c,d}, how many elements are in the Cartesian product A×B?
5
6
8
9
In a relation defined by a collection of ordered pairs (x,y), the set of all x-values is called the:
Range
Co-domain
Domain
Image
In a relation defined by a collection of ordered pairs (x,y), the set of all y-values is called the:
Domain
Co-domain
Range
Subset
A Relation (R) between two sets is defined as a:
Function that maps one set to another.
Set of all possible pairs from the two sets.
Collection of ordered pairs containing one object from each set.
Proper subset of a Cartesian product.
