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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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Study First
Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
Additive Inverse:
4 + x = 12
Box Diagram
2. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Stereographic Projection
Rational
Group
Properties of Equality
3. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that
Primes
Fourier Analysis and Synthesis
Hyperbolic Geometry
Hypercube
4. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.
Solve the Equation
Products and Factors
The BML Traffic Model
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
5. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Transfinite
Irrational
The BML Traffic Model
Genus
6. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Probability
Set up an Equation
Frequency
Periodic Function
7. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).
A number is divisible by 3
Permutation
Equivalent Equations
Cardinality
8. Every whole number can be uniquely factored as a product of primes. This result guarantees that if the prime factors are ordered from smallest to largest - everyone will get the same result when breaking a number into a product of prime factors.
De Bruijn Sequence
Set up an Equation
Unique Factorization Theorem
Transfinite
9. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Prime Deserts
Figurate Numbers
a · c = b · c for c does not equal 0
1. The unit 2. Prime numbers 3. Composite numbers
10. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Primes
General Relativity
Expected Value
Continuous
11. Aka The Osculating Circle - a way to measure the curvature of a line.
The inverse of multiplication is division
Multiplication by Zero
The Kissing Circle
Fourier Analysis
12. Dimension is how mathematicians express the idea of degrees of freedom
a divided by b
Dimension
Divisible
Additive Inverse:
13. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Cayley's Theorem
Tone
bar graph
Additive Identity:
14. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
The Commutative Property of Addition
Grouping Symbols
Commutative Property of Multiplication:
Solution
15. If a = b then
Continuous Symmetry
a + c = b + c
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Set up an Equation
16. 1. Find the prime factorizations of each number.
Fourier Analysis
Frequency
Greatest Common Factor (GCF)
1. Find a relationship between the first and second numbers. 2. Then we see if the relationship is true for the second and third numbers - the third and fourth - and so on.
17. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -
Continuous Symmetry
The inverse of addition is subtraction
Problem of the Points
Law of Large Numbers
18. Is a symbol (usually a letter) that stands for a value that may vary.
Equation
The Associative Property of Multiplication
The inverse of subtraction is addition
Variable
19. All integers are thus divided into three classes:
1. The unit 2. Prime numbers 3. Composite numbers
Box Diagram
prime factors
Fourier Analysis
20. A
a · c = b · c for c does not equal 0
Division is not Commutative
set
Spaceland
21. (a · b) · c = a · (b · c)
repeated addition
Non-Orientability
Factor Trees
Associative Property of Multiplication:
22. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab
Galton Board
Set up a Variable Dictionary.
Countable
Intrinsic View
23. Cannot be written as a ratio of natural numbers.
prime factors
Associative Property of Addition:
Galton Board
Irrational
24. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
The Distributive Property (Subtraction)
Prime Deserts
Comparison Property
A number is divisible by 10
25. Is the shortest string that contains all possible permutations of a particular length from a given set.
inline
Non-Euclidian Geometry
De Bruijn Sequence
left to right
26. The system that Euclid used in The Elements
Markov Chains
Multiplicative Inverse:
Modular Arithmetic
Axiomatic Systems
27. The fundamental theorem of arithmetic says that
each whole number can be uniquely decomposed into products of primes.
Primes
Pigeonhole Principle
a
28. The process of taking a complicated signal and breaking it into sine and cosine components.
Fourier Analysis
Symmetry
Fundamental Theorem of Arithmetic
Hyperbolic Geometry
29. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Expected Value
The inverse of multiplication is division
˜
Overtone
30. This method can create a flat map from a curved surface while preserving all angles in any features present.
Spaceland
The inverse of subtraction is addition
Stereographic Projection
Public Key Encryption
31. Add and subtract
Answer the Question
inline
The BML Traffic Model
Group
32. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Prime Number
Composite Numbers
Distributive Property:
Associate Property of Addition
33. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.
Solution
The Set of Whole Numbers
The Multiplicative Identity Property
Genus
34. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.
does not change the solution set.
The Same
Commutative Property of Multiplication
Distributive Property:
35. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Division is not Associative
Fourier Analysis and Synthesis
Non-Euclidian Geometry
Axiomatic Systems
36. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.
Multiplicative Identity:
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Cardinality
Grouping Symbols
37. A + b = b + a
Commutative Property of Addition:
Factor Trees
Exponents
Box Diagram
38. A group is just a collection of objects (i.e. - elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation - each element must have an inverse - the set mu
Aleph-Null
Division is not Associative
Group
Denominator
39. In the expression 3
repeated addition
Geometry
set
Products and Factors
40. The expression a/b means
Distributive Property:
a divided by b
Solve the Equation
One equal sign per line
41. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.
Exponents
Frequency
Public Key Encryption
The Associative Property of Multiplication
42. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.
A number is divisible by 3
Periodic Function
Rarefactior
Geometry
43. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Aleph-Null
Greatest Common Factor (GCF)
Bijection
Problem of the Points
44. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a
˜
Multiplying both Sides of an Equation by the Same Quantity
Additive Inverse:
Spaceland
45. A factor tree is a way to visualize a number's
Flat Land
Multiplicative Inverse:
prime factors
Factor Trees
46. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Greatest Common Factor (GCF)
Invarient
bar graph
The Set of Whole Numbers
47. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Comparison Property
Solution
a divided by b
Overtone
48. Negative
Sign Rules for Division
a divided by b
A number is divisible by 5
Commutative Property of Multiplication:
49. Positive integers are
Irrational
counting numbers
Grouping Symbols
Noether's Theorem
50. The state of appearing unchanged.
Invarient
Problem of the Points
does not change the solution set.
The inverse of subtraction is addition