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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
Start Test
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. The expression a/b means
Additive Identity:
a divided by b
Cayley's Theorem
A number is divisible by 10
2. A flat map of hyperbolic space.
Expected Value
Public Key Encryption
Solution
Poincare Disk
3. A + (-a) = (-a) + a = 0
each whole number can be uniquely decomposed into products of primes.
Additive Inverse:
Ramsey Theory
counting numbers
4. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Exponents
Non-Orientability
Geometry
Box Diagram
5. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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6. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Topology
Comparison Property
inline
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.
7. 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.
Public Key Encryption
The Prime Number Theorem
Hypersphere
Additive Identity:
8. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a
The inverse of multiplication is division
Products and Factors
Bijection
Probability
9. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.
Invarient
Noether's Theorem
Continuous Symmetry
Extrinsic View
10. If a = b then
The inverse of subtraction is addition
Bijection
a + c = b + c
a
11. The amount of displacement - as measured from the still surface line.
Answer the Question
Law of Large Numbers
Hyperbolic Geometry
Amplitude
12. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Equivalent Equations
Greatest Common Factor (GCF)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Continuous
13. Division by zero is undefined. Each of the expressions 6
Least Common Multiple (LCM)
Division by Zero
Spaceland
A prime number
14. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Cardinality
Non-Orientability
Expected Value
Commensurability
15. The process of taking a complicated signal and breaking it into sine and cosine components.
division
Fourier Analysis
General Relativity
Polynomial
16. The state of appearing unchanged.
Standard Deviation
Wave Equation
Variable
Invarient
17. 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.
Unique Factorization Theorem
Set up a Variable Dictionary.
division
Grouping Symbols
18. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'
Unique Factorization Theorem
Normal Distribution
Divisible
per line
19. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t
Dividing both Sides of an Equation by the Same Quantity
Products and Factors
Factor Tree Alternate Approach
Spherical Geometry
20. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Continuous
Grouping Symbols
Aleph-Null
Irrational
21. To describe and extend a numerical pattern
Additive Inverse:
The Distributive Property (Subtraction)
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.
left to right
22. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is
Probability
Multiplication by Zero
The Same
Divisible
23. The expression a^m means a multiplied by itself m times. The number a is called the base of the exponential expression and the number m is called the exponent. The exponent m tells us to repeat the base a as a factor m times.
Continuous
Exponents
variable
left to right
24. Mathematical statement that equates two mathematical expressions.
Primes
4 + x = 12
Overtone
Equation
25. If a = b then
a + c = b + c
Set up an Equation
Group
does not change the solution set.
26. Is a path that visits every node in a graph and ends where it began.
Central Limit Theorem
The Same
Hamilton Cycle
Euclid's Postulates
27. (a · b) · c = a · (b · c)
set
The Same
Associative Property of Multiplication:
Associative Property of Addition:
28. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina
bar graph
Exponents
Multiplicative Inverse:
Factor Trees
29. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.
Intrinsic View
Normal Distribution
Law of Large Numbers
Non-Euclidian Geometry
30. Solving Equations
1. Simplify the expression on either side of the equation. 2. Gather the variable term on the left-hand side (LHS) by adding to both sides. the opposite of the variable term on the right-hand side (RHS). Note: either side is fine but we will consiste
Polynomial
Tone
A prime number
31. Two equations if they have the same solution set.
Continuous Symmetry
Modular Arithmetic
Equivalent Equations
Central Limit Theorem
32. If a - b - and c are any whole numbers - then a
Periodic Function
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The Associative Property of Multiplication
Noether's Theorem
33. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.
Multiplication by Zero
Associate Property of Addition
Bijection
Axiomatic Systems
34. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
set
Countable
Additive Inverse:
The Prime Number Theorem
35. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
evaluate the expression in the innermost pair of grouping symbols first.
Public Key Encryption
Galton Board
Fourier Analysis and Synthesis
36. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
prime factors
Comparison Property
Irrational
repeated addition
37. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Amplitude
Commutative Property of Multiplication:
Set up an Equation
Markov Chains
38. A topological object that can be used to study the allowable states of a given system.
Galois Theory
Configuration Space
division
Genus
39. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to
Distributive Property:
Probability
Solve the Equation
Additive Identity:
40. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Frequency
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Associate Property of Addition
The Additive Identity Property
41. A number is divisible by 2
per line
The Kissing Circle
Dividing both Sides of an Equation by the Same Quantity
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
42. If a whole number is not a prime number - then it is called a...
Composite Numbers
Galton Board
Commutative Property of Addition:
Pigeonhole Principle
43. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
Discrete
Stereographic Projection
Comparison Property
44. The surface of a standard 'donut shape'.
Continuous Symmetry
Torus
Solve the Equation
A number is divisible by 10
45. Are the fundamental building blocks of arithmetic.
Primes
Permutation
each whole number can be uniquely decomposed into products of primes.
In Euclidean four-space
46. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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47. A way to measure how far away a given individual result is from the average result.
Commutative Property of Addition:
Standard Deviation
Periodic Function
1. Simplify the expression on either side of the equation. 2. Gather the variable term on the left-hand side (LHS) by adding to both sides. the opposite of the variable term on the right-hand side (RHS). Note: either side is fine but we will consiste
48. Dimension is how mathematicians express the idea of degrees of freedom
Set up an Equation
Law of Large Numbers
Variable
Dimension
49. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'
Multiplication
the set of natural numbers
Hyperland
Problem of the Points
50. Says that when a random process - such as dropping marbles through a Galton board - is repeated many times - the frequencies of the observed outcomes get increasingly closer to the theoretical probabilities.
Commutative Property of Addition:
Hypersphere
Law of Large Numbers
The inverse of addition is subtraction