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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. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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2. Writing Mathematical equations - arrange your work one equation
Spherical Geometry
Frequency
per line
Commutative Property of Addition:
3. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t
perimeter
Hyperland
Frequency
A number is divisible by 3
4. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Transfinite
The inverse of addition is subtraction
Prime Number
Distributive Property:
5. Mathematical statement that equates two mathematical expressions.
Configuration Space
Hamilton Cycle
bar graph
Equation
6. Index p radicand
The Set of Whole Numbers
a - c = b - c
Noether's Theorem
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
7. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Aleph-Null
General Relativity
Torus
Division by Zero
8. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even
Set up an Equation
Stereographic Projection
Multiplication
the set of natural numbers
9. Negative
Sign Rules for Division
Commutative Property of Multiplication:
Division is not Associative
Continuous Symmetry
10. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Factor Trees
Aleph-Null
Fundamental Theorem of Arithmetic
General Relativity
11. 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.
Divisible
Dimension
˜
Unique Factorization Theorem
12. Arise from the attempt to measure all quantities with a common unit of measure.
Continuous Symmetry
Commutative Property of Addition:
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Rational
13. 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.
Law of Large Numbers
Division is not Associative
Axiomatic Systems
Irrational
14. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar
counting numbers
One equal sign per line
Least Common Multiple (LCM)
Rational
15. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Configuration Space
Prime Deserts
Aleph-Null
Non-Euclidian Geometry
16. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.
Standard Deviation
Grouping Symbols
Non-Orientability
Ramsey Theory
17. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Ramsey Theory
Genus
A number is divisible by 3
Products and Factors
18. 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.
The BML Traffic Model
The inverse of subtraction is addition
Pigeonhole Principle
The Multiplicative Identity Property
19. Aka The Osculating Circle - a way to measure the curvature of a line.
Fourier Analysis and Synthesis
Factor Trees
Equivalent Equations
The Kissing Circle
20. Determines the likelihood of events that are not independent of one another.
1. Mark the place you wish to round to. This is called the rounding digit . 2. Check the next digit to the right of your digit marked in step 1. This is called the test digit . If the test digit is greater than or equal to 5 - add 1 to the rounding d
Products and Factors
Conditional Probability
Multiplication
21. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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22. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com
Frequency
Discrete
Properties of Equality
a divided by b
23. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression
Continuous Symmetry
Ramsey Theory
Expected Value
Rarefactior
24. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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25. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Non-Euclidian Geometry
Associative Property of Multiplication:
Prime Deserts
One equal sign per line
26. 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.'
Principal Curvatures
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Hyperland
Permutation
27. The state of appearing unchanged.
1. Mark the place you wish to round to. This is called the rounding digit . 2. Check the next digit to the right of your digit marked in step 1. This is called the test digit . If the test digit is greater than or equal to 5 - add 1 to the rounding d
Invarient
The Same
Poincare Disk
28. If the sum of its digits is divisible by 9 (ex: 3591 is divisible by 9 since 3 + 5 + 9 + 1 = 18 is divisible by 9).
The Same
The Commutative Property of Addition
Products and Factors
A number is divisible by 9
29. Requirements for Word Problem Solutions.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
a · c = b · c for c does not equal 0
Division is not Commutative
The inverse of addition is subtraction
30. 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.'
Divisible
The Set of Whole Numbers
Periodic Function
Multiplying both Sides of an Equation by the Same Quantity
31. An important part of problem solving is identifying
variable
Geometry
Associative Property of Multiplication:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
32. To describe and extend a numerical pattern
Countable
Products and Factors
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.
Wave Equation
33. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
a + c = b + c
Variable
Fourier Analysis and Synthesis
Irrational
34. This means that for any two magnitudes - one should always be able to find a fundamental unit that fits some whole number of times into each of them (i.e. - a unit whose magnitude is a whole number factor of each of the original magnitudes)
repeated addition
Commensurability
Ramsey Theory
Discrete
35. If a = b then
Hypersphere
a - c = b - c
De Bruijn Sequence
Set up a Variable Dictionary.
36. 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
Hypercube
a · c = b · c for c does not equal 0
1. Mark the place you wish to round to. This is called the rounding digit . 2. Check the next digit to the right of your digit marked in step 1. This is called the test digit . If the test digit is greater than or equal to 5 - add 1 to the rounding d
a divided by b
37. 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
Greatest Common Factor (GCF)
The Associative Property of Multiplication
Standard Deviation
38. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Markov Chains
set
Flat Land
Non-Euclidian Geometry
39. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Non-Euclidian Geometry
Hamilton Cycle
Countable
Distributive Property:
40. The surface of a standard 'donut shape'.
Extrinsic View
Fourier Analysis
Probability
Torus
41. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
The Riemann Hypothesis
Line Land
Bijection
General Relativity
42. 4 more than a certain number is 12
a - c = b - c
counting numbers
Equivalent Equations
4 + x = 12
43. Reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.
Products and Factors
Pigeonhole Principle
Ramsey Theory
Normal Distribution
44. If a represents any whole number - then a
Primes
One equal sign per line
Set up an Equation
Multiplication by Zero
45. Means approximately equal.
The Same
Answer the Question
˜
Non-Euclidian Geometry
46. An arrangement where order matters.
the set of natural numbers
Hamilton Cycle
Equation
Permutation
47. If a = b then
a
Hyperland
bar graph
Cayley's Theorem
48. The study of shape from the perspective of being on the surface of the shape.
Standard Deviation
Continuous
Commensurability
Intrinsic View
49. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
De Bruijn Sequence
prime factors
Properties of Equality
Multiplicative Inverse:
50. A topological invariant that relates a surface's vertices - edges - and faces.
Topology
Euler Characteristic
Tone
Configuration Space