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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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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 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)
Countable
Continuous Symmetry
Overtone
Commensurability
2. 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.
Continuous Symmetry
Commutative Property of Multiplication
Hamilton Cycle
Division by Zero
3. 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.
Answer the Question
Public Key Encryption
B - 125 = 1200
˜
4. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Factor Trees
Box Diagram
Poincare Disk
One equal sign per line
5. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Bijection
Multiplying both Sides of an Equation by the Same Quantity
Fourier Analysis
Discrete
6. The inverse of multiplication
a · c = b · c for c does not equal 0
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Division is not Associative
division
7. The expression a/b means
a divided by b
Associative Property of Multiplication:
Commutative Property of Multiplication:
The Set of Whole Numbers
8. A · 1 = 1 · a = a
Commutative Property of Addition:
Multiplicative Identity:
Hamilton Cycle
Frequency
9. × - ( )( ) - · - 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
Aleph-Null
Associative Property of Multiplication:
Hyperland
Multiplication
10. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
The inverse of subtraction is addition
Markov Chains
counting numbers
a divided by b
11. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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12. An algebraic 'sentence' containing an unknown quantity.
Aleph-Null
a - c = b - c
Polynomial
Pigeonhole Principle
13. 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.
Variable
Solve the Equation
Divisible
Non-Orientability
14. Let a - b - and c be any whole numbers. Then - a
The Distributive Property (Subtraction)
Figurate Numbers
Probability
inline
15. 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
Principal Curvatures
The BML Traffic Model
Flat Land
perimeter
16. An arrangement where order matters.
Hyperland
Discrete
Permutation
A number is divisible by 10
17. This method can create a flat map from a curved surface while preserving all angles in any features present.
Countable
Expected Value
Solve the Equation
Stereographic Projection
18. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A
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19. When writing mathematical statements - follow the mantra:
Continuous Symmetry
Probability
One equal sign per line
Commensurability
20. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Solve the Equation
Additive Inverse:
Figurate Numbers
Principal Curvatures
21. 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
Factor Trees
Denominator
In Euclidean four-space
One equal sign per line
22. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
Associate Property of Addition
Transfinite
The Commutative Property of Addition
23. (a · b) · c = a · (b · c)
Commutative Property of Multiplication:
Associative Property of Multiplication:
One equal sign per line
Spherical Geometry
24. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
bar graph
Continuous
Irrational
Dimension
25. 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).
Sign Rules for Division
Variable
Extrinsic View
A number is divisible by 3
26. 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.
Division by Zero
Denominator
does not change the solution set.
The Distributive Property (Subtraction)
27. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
each whole number can be uniquely decomposed into products of primes.
Commensurability
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Periodic Function
28. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Irrational
prime factors
Cardinality
29. Are the fundamental building blocks of arithmetic.
Standard Deviation
Symmetry
Ramsey Theory
Primes
30. Positive integers are
counting numbers
Tone
Central Limit Theorem
a
31. 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
General Relativity
Configuration Space
Division is not Commutative
32. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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33. 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
Aleph-Null
bar graph
Hypercube
Public Key Encryption
34. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Prime Number
Galton Board
Fundamental Theorem of Arithmetic
Grouping Symbols
35. 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
Rarefactior
Additive Identity:
Euler Characteristic
A number is divisible by 3
36. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'
Fundamental Theorem of Arithmetic
Equation
The Prime Number Theorem
Ramsey Theory
37. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Spherical Geometry
Galton Board
Flat Land
Prime Deserts
38. 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
Amplitude
repeated addition
Properties of Equality
39. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Central Limit Theorem
Hypercube
The Associative Property of Multiplication
Prime Number
40. 1. Find the prime factorizations of each number.
Greatest Common Factor (GCF)
Ramsey Theory
Least Common Multiple (LCM)
Composite Numbers
41. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.
Genus
Modular Arithmetic
The Riemann Hypothesis
Intrinsic View
42. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Stereographic Projection
In Euclidean four-space
The Riemann Hypothesis
Transfinite
43. The process of taking a complicated signal and breaking it into sine and cosine components.
A prime number
Fourier Analysis
Multiplication by Zero
Figurate Numbers
44. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
In Euclidean four-space
Commutative Property of Multiplication:
Extrinsic View
Conditional Probability
45. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Distributive Property:
Frequency
Problem of the Points
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
46. 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.
Markov Chains
Tone
Ramsey Theory
Set up a Variable Dictionary.
47. A · b = b · a
Bijection
a
Commutative Property of Multiplication:
Hypersphere
48. Cannot be written as a ratio of natural numbers.
Multiplicative Identity:
Irrational
the set of natural numbers
Hypercube
49. 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
The Same
Division is not Commutative
The Commutative Property of Addition
Rarefactior
50. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
set
Wave Equation
Multiplicative Inverse:
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.