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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 + (-a) = (-a) + a = 0
per line
Divisible
Additive Inverse:
Cayley's Theorem
2. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Division by Zero
Multiplication
In Euclidean four-space
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
3. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
prime factors
Galois Theory
General Relativity
Torus
4. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Grouping Symbols
the set of natural numbers
Law of Large Numbers
Box Diagram
5. ____________ 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
Unique Factorization Theorem
Probability
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Answer the Question
6. Uses second derivatives to relate acceleration in space to acceleration in time.
Factor Trees
Wave Equation
The BML Traffic Model
Commutative Property of Multiplication:
7. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
A number is divisible by 10
Least Common Multiple (LCM)
Distributive Property:
Greatest Common Factor (GCF)
8. Mathematical statement that equates two mathematical expressions.
The Associative Property of Multiplication
Distributive Property:
A prime number
Equation
9. This method can create a flat map from a curved surface while preserving all angles in any features present.
Hypersphere
Stereographic Projection
a divided by b
Modular Arithmetic
10. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Periodic Function
˜
Torus
11. Arise from the attempt to measure all quantities with a common unit of measure.
The Same
Division by Zero
Rational
B - 125 = 1200
12. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
The Riemann Hypothesis
Factor Tree Alternate Approach
Aleph-Null
Frequency
13. 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.
Transfinite
Ramsey Theory
Stereographic Projection
Additive Inverse:
14. Index p radicand
Fourier Analysis and Synthesis
The Prime Number Theorem
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Associative Property of Multiplication:
15. Is a path that visits every node in a graph and ends where it began.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The Same
Hamilton Cycle
Grouping Symbols
16. If a represents any whole number - then a
Tone
Standard Deviation
Set up an Equation
Multiplication by Zero
17. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Continuous
Associative Property of Multiplication:
Transfinite
Look Back
18. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Standard Deviation
Fundamental Theorem of Arithmetic
Stereographic Projection
Factor Trees
19. 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.
Least Common Multiple (LCM)
Variable
Cardinality
Periodic Function
20. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo
Pigeonhole Principle
B - 125 = 1200
Hypersphere
Frequency
21. The process of taking a complicated signal and breaking it into sine and cosine components.
Fourier Analysis
variable
Commutative Property of Multiplication:
Figurate Numbers
22. 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
Least Common Multiple (LCM)
Solution
Line Land
23. N = {1 - 2 - 3 - 4 - 5 - . . .}.
does not change the solution set.
the set of natural numbers
Principal Curvatures
Fundamental Theorem of Arithmetic
24. If a = b then
a divided by b
Multiplying both Sides of an Equation by the Same Quantity
Products and Factors
a - c = b - c
25. An important part of problem solving is identifying
variable
Modular Arithmetic
Composite Numbers
Galois Theory
26. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.
Associative Property of Multiplication:
Principal Curvatures
Expected Value
Answer the Question
27. A + b = b + a
Central Limit Theorem
Noether's Theorem
counting numbers
Commutative Property of Addition:
28. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of
Multiplicative Identity:
The Additive Identity Property
Hypersphere
Configuration Space
29. 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 number is divisible by 9
Equivalent Equations
Fourier Analysis and Synthesis
Box Diagram
30. 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.
Torus
The Riemann Hypothesis
Law of Large Numbers
De Bruijn Sequence
31. When writing mathematical statements - follow the mantra:
The BML Traffic Model
One equal sign per line
Intrinsic View
Tone
32. The state of appearing unchanged.
Amplitude
inline
Invarient
Extrinsic View
33. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -
set
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The inverse of subtraction is addition
Configuration Space
34. 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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35. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.
Galton Board
A number is divisible by 3
The inverse of subtraction is addition
Permutation
36. If a and b are any whole numbers - then a
Configuration Space
Commutative Property of Multiplication
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Flat Land
37. The surface of a standard 'donut shape'.
Torus
Look Back
Galois Theory
Topology
38. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
B - 125 = 1200
Genus
Markov Chains
Symmetry
39. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.
Hyperbolic Geometry
Products and Factors
Stereographic Projection
˜
40. 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 -
Answer the Question
Invarient
The inverse of addition is subtraction
Composite Numbers
41. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Tone
Transfinite
The Set of Whole Numbers
Modular Arithmetic
42. 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
A number is divisible by 3
a
Set up a Variable Dictionary.
43. 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
Set up a Variable Dictionary.
Variable
The Kissing Circle
Amplitude
44. 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
Factor Trees
Topology
The inverse of addition is subtraction
45. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
perimeter
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
Conditional Probability
Central Limit Theorem
46. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Torus
B - 125 = 1200
counting numbers
Non-Euclidian Geometry
47. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
Greatest Common Factor (GCF)
Division by Zero
Periodic Function
48. If its final digit is a 0 or 5.
Multiplication
Expected Value
A number is divisible by 5
a
49. Determines the likelihood of events that are not independent of one another.
Solution
Conditional Probability
Comparison Property
Configuration Space
50. If a whole number is not a prime number - then it is called a...
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.
Cayley's Theorem
Composite Numbers
Aleph-Null