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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. 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
Look Back
Sign Rules for Division
a - c = b - c
Factor Tree Alternate Approach
2. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Intrinsic View
left to right
4 + x = 12
Continuous
3. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.
Transfinite
Periodic Function
Additive Identity:
Equation
4. If a = b then
Galton Board
Amplitude
a · c = b · c for c does not equal 0
counting numbers
5. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
Rational
repeated addition
4 + x = 12
6. 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.
Countable
Public Key Encryption
Euclid's Postulates
Factor Trees
7. A flat map of hyperbolic space.
Overtone
Least Common Multiple (LCM)
A number is divisible by 5
Poincare Disk
8. A · 1 = 1 · a = a
One equal sign per line
Fourier Analysis and Synthesis
Multiplicative Identity:
Extrinsic View
9. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Factor Trees
Ramsey Theory
Multiplication by Zero
Expected Value
10. Division by zero is undefined. Each of the expressions 6
Associative Property of Addition:
Division by Zero
Equivalent Equations
The Multiplicative Identity Property
11. A way to measure how far away a given individual result is from the average result.
Standard Deviation
B - 125 = 1200
Prime Number
Invarient
12. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
left to right
perimeter
Line Land
Markov Chains
13. Index p radicand
Genus
Complete Graph
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The Riemann Hypothesis
14. The system that Euclid used in The Elements
Commensurability
Axiomatic Systems
Complete Graph
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
15. 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
Division by Zero
Geometry
Equivalent Equations
16. 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.'
Factor Tree Alternate Approach
The Prime Number Theorem
Fourier Analysis
Normal Distribution
17. The study of shape from the perspective of being on the surface of the shape.
The Set of Whole Numbers
Symmetry
Irrational
Intrinsic View
18. An important part of problem solving is identifying
variable
Figurate Numbers
Intrinsic View
Law of Large Numbers
19. 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 -
Frequency
The BML Traffic Model
The inverse of addition is subtraction
De Bruijn Sequence
20. A factor tree is a way to visualize a number's
Multiplication
prime factors
Polynomial
The BML Traffic Model
21. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
inline
The inverse of multiplication is division
Continuous Symmetry
The Set of Whole Numbers
22. Originally known as analysis situs
Topology
Rational
The inverse of addition is subtraction
The Commutative Property of Addition
23. If a represents any whole number - then a
Multiplication by Zero
Multiplicative Identity:
Frequency
The Multiplicative Identity Property
24. 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
Aleph-Null
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Answer the Question
Frequency
25. Positive integers are
Flat Land
Transfinite
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.
counting numbers
26. If a = b then
Multiplication
a
prime factors
the set of natural numbers
27. Is the shortest string that contains all possible permutations of a particular length from a given set.
Problem of the Points
Answer the Question
Tone
De Bruijn Sequence
28. The amount of displacement - as measured from the still surface line.
left to right
Amplitude
One equal sign per line
Hamilton Cycle
29. 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
Commutative Property of Addition:
Group
Factor Trees
Polynomial
30. Two equations if they have the same solution set.
Denominator
Associative Property of Multiplication:
Irrational
Equivalent Equations
31. This method can create a flat map from a curved surface while preserving all angles in any features present.
Stereographic Projection
left to right
Expected Value
Transfinite
32. Let a - b - and c be any whole numbers. Then - a
Divisible
counting numbers
The Distributive Property (Subtraction)
Line Land
33. 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
Hyperbolic Geometry
Problem of the Points
does not change the solution set.
34. ____________ 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
Solution
Hyperland
Probability
A number is divisible by 5
35. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).
Prime Number
a · c = b · c for c does not equal 0
Cayley's Theorem
A number is divisible by 5
36. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Irrational
Non-Euclidian Geometry
inline
Expected Value
37. If a is any whole number - then a
One equal sign per line
Irrational
Invarient
The Multiplicative Identity Property
38. All integers are thus divided into three classes:
Public Key Encryption
each whole number can be uniquely decomposed into products of primes.
1. The unit 2. Prime numbers 3. Composite numbers
a · c = b · c for c does not equal 0
39. The state of appearing unchanged.
a + c = b + c
A number is divisible by 10
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.
Invarient
40. 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
Irrational
Overtone
A number is divisible by 9
Hypercube
41. The process of taking a complicated signal and breaking it into sine and cosine components.
division
a divided by b
Hypersphere
Fourier Analysis
42. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Equivalent Equations
a - c = b - c
Distributive Property:
Division is not Associative
43. 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.
A number is divisible by 5
Fourier Analysis
does not change the solution set.
Overtone
44. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Poincare Disk
Grouping Symbols
left to right
Ramsey Theory
45. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Complete Graph
Pigeonhole Principle
Set up an Equation
Principal Curvatures
46. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
left to right
Answer the Question
Rational
47. 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.'
Set up a Variable Dictionary.
Hyperland
Topology
Complete Graph
48. 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.
The Same
Greatest Common Factor (GCF)
Law of Large Numbers
Exponents
49. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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50. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
A prime number
Irrational
Countable
General Relativity