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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. 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.
Ramsey Theory
Multiplying both Sides of an Equation by the Same Quantity
Topology
Variable
2. 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).
Least Common Multiple (LCM)
Composite Numbers
The inverse of addition is subtraction
Prime Number
3. Originally known as analysis situs
Standard Deviation
Topology
Countable
Transfinite
4. When writing mathematical statements - follow the mantra:
a · c = b · c for c does not equal 0
One equal sign per line
a divided by b
Non-Orientability
5. A factor tree is a way to visualize a number's
Additive Identity:
The inverse of subtraction is addition
The Associative Property of Multiplication
prime factors
6. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Box Diagram
Multiplicative Identity:
Markov Chains
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
7. Rules for Rounding - To round a number to a particular place - follow these steps:
Non-Orientability
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
Figurate Numbers
Axiomatic Systems
8. 1. Find the prime factorizations of each number.
Transfinite
Greatest Common Factor (GCF)
Bijection
Hyperbolic Geometry
9. Add and subtract
prime factors
inline
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Euler Characteristic
10. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Probability
Divisible
Flat Land
Bijection
11. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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12. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Cayley's Theorem
Pigeonhole Principle
Periodic Function
Hyperbolic Geometry
13. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
the set of natural numbers
perimeter
Symmetry
Euclid's Postulates
14. A
Hyperbolic Geometry
Division is not Commutative
The Prime Number Theorem
Division by Zero
15. An algebraic 'sentence' containing an unknown quantity.
repeated addition
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Polynomial
Aleph-Null
16. 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).
Central Limit Theorem
Ramsey Theory
A number is divisible by 3
a + c = b + c
17. If a is any whole number - then a
Continuous
Permutation
Associative Property of Multiplication:
The Multiplicative Identity Property
18. 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.
Extrinsic View
Tone
Composite Numbers
Galton Board
19. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
repeated addition
Torus
Unique Factorization Theorem
Central Limit Theorem
20. 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
Least Common Multiple (LCM)
Unique Factorization Theorem
The inverse of multiplication is division
˜
21. If grouping symbols are nested
The inverse of addition is subtraction
evaluate the expression in the innermost pair of grouping symbols first.
Wave Equation
Equivalent Equations
22. 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.
Multiplication
Law of Large Numbers
Hamilton Cycle
Public Key Encryption
23. 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
Stereographic Projection
Galois Theory
Rarefactior
The Same
24. 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.
Genus
Variable
Solution
Bijection
25. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Dimension
Continuous Symmetry
the set of natural numbers
a
26. A topological object that can be used to study the allowable states of a given system.
Exponents
Configuration Space
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Non-Orientability
27. The expression a/b means
Topology
a divided by b
Associative Property of Addition:
Commutative Property of Addition:
28. Arise from the attempt to measure all quantities with a common unit of measure.
Irrational
Rational
Denominator
Divisible
29. A point in three-dimensional space requires three numbers to fix its location.
repeated addition
The Set of Whole Numbers
Conditional Probability
Spaceland
30. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in
Answer the Question
Prime Number
Hamilton Cycle
Probability
31. 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
Modular Arithmetic
Aleph-Null
Multiplication by Zero
32. Multiplication is equivalent to
repeated addition
inline
Aleph-Null
a · c = b · c for c does not equal 0
33. The study of shape from the perspective of being on the surface of the shape.
Cayley's Theorem
Intrinsic View
Conditional Probability
bar graph
34. This method can create a flat map from a curved surface while preserving all angles in any features present.
Overtone
bar graph
Continuous Symmetry
Stereographic Projection
35. Writing Mathematical equations - arrange your work one equation
Comparison Property
Fourier Analysis
per line
Divisible
36. 4 more than a certain number is 12
Topology
Factor Tree Alternate Approach
Galton Board
4 + x = 12
37. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Spherical Geometry
The Set of Whole Numbers
B - 125 = 1200
Symmetry
38. Negative
Sign Rules for Division
Rarefactior
Aleph-Null
The Commutative Property of Addition
39. 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.'
Galois Theory
Associate Property of Addition
Continuous
Hyperland
40. 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.'
a · c = b · c for c does not equal 0
Primes
The Prime Number Theorem
Commensurability
41. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Standard Deviation
Frequency
Grouping Symbols
Associative Property of Addition:
42. 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
Factor Tree Alternate Approach
a + c = b + c
Probability
43. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Stereographic Projection
Countable
Greatest Common Factor (GCF)
Invarient
44. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
Spherical Geometry
The Set of Whole Numbers
Commutative Property of Multiplication:
45. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
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
4 + x = 12
Irrational
Normal Distribution
46. Original Balance minus River Tam's Withdrawal is Current Balance
B - 125 = 1200
Ramsey Theory
Law of Large Numbers
Hypersphere
47. A way to measure how far away a given individual result is from the average result.
counting numbers
˜
One equal sign per line
Standard Deviation
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.
Law of Large Numbers
Box Diagram
Irrational
a · c = b · c for c does not equal 0
49. Has no factors other than 1 and itself
A prime number
Commutative Property of Multiplication
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Dividing both Sides of an Equation by the Same Quantity
50. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Figurate Numbers
Periodic Function
The BML Traffic Model
Irrational