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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. 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.
Genus
A number is divisible by 10
Distributive Property:
Galton Board
2. 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
variable
The BML Traffic Model
Flat Land
Rarefactior
3. Is a symbol (usually a letter) that stands for a value that may vary.
Products and Factors
set
Least Common Multiple (LCM)
Variable
4. 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)
a - c = b - c
inline
Continuous
Commensurability
5. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.
Axiomatic Systems
repeated addition
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.
Spherical Geometry
6. 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).
A number is divisible by 9
A number is divisible by 3
Fourier Analysis and Synthesis
Factor Trees
7. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Configuration Space
Galton Board
In Euclidean four-space
Fundamental Theorem of Arithmetic
8. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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9. 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
Rational
Discrete
counting numbers
10. If a = b then
a - c = b - c
Flat Land
Symmetry
Conditional Probability
11. 4 more than a certain number is 12
4 + x = 12
Multiplicative Inverse:
a - c = b - c
The Multiplicative Identity Property
12. Originally known as analysis situs
Topology
Amplitude
Fourier Analysis
Euler Characteristic
13. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Configuration Space
Irrational
Comparison Property
Geometry
14. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Galois Theory
Periodic Function
The Prime Number Theorem
Ramsey Theory
15. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
variable
Continuous
Public Key Encryption
Answer the Question
16. An important part of problem solving is identifying
each whole number can be uniquely decomposed into products of primes.
Denominator
Extrinsic View
variable
17. Writing Mathematical equations - arrange your work one equation
a · c = b · c for c does not equal 0
The Prime Number Theorem
Distributive Property:
per line
18. 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.'
Multiplication by Zero
The Prime Number Theorem
Bijection
Equation
19. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Geometry
Irrational
Grouping Symbols
Non-Euclidian Geometry
20. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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21. The expression a/b means
Invarient
a divided by b
Grouping Symbols
Properties of Equality
22. The system that Euclid used in The Elements
Principal Curvatures
Division is not Associative
Axiomatic Systems
The Additive Identity Property
23. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
One equal sign per line
Pigeonhole Principle
Equivalent Equations
Set up an Equation
24. 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.
Figurate Numbers
bar graph
Public Key Encryption
1. The unit 2. Prime numbers 3. Composite numbers
25. Has no factors other than 1 and itself
Hamilton Cycle
A prime number
Frequency
Multiplicative Identity:
26. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Hamilton Cycle
Polynomial
inline
Associate Property of Addition
27. ____________ 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
Set up an Equation
Commutative Property of Multiplication
Dimension
Probability
28. The study of shape from an external perspective.
Multiplication
The Same
Extrinsic View
The BML Traffic Model
29. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Rarefactior
Prime Number
Composite Numbers
Non-Euclidian Geometry
30. If a represents any whole number - then a
Multiplication by Zero
Bijection
Periodic Function
Denominator
31. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Galton Board
Prime Deserts
The Kissing Circle
the set of natural numbers
32. 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
Hamilton Cycle
The inverse of subtraction is addition
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
33. 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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34. 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.'
Box Diagram
Wave Equation
Hyperland
Divisible
35. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Geometry
The Riemann Hypothesis
Axiomatic Systems
Set up an Equation
36. Requirements for Word Problem Solutions.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Divisible
does not change the solution set.
The Associative Property of Multiplication
37. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Associative Property of Addition:
Prime Deserts
Countable
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
38. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Hyperbolic Geometry
Solution
Galois Theory
Grouping Symbols
39. (a · b) · c = a · (b · c)
Problem of the Points
Associative Property of Multiplication:
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
The Prime Number Theorem
40. 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.
A prime number
repeated addition
The inverse of addition is subtraction
Principal Curvatures
41. 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).
The Prime Number Theorem
Prime Number
Markov Chains
The Associative Property of Multiplication
42. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Modular Arithmetic
Division is not Commutative
a · c = b · c for c does not equal 0
Line Land
43. A graph in which every node is connected to every other node is called a complete graph.
Complete Graph
Polynomial
evaluate the expression in the innermost pair of grouping symbols first.
Spaceland
44. Cannot be written as a ratio of natural numbers.
The Multiplicative Identity Property
Irrational
Rational
prime factors
45. A way to measure how far away a given individual result is from the average result.
A number is divisible by 3
Standard Deviation
The Riemann Hypothesis
Grouping Symbols
46. 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
Continuous
Figurate Numbers
Galois Theory
47. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Galton Board
Transfinite
Intrinsic View
Discrete
48. 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
1. The unit 2. Prime numbers 3. Composite numbers
The inverse of addition is subtraction
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.
49. Index p radicand
Multiplicative Inverse:
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The BML Traffic Model
Tone
50. A · 1 = 1 · a = a
Comparison Property
Unique Factorization Theorem
Conditional Probability
Multiplicative Identity: