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CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
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.
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. If a - b - and c are any whole numbers - then a
In Euclidean four-space
The Associative Property of Multiplication
Division by Zero
The inverse of multiplication is division
2. A number is divisible by 2
Hypercube
Associative Property of Addition:
Distributive Property:
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
3. Division by zero is undefined. Each of the expressions 6
Law of Large Numbers
The Kissing Circle
a divided by b
Division by Zero
4. Einstein's famous theory - relates gravity to the curvature of spacetime.
A number is divisible by 3
Intrinsic View
Fourier Analysis and Synthesis
General Relativity
5. Let a - b - and c be any whole numbers. Then - a
Probability
Group
Problem of the Points
The Distributive Property (Subtraction)
6. 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
Sign Rules for Division
Rational
The Additive Identity Property
7. If a = b then
Equation
Modular Arithmetic
a · c = b · c for c does not equal 0
per line
8. The fundamental theorem of arithmetic says that
each whole number can be uniquely decomposed into products of primes.
Multiplication by Zero
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Commutative Property of Multiplication:
9. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Dividing both Sides of an Equation by the Same Quantity
Overtone
Axiomatic Systems
The Distributive Property (Subtraction)
10. A + 0 = 0 + a = a
Additive Identity:
Multiplicative Inverse:
Euclid's Postulates
Group
11. When writing mathematical statements - follow the mantra:
each whole number can be uniquely decomposed into products of primes.
Normal Distribution
prime factors
One equal sign per line
12. 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 inverse of multiplication is division
repeated addition
Law of Large Numbers
each whole number can be uniquely decomposed into products of primes.
13. 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.
Configuration Space
Unique Factorization Theorem
General Relativity
Invarient
14. Multiplication is equivalent to
division
repeated addition
Division is not Commutative
Rational
15. Determines the likelihood of events that are not independent of one another.
Conditional Probability
The inverse of subtraction is addition
Hypersphere
Poincare Disk
16. Aka The Osculating Circle - a way to measure the curvature of a line.
Stereographic Projection
Topology
Multiplicative Identity:
The Kissing Circle
17. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.
The Same
Geometry
perimeter
Sign Rules for Division
18. 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.
Dimension
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Spaceland
19. Requirements for Word Problem Solutions.
bar graph
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Variable
Intrinsic View
20. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
Poincare Disk
Frequency
The Commutative Property of Addition
21. If the sum of its digits is divisible by 9 (ex: 3591 is divisible by 9 since 3 + 5 + 9 + 1 = 18 is divisible by 9).
Invarient
Noether's Theorem
Additive Inverse:
A number is divisible by 9
22. 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.'
The Prime Number Theorem
Euler Characteristic
Spaceland
Unique Factorization Theorem
23. This method can create a flat map from a curved surface while preserving all angles in any features present.
Stereographic Projection
Dividing both Sides of an Equation by the Same Quantity
Hyperland
a · c = b · c for c does not equal 0
24. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.
The Distributive Property (Subtraction)
The Riemann Hypothesis
Normal Distribution
Greatest Common Factor (GCF)
25. If a = b then
Modular Arithmetic
a
Multiplication
Associative Property of Addition:
26. A + b = b + a
Commutative Property of Addition:
Rarefactior
Principal Curvatures
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
27. A graph in which every node is connected to every other node is called a complete graph.
division
Complete Graph
Symmetry
Principal Curvatures
28. 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
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
The inverse of multiplication is division
Associative Property of Multiplication:
Non-Orientability
29. Two equations if they have the same solution set.
Box Diagram
Equivalent Equations
inline
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
30. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Rational
Prime Deserts
Countable
A prime number
31. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar
Hypercube
Principal Curvatures
A number is divisible by 9
Least Common Multiple (LCM)
32. 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
Symmetry
Pigeonhole Principle
Galois Theory
repeated addition
33. A way to measure how far away a given individual result is from the average result.
Solution
Axiomatic Systems
Standard Deviation
Additive Inverse:
34. (a
Division is not Associative
Divisible
Probability
Geometry
35. A group is just a collection of objects (i.e. - elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation - each element must have an inverse - the set mu
Group
Distributive Property:
Bijection
perimeter
36. A · 1 = 1 · a = a
Non-Euclidian Geometry
De Bruijn Sequence
Permutation
Multiplicative Identity:
37. 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.
Spherical Geometry
The Set of Whole Numbers
Division is not Associative
Solution
38. 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
Symmetry
Configuration Space
Genus
39. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Permutation
The Set of Whole Numbers
Galois Theory
The BML Traffic Model
40. 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
Flat Land
Extrinsic View
Symmetry
Commensurability
41. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
a · c = b · c for c does not equal 0
Continuous
Prime Deserts
each whole number can be uniquely decomposed into products of primes.
42. To describe and extend a numerical pattern
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.
Galois Theory
Associative Property of Addition:
B - 125 = 1200
43. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Irrational
Prime Deserts
each whole number can be uniquely decomposed into products of primes.
Solution
44. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Extrinsic View
Equivalent Equations
Problem of the Points
Hyperbolic Geometry
45. 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
Geometry
a + c = b + c
Rarefactior
The Multiplicative Identity Property
46. Uses second derivatives to relate acceleration in space to acceleration in time.
Central Limit Theorem
Group
Problem of the Points
Wave Equation
47. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Non-Euclidian Geometry
Aleph-Null
Look Back
Pigeonhole Principle
48. 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.
Division is not Associative
each whole number can be uniquely decomposed into products of primes.
Galton Board
Extrinsic View
49. 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.
Additive Identity:
Continuous Symmetry
Bijection
Flat Land
50. 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.
Wave Equation
Continuous Symmetry
Multiplying both Sides of an Equation by the Same Quantity
Group
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