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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.
Galton Board
Greatest Common Factor (GCF)
Public Key Encryption
Tone
2. A
The Additive Identity Property
Division is not Commutative
The Set of Whole Numbers
Solution
3. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Prime Deserts
Problem of the Points
Denominator
1. The unit 2. Prime numbers 3. Composite numbers
4. Cannot be written as a ratio of natural numbers.
Non-Orientability
Irrational
bar graph
Division by Zero
5. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
The inverse of addition is subtraction
the set of natural numbers
Irrational
Factor Tree Alternate Approach
6. A · 1/a = 1/a · a = 1
Spherical Geometry
Multiplicative Inverse:
Commutative Property of Multiplication
repeated addition
7. 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
Rarefactior
Associative Property of Addition:
variable
The Same
8. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'
Markov Chains
Fourier Analysis and Synthesis
Group
Divisible
9. 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
The Same
Continuous Symmetry
The BML Traffic Model
Pigeonhole Principle
10. 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.
Cardinality
a + c = b + c
Hyperbolic Geometry
Transfinite
11. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Conditional Probability
does not change the solution set.
Box Diagram
Normal Distribution
12. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
Periodic Function
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Fourier Analysis and Synthesis
13. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Fourier Analysis and Synthesis
Factor Trees
set
Division is not Commutative
14. Is a path that visits every node in a graph and ends where it began.
Hamilton Cycle
Galois Theory
Primes
Cardinality
15. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Pigeonhole Principle
Greatest Common Factor (GCF)
Line Land
Expected Value
16. 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.
Noether's Theorem
Invarient
The BML Traffic Model
Frequency
17. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Solution
Look Back
In Euclidean four-space
Hyperbolic Geometry
18. Index p radicand
Invarient
Topology
Axiomatic Systems
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
19. 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.'
Divisible
Answer the Question
Rational
The Prime Number Theorem
20. Mathematical statement that equates two mathematical expressions.
Non-Euclidian Geometry
Continuous
Fundamental Theorem of Arithmetic
Equation
21. Uses second derivatives to relate acceleration in space to acceleration in time.
Dimension
Irrational
Group
Wave Equation
22. If a = b then
Fundamental Theorem of Arithmetic
per line
a · c = b · c for c does not equal 0
De Bruijn Sequence
23. Is a symbol (usually a letter) that stands for a value that may vary.
˜
Variable
prime factors
Ramsey Theory
24. A + b = b + a
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Distributive Property:
Dimension
Commutative Property of Addition:
25. This method can create a flat map from a curved surface while preserving all angles in any features present.
Multiplication by Zero
1. The unit 2. Prime numbers 3. Composite numbers
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
Stereographic Projection
26. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Properties of Equality
Equivalent Equations
Countable
Torus
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
Probability
Permutation
The BML Traffic Model
Multiplication by Zero
28. A · 1 = 1 · a = a
Division is not Commutative
A number is divisible by 3
Multiplicative Identity:
Euler Characteristic
29. 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.
Multiplication
Problem of the Points
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Transfinite
30. If grouping symbols are nested
Prime Deserts
Countable
evaluate the expression in the innermost pair of grouping symbols first.
a
31. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Periodic Function
set
The Distributive Property (Subtraction)
Hypercube
32. 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).
Flat Land
Multiplication by Zero
Euler Characteristic
A number is divisible by 9
33. Let a - b - and c be any whole numbers. Then - a
Probability
The Distributive Property (Subtraction)
Periodic Function
counting numbers
34. 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.
Galois Theory
Normal Distribution
Cardinality
Additive Inverse:
35. If a = b then
a + c = b + c
The Set of Whole Numbers
Multiplication
Cayley's Theorem
36. The system that Euclid used in The Elements
Axiomatic Systems
Least Common Multiple (LCM)
Discrete
Additive Identity:
37. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
The Kissing Circle
Fourier Analysis and Synthesis
A number is divisible by 9
Geometry
38. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Prime Number
the set of natural numbers
bar graph
Figurate Numbers
39. Requirements for Word Problem Solutions.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Factor Tree Alternate Approach
Central Limit Theorem
Galois Theory
40. The inverse of multiplication
division
Symmetry
1. The unit 2. Prime numbers 3. Composite numbers
Answer the Question
41. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco
Look Back
variable
Conditional Probability
A number is divisible by 3
42. A topological invariant that relates a surface's vertices - edges - and faces.
Euler Characteristic
Ramsey Theory
Hyperland
Euclid's Postulates
43. Originally known as analysis situs
Continuous
does not change the solution set.
Normal Distribution
Topology
44. 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
Symmetry
˜
Prime Deserts
Probability
45. Dimension is how mathematicians express the idea of degrees of freedom
The inverse of subtraction is addition
Dimension
Division by Zero
prime factors
46. A flat map of hyperbolic space.
Primes
Poincare Disk
Torus
Commensurability
47. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Torus
Principal Curvatures
Solution
Flat Land
48. 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.
Topology
Bijection
The Kissing Circle
A number is divisible by 9
49. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.
Solution
Multiplying both Sides of an Equation by the Same Quantity
Additive Inverse:
Commensurability
50. 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
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Hypersphere
perimeter
A number is divisible by 5
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