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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. 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
a
Factor Trees
Grouping Symbols
Continuous Symmetry
2. A + b = b + a
Commutative Property of Addition:
Normal Distribution
Transfinite
Exponents
3. The expression a^m means a multiplied by itself m times. The number a is called the base of the exponential expression and the number m is called the exponent. The exponent m tells us to repeat the base a as a factor m times.
Exponents
Primes
Genus
Cayley's Theorem
4. 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.
Hamilton Cycle
Galton Board
Flat Land
Geometry
5. A · 1/a = 1/a · a = 1
Standard Deviation
Multiplicative Inverse:
Set up an Equation
Amplitude
6. The surface of a standard 'donut shape'.
each whole number can be uniquely decomposed into products of primes.
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.
Wave Equation
Torus
7. (a
Associative Property of Addition:
Division is not Associative
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Axiomatic Systems
8. The amount of displacement - as measured from the still surface line.
Countable
Continuous
Amplitude
Denominator
9. The process of taking a complicated signal and breaking it into sine and cosine components.
Non-Euclidian Geometry
bar graph
Fourier Analysis
Denominator
10. An arrangement where order matters.
Comparison Property
Continuous Symmetry
Additive Identity:
Permutation
11. 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)
Commensurability
Central Limit Theorem
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.
Non-Euclidian Geometry
12. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.
Geometry
Non-Orientability
Wave Equation
Prime Deserts
13. If a is any whole number - then a
The Multiplicative Identity Property
Division is not Commutative
B - 125 = 1200
Hamilton Cycle
14. 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 Kissing Circle
The Set of Whole Numbers
Look Back
Irrational
15. Uses second derivatives to relate acceleration in space to acceleration in time.
Hypersphere
Wave Equation
counting 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
16. Is the shortest string that contains all possible permutations of a particular length from a given set.
Euclid's Postulates
De Bruijn Sequence
Commensurability
Figurate Numbers
17. 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
Normal Distribution
Topology
Group
18. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Wave Equation
Tone
In Euclidean four-space
Non-Orientability
19. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of
Products and Factors
Figurate Numbers
Hypersphere
Least Common Multiple (LCM)
20. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Prime Number
The Prime Number Theorem
Central Limit Theorem
Line Land
21. The fundamental theorem of arithmetic says that
each whole number can be uniquely decomposed into products of primes.
Solution
In Euclidean four-space
A number is divisible by 5
22. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Set up an Equation
De Bruijn Sequence
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Factor Tree Alternate Approach
23. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
a · c = b · c for c does not equal 0
Commensurability
Fourier Analysis and Synthesis
Denominator
24. If a whole number is not a prime number - then it is called a...
Composite Numbers
Frequency
Symmetry
Hyperland
25. 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
prime factors
Discrete
In Euclidean four-space
Rarefactior
26. A factor tree is a way to visualize a number's
Look Back
prime factors
A number is divisible by 3
Noether's Theorem
27. Original Balance minus River Tam's Withdrawal is Current Balance
B - 125 = 1200
Equivalent Equations
Overtone
Probability
28. 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.'
per line
does not change the solution set.
inline
Divisible
29. Two equations if they have the same solution set.
Cardinality
Dimension
Equivalent Equations
The Additive Identity Property
30. Does not change the solution set. That is - if a = b - then dividing both sides of the equation by c produces the equivalent equation a/c = b/c - provided c = 0.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Galton Board
Dividing both Sides of an Equation by the Same Quantity
The inverse of addition is subtraction
31. ____________ 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
Primes
Euler Characteristic
Extrinsic View
32. 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.
The Same
Hyperland
Fourier Analysis
Public Key Encryption
33. 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.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The Associative Property of Multiplication
Galton Board
Solution
34. The study of shape from an external perspective.
Figurate Numbers
Genus
Extrinsic View
Irrational
35. 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.
counting numbers
Normal Distribution
Non-Euclidian Geometry
division
36. 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.
Cardinality
One equal sign per line
Principal Curvatures
Additive Identity:
37. Cannot be written as a ratio of natural numbers.
Prime Deserts
Irrational
per line
Greatest Common Factor (GCF)
38. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Extrinsic View
Public Key Encryption
Hypercube
Overtone
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.'
bar graph
does not change the solution set.
Hyperland
The Distributive Property (Subtraction)
40. Index p radicand
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Spaceland
per line
Greatest Common Factor (GCF)
41. The state of appearing unchanged.
inline
Overtone
Invarient
Variable
42. 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 Additive Identity Property
The Set of Whole Numbers
A prime number
The BML Traffic Model
43. 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
Exponents
Answer the Question
Associative Property of Addition:
Multiplication
44. A · b = b · a
A number is divisible by 5
Commutative Property of Multiplication:
Noether's Theorem
The Prime Number Theorem
45. Originally known as analysis situs
Hyperbolic Geometry
Topology
a
Composite Numbers
46. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Additive Identity:
The Multiplicative Identity Property
4 + x = 12
47. 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
Genus
Aleph-Null
a
Symmetry
48. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Box Diagram
prime factors
Properties of Equality
Genus
49. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
The inverse of multiplication is division
Flat Land
Markov Chains
Ramsey Theory
50. 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.
Commutative Property of Multiplication
Cayley's Theorem
Associative Property of Addition: