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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. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Standard Deviation
Continuous
Configuration Space
Galois Theory
2. 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.'
Factor Trees
Law of Large Numbers
Divisible
Prime Deserts
3. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that
Multiplying both Sides of an Equation by the Same Quantity
the set of natural numbers
Greatest Common Factor (GCF)
Hypercube
4. Is a path that visits every node in a graph and ends where it began.
4 + x = 12
Sign Rules for Division
Complete Graph
Hamilton Cycle
5. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -
a · c = b · c for c does not equal 0
Spaceland
The inverse of addition is subtraction
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
6. 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
Spaceland
repeated addition
Properties of Equality
7. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
The Same
Discrete
Probability
Multiplicative Inverse:
8. 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.'
Overtone
Variable
The Prime Number Theorem
Irrational
9. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Galois Theory
1. The unit 2. Prime numbers 3. Composite numbers
Division is not Commutative
Greatest Common Factor (GCF)
10. 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.
Hypercube
Division is not Associative
Dividing both Sides of an Equation by the Same Quantity
division
11. This method can create a flat map from a curved surface while preserving all angles in any features present.
Fourier Analysis and Synthesis
Spherical Geometry
A number is divisible by 10
Stereographic Projection
12. Add and subtract
Equivalent Equations
inline
Figurate Numbers
division
13. 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
Fundamental Theorem of Arithmetic
The inverse of multiplication is division
The Associative Property of Multiplication
14. Two equations if they have the same solution set.
a · c = b · c for c does not equal 0
Grouping Symbols
Factor Tree Alternate Approach
Equivalent Equations
15. 1. Find the prime factorizations of each number.
Prime Number
a
Greatest Common Factor (GCF)
Complete Graph
16. 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.
Genus
variable
Normal Distribution
Continuous Symmetry
17. If a = b then
Galton Board
evaluate the expression in the innermost pair of grouping symbols first.
Aleph-Null
a - c = b - c
18. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Complete Graph
Configuration Space
perimeter
Line Land
19. 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
Geometry
Additive Inverse:
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
20. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.
B - 125 = 1200
bar graph
The Set of Whole Numbers
The inverse of multiplication is division
21. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
4 + x = 12
Modular Arithmetic
a divided by b
22. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Galton Board
Fundamental Theorem of Arithmetic
Additive Identity:
1. The unit 2. Prime numbers 3. Composite numbers
23. Uses second derivatives to relate acceleration in space to acceleration in time.
Flat Land
Bijection
variable
Wave Equation
24. Let a and b represent two whole numbers. Then - a + b = b + a.
Expected Value
The Distributive Property (Subtraction)
The Commutative Property of Addition
Associative Property of Multiplication:
25. Originally known as analysis situs
Central Limit Theorem
Factor Tree Alternate Approach
Topology
Equation
26. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.
Cardinality
Modular Arithmetic
Intrinsic View
The inverse of subtraction is addition
27. Means approximately equal.
prime factors
˜
Problem of the Points
Expected Value
28. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Equation
Grouping Symbols
Extrinsic View
Additive Inverse:
29. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Fourier Analysis and Synthesis
Modular Arithmetic
Figurate Numbers
Geometry
30. 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
Extrinsic View
The inverse of multiplication is division
Hypercube
Torus
31. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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32. 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.
Unique Factorization Theorem
Symmetry
The inverse of subtraction is addition
Equivalent Equations
33. The state of appearing unchanged.
Solve the Equation
Amplitude
A number is divisible by 5
Invarient
34. If its final digit is a 0 or 5.
Associative Property of Multiplication:
A number is divisible by 9
Division is not Associative
A number is divisible by 5
35. (a
Principal Curvatures
Configuration Space
Division is not Associative
Primes
36. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Sign Rules for Division
In Euclidean four-space
Distributive Property:
Figurate Numbers
37. If a and b are any whole numbers - then a
Law of Large Numbers
Intrinsic View
Commutative Property of Multiplication
A number is divisible by 5
38. Cannot be written as a ratio of natural numbers.
a divided by b
Irrational
Solution
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.
39. A factor tree is a way to visualize a number's
B - 125 = 1200
Commensurability
A number is divisible by 10
prime factors
40. 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
Multiplication by Zero
Irrational
Denominator
Hypersphere
41. 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.
a + c = b + c
Invarient
Transfinite
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
42. 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
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Set up an Equation
A number is divisible by 3
43. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
does not change the solution set.
Box Diagram
De Bruijn Sequence
a - c = b - c
44. 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.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Bijection
Extrinsic View
Public Key Encryption
45. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Composite Numbers
Answer the Question
Problem of the Points
The Riemann Hypothesis
46. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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47. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.
Look Back
The Associative Property of Multiplication
Associative Property of Multiplication:
Cardinality
48. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Least Common Multiple (LCM)
General Relativity
The Set of Whole Numbers
Division by Zero
49. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t
Factor Tree Alternate Approach
˜
Hypercube
Dividing both Sides of an Equation by the Same Quantity
50. 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.
General Relativity
Pigeonhole Principle
One equal sign per line
Public Key Encryption