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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. 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.
Primes
Public Key Encryption
Amplitude
evaluate the expression in the innermost pair of grouping symbols first.
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
A number is divisible by 5
Rarefactior
Division is not Associative
Divisible
3. A
Euclid's Postulates
The Set of Whole Numbers
A prime number
Division is not Commutative
4. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Fourier Analysis and Synthesis
Division is not Commutative
Dimension
the set of natural numbers
5. 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
Associative Property of Addition:
Primes
Noether's Theorem
Hypercube
6. 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.
Symmetry
Hyperbolic Geometry
Hypercube
Comparison Property
7. Perform all additions and subtractions in the order presented
Axiomatic Systems
The Set of Whole Numbers
Hyperbolic Geometry
left to right
8. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Law of Large Numbers
Torus
Associate Property of Addition
The Prime Number Theorem
9. 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
Line Land
Look Back
The Additive Identity Property
Standard Deviation
10. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Rarefactior
Overtone
Commutative Property of Multiplication:
Equation
11. Is the shortest string that contains all possible permutations of a particular length from a given set.
De Bruijn Sequence
a + c = b + c
repeated addition
Hypercube
12. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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13. Einstein's famous theory - relates gravity to the curvature of spacetime.
1. The unit 2. Prime numbers 3. Composite numbers
General Relativity
Distributive Property:
Genus
14. 1. Find the prime factorizations of each number.
Division by Zero
Discrete
The Kissing Circle
Greatest Common Factor (GCF)
15. 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.
Intrinsic View
Solution
a + c = b + c
Spherical Geometry
16. If a = b then
Cardinality
Poincare Disk
a + c = b + c
Prime Deserts
17. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
prime factors
a - c = b - c
Non-Orientability
set
18. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Central Limit Theorem
Factor Tree Alternate Approach
Modular Arithmetic
Expected Value
19. Determines the likelihood of events that are not independent of one another.
Extrinsic View
Spherical Geometry
Configuration Space
Conditional Probability
20. Let a - b - and c be any whole numbers. Then - a
bar graph
Multiplicative Identity:
The Distributive Property (Subtraction)
left to right
21. 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.
Equivalent Equations
The BML Traffic Model
Rational
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
22. If a = b then
set
Non-Euclidian Geometry
a
Associative Property of Multiplication:
23. The surface of a standard 'donut shape'.
The Kissing Circle
Torus
Extrinsic View
Periodic Function
24. Dimension is how mathematicians express the idea of degrees of freedom
Commutative Property of Multiplication
Dimension
Multiplicative Inverse:
Composite Numbers
25. 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
Axiomatic Systems
Figurate Numbers
In Euclidean four-space
26. 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 Kissing Circle
Multiplicative Inverse:
The Prime Number Theorem
The Riemann Hypothesis
27. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Associative Property of Addition:
Continuous
Distributive Property:
Associative Property of Multiplication:
28. A · 1/a = 1/a · a = 1
Geometry
Multiplicative Inverse:
Ramsey Theory
Figurate Numbers
29. A graph in which every node is connected to every other node is called a complete graph.
Complete Graph
The Set of Whole Numbers
A number is divisible by 5
Geometry
30. The state of appearing unchanged.
Complete Graph
Invarient
The Prime Number Theorem
Associate Property of Addition
31. 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
B - 125 = 1200
Hypersphere
Symmetry
Rarefactior
32. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.
does not change the solution set.
Commutative Property of Addition:
Galton Board
Extrinsic View
33. You must always solve the equation set up in the previous step.
Prime Deserts
Multiplication
a divided by b
Solve the Equation
34. 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.
Discrete
set
per line
Non-Orientability
35. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
per line
Symmetry
Genus
Extrinsic View
36. Mathematical statement that equates two mathematical expressions.
Central Limit Theorem
Figurate Numbers
Divisible
Equation
37. Has no factors other than 1 and itself
Aleph-Null
A prime number
Multiplying both Sides of an Equation by the Same Quantity
Modular Arithmetic
38. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -
4 + x = 12
Geometry
The inverse of subtraction is addition
A number is divisible by 9
39. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Galois Theory
The inverse of subtraction is addition
Rational
Non-Euclidian Geometry
40. A + (-a) = (-a) + a = 0
Additive Inverse:
A number is divisible by 3
Spaceland
Fourier Analysis
41. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Fourier Analysis
Box Diagram
Intrinsic View
the set of natural numbers
42. 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.
variable
Symmetry
Continuous
Normal Distribution
43. 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).
Markov Chains
Axiomatic Systems
Prime Number
Sign Rules for Division
44. 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.
1. The unit 2. Prime numbers 3. Composite numbers
The Distributive Property (Subtraction)
Non-Orientability
Cardinality
45. 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.
Multiplication
Public Key Encryption
bar graph
Unique Factorization Theorem
46. Writing Mathematical equations - arrange your work one equation
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
A number is divisible by 10
Multiplying both Sides of an Equation by the Same Quantity
per line
47. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Solve the Equation
Central Limit Theorem
Additive Identity:
Periodic Function
48. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
set
Look Back
Permutation
49. 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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50. 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.
Dimension
Ramsey Theory
Additive Inverse:
The Prime Number Theorem