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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. Original Balance minus River Tam's Withdrawal is Current Balance
Multiplication
Grouping Symbols
Law of Large Numbers
B - 125 = 1200
2. Mathematical statement that equates two mathematical expressions.
Grouping Symbols
Multiplicative Identity:
Equation
Euclid's Postulates
3. 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 Multiplicative Identity Property
Wave Equation
Law of Large Numbers
a + c = b + c
4. 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
In Euclidean four-space
Group
Symmetry
Set up an Equation
5. 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.
A number is divisible by 10
Intrinsic View
Public Key Encryption
Tone
6. The fundamental theorem of arithmetic says that
Standard Deviation
a
each whole number can be uniquely decomposed into products of primes.
The inverse of multiplication is division
7. A + 0 = 0 + a = a
Additive Identity:
Stereographic Projection
The inverse of subtraction is addition
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.
8. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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9. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Extrinsic View
Pigeonhole Principle
The Prime Number Theorem
The Additive Identity Property
10. An important part of problem solving is identifying
Markov Chains
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
variable
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
11. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Line Land
Least Common Multiple (LCM)
Set up a Variable Dictionary.
12. The amount of displacement - as measured from the still surface line.
Amplitude
Rarefactior
Solve the Equation
Torus
13. 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.
Continuous Symmetry
˜
Prime Deserts
Hypersphere
14. The process of taking a complicated signal and breaking it into sine and cosine components.
Multiplying both Sides of an Equation by the Same Quantity
The Commutative Property of Addition
Division is not Commutative
Fourier Analysis
15. Determines the likelihood of events that are not independent of one another.
Principal Curvatures
set
Multiplicative Inverse:
Conditional Probability
16. 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.
Hyperbolic Geometry
Continuous Symmetry
B - 125 = 1200
Galois Theory
17. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Amplitude
Multiplying both Sides of an Equation by the Same Quantity
Properties of Equality
Distributive Property:
18. 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.
Extrinsic View
Normal Distribution
a + c = b + c
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.
19. A number is divisible by 2
Multiplicative Identity:
The Commutative Property of Addition
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Frequency
20. 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).
A number is divisible by 9
bar graph
Prime Number
Associative Property of Multiplication:
21. In the expression 3
Exponents
Products and Factors
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Cardinality
22. 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.
Probability
Additive Identity:
Galton Board
Axiomatic Systems
23. A way to measure how far away a given individual result is from the average result.
prime factors
Comparison Property
Central Limit Theorem
Standard Deviation
24. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
Periodic Function
The Additive Identity Property
Rational
25. Writing Mathematical equations - arrange your work one equation
Hypersphere
Solve the Equation
variable
per line
26. All integers are thus divided into three classes:
1. The unit 2. Prime numbers 3. Composite numbers
Division by Zero
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
Rarefactior
27. 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
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.
Markov Chains
Answer the Question
A number is divisible by 10
28. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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29. A · 1 = 1 · a = a
Division is not Commutative
per line
Euclid's Postulates
Multiplicative Identity:
30. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Properties of Equality
Factor Tree Alternate Approach
Figurate Numbers
The Associative Property of Multiplication
31. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
The Distributive Property (Subtraction)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Prime Deserts
Principal Curvatures
32. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Properties of Equality
Fourier Analysis and Synthesis
a + c = b + c
Hypersphere
33. The expression a/b means
Factor Trees
Division is not Commutative
Conditional Probability
a divided by b
34. If a = b then
a + c = b + c
Frequency
Set up a Variable Dictionary.
Polynomial
35. Einstein's famous theory - relates gravity to the curvature of spacetime.
Standard Deviation
Fundamental Theorem of Arithmetic
Tone
General Relativity
36. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
per line
Products and Factors
Galois Theory
Multiplication by Zero
37. Means approximately equal.
The Kissing Circle
A number is divisible by 9
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
˜
38. Rules for Rounding - To round a number to a particular place - follow these steps:
Hyperland
Normal Distribution
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
The inverse of subtraction is addition
39. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
Multiplication
Grouping Symbols
Irrational
40. 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.
a + c = b + c
Ramsey Theory
Equation
Set up a Variable Dictionary.
41. A flat map of hyperbolic space.
The Kissing Circle
A number is divisible by 5
Poincare Disk
Torus
42. 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
Division is not Associative
A number is divisible by 9
Periodic Function
Look Back
43. If a is any whole number - then a
Greatest Common Factor (GCF)
The Multiplicative Identity Property
Poincare Disk
In Euclidean four-space
44. Uses second derivatives to relate acceleration in space to acceleration in time.
Division is not Commutative
Wave Equation
Additive Inverse:
Modular Arithmetic
45. 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
evaluate the expression in the innermost pair of grouping symbols first.
Standard Deviation
Continuous
Pigeonhole Principle
46. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Associate Property of Addition
Complete Graph
Euler Characteristic
Continuous Symmetry
47. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Continuous
Associate Property of Addition
Bijection
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
48. Are the fundamental building blocks of arithmetic.
Primes
Line Land
Multiplication
Irrational
49. A graph in which every node is connected to every other node is called a complete graph.
Primes
The Same
Complete Graph
A number is divisible by 5
50. If grouping symbols are nested
Non-Euclidian Geometry
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
evaluate the expression in the innermost pair of grouping symbols first.
Modular Arithmetic