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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. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar
Least Common Multiple (LCM)
set
Commutative Property of Addition:
Additive Identity:
2. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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3. 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.
Public Key Encryption
Bijection
Amplitude
Flat Land
4. 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
The Distributive Property (Subtraction)
Divisible
Spaceland
5. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
Associate Property of Addition
Prime Number
A number is divisible by 3
6. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Principal Curvatures
A number is divisible by 10
Periodic Function
set
7. Solving Equations
The Kissing Circle
Flat Land
1. Simplify the expression on either side of the equation. 2. Gather the variable term on the left-hand side (LHS) by adding to both sides. the opposite of the variable term on the right-hand side (RHS). Note: either side is fine but we will consiste
The Multiplicative Identity Property
8. Writing Mathematical equations - arrange your work one equation
per line
Hypercube
Hamilton Cycle
Bijection
9. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
˜
Extrinsic View
Galois Theory
Wave Equation
10. You must always solve the equation set up in the previous step.
Additive Inverse:
Solve the Equation
counting numbers
Division by Zero
11. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Normal Distribution
Solve the Equation
Box Diagram
Aleph-Null
12. 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.
Commutative Property of Addition:
Euler Characteristic
Dividing both Sides of an Equation by the Same Quantity
Ramsey Theory
13. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
The Kissing Circle
Expected Value
Figurate Numbers
Continuous
14. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).
Irrational
A number is divisible by 3
left to right
Law of Large Numbers
15. In the expression 3
a · c = b · c for c does not equal 0
Fundamental Theorem of Arithmetic
Products and Factors
Amplitude
16. 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
Answer the Question
a · c = b · c for c does not equal 0
Probability
Problem of the Points
17. Einstein's famous theory - relates gravity to the curvature of spacetime.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
General Relativity
A number is divisible by 5
Hyperland
18. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Dimension
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
inline
In Euclidean four-space
19. Cannot be written as a ratio of natural numbers.
Problem of the Points
The Riemann Hypothesis
Properties of Equality
Irrational
20. 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.
Noether's Theorem
Configuration Space
Bijection
does not change the solution set.
21. A way to measure how far away a given individual result is from the average result.
Poincare Disk
Fourier Analysis
B - 125 = 1200
Standard Deviation
22. Dimension is how mathematicians express the idea of degrees of freedom
Primes
Dimension
Law of Large Numbers
The Same
23. (a · b) · c = a · (b · c)
Associative Property of Multiplication:
Principal Curvatures
Markov Chains
The Prime Number Theorem
24. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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25. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is
Associate Property of Addition
Cayley's Theorem
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The Same
26. The system that Euclid used in The Elements
Axiomatic Systems
Line Land
Fundamental Theorem of Arithmetic
Genus
27. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a
Multiplying both Sides of an Equation by the Same Quantity
Overtone
4 + x = 12
Look Back
28. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Non-Orientability
Irrational
a + c = b + c
Probability
29. A + (-a) = (-a) + a = 0
Wave Equation
does not change the solution set.
Spherical Geometry
Additive Inverse:
30. Two equations if they have the same solution set.
Properties of Equality
Equivalent Equations
Fundamental Theorem of Arithmetic
set
31. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Commutative Property of Multiplication:
Aleph-Null
Associative Property of Multiplication:
repeated addition
32. 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.
Ramsey Theory
Cardinality
A number is divisible by 9
Transfinite
33. 1. Find the prime factorizations of each number.
Greatest Common Factor (GCF)
One equal sign per line
Set up an Equation
Multiplying both Sides of an Equation by the Same Quantity
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.
Normal Distribution
1. The unit 2. Prime numbers 3. Composite numbers
The Kissing Circle
Fundamental Theorem of Arithmetic
35. Mathematical statement that equates two mathematical expressions.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Hypercube
Commensurability
Equation
36. A · 1 = 1 · a = a
Multiplicative Identity:
Noether's Theorem
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Cayley's Theorem
37. If a is any whole number - then a
The inverse of addition is subtraction
Division is not Commutative
The Multiplicative Identity Property
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
38. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com
Solve the Equation
The Commutative Property of Addition
Look Back
Frequency
39. If a = b then
a
Hyperland
Complete Graph
Rarefactior
40. 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
A number is divisible by 3
perimeter
Group
41. Is a path that visits every node in a graph and ends where it began.
Hamilton Cycle
A number is divisible by 3
perimeter
Axiomatic Systems
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
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Commutative Property of Multiplication
Associative Property of Multiplication:
Look Back
43. Perform all additions and subtractions in the order presented
Multiplication
does not change the solution set.
left to right
Configuration Space
44. 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).
Cardinality
Aleph-Null
A number is divisible by 9
Ramsey Theory
45. 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
Equation
Multiplication by Zero
Rarefactior
Discrete
46. 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.
Normal Distribution
Products and Factors
A number is divisible by 9
Non-Orientability
47. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Discrete
Comparison Property
The Distributive Property (Subtraction)
Overtone
48. 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.
Grouping Symbols
Exponents
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Cayley's Theorem
49. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
the set of natural numbers
Problem of the Points
Cardinality
Unique Factorization Theorem
50. A
Division is not Commutative
Tone
Commensurability
Properties of Equality