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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. A
Division is not Commutative
Properties of Equality
The Set of Whole Numbers
A prime number
2. The amount of displacement - as measured from the still surface line.
In Euclidean four-space
Probability
Amplitude
Commutative Property of Multiplication:
3. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Division is not Commutative
The Distributive Property (Subtraction)
set
Exponents
4. 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
The BML Traffic Model
4 + x = 12
A number is divisible by 3
5. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
The BML Traffic Model
In Euclidean four-space
Set up an Equation
Associative Property of Multiplication:
6. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
The Multiplicative Identity Property
Aleph-Null
prime factors
Discrete
7. A + b = b + a
Commutative Property of Addition:
Geometry
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
repeated addition
8. Is a path that visits every node in a graph and ends where it began.
Hamilton Cycle
Bijection
The inverse of subtraction is addition
Problem of the Points
9. A topological invariant that relates a surface's vertices - edges - and faces.
a - c = b - c
Division is not Commutative
Euler Characteristic
Axiomatic Systems
10. 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)
The BML Traffic Model
Conditional Probability
Commensurability
Line Land
11. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
counting numbers
A number is divisible by 10
Set up an Equation
Associate Property of Addition
12. An arrangement where order matters.
Normal Distribution
the set of natural numbers
Permutation
Division by Zero
13. Add and subtract
the set of natural numbers
Commutative Property of Multiplication:
Comparison Property
inline
14. When writing mathematical statements - follow the mantra:
Configuration Space
One equal sign per line
In Euclidean four-space
The inverse of addition is subtraction
15. 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.
counting numbers
Multiplying both Sides of an Equation by the Same Quantity
Continuous Symmetry
Poincare Disk
16. Division by zero is undefined. Each of the expressions 6
each whole number can be uniquely decomposed into products of primes.
inline
Division by Zero
a · c = b · c for c does not equal 0
17. 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.
Solve the Equation
Law of Large Numbers
Spherical Geometry
Denominator
18. You must always solve the equation set up in the previous step.
Division is not Commutative
Solve the Equation
Conditional Probability
Comparison Property
19. The surface of a standard 'donut shape'.
Extrinsic View
Torus
Look Back
Factor Tree Alternate Approach
20. 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
Group
Prime Number
Look Back
The inverse of multiplication is division
21. In the expression 3
Products and Factors
Group
Commutative Property of Addition:
Irrational
22. Mathematical statement that equates two mathematical expressions.
inline
Periodic Function
Fundamental Theorem of Arithmetic
Equation
23. Determines the likelihood of events that are not independent of one another.
does not change the solution set.
Conditional Probability
counting numbers
Answer the Question
24. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Complete Graph
Overtone
Properties of Equality
A prime number
25. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
Standard Deviation
Axiomatic Systems
Dimension
26. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Multiplicative Inverse:
In Euclidean four-space
a divided by b
Irrational
27. Let a and b represent two whole numbers. Then - a + b = b + a.
Multiplicative Inverse:
Complete Graph
The Commutative Property of Addition
A number is divisible by 9
28. 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
each whole number can be uniquely decomposed into products of primes.
The inverse of multiplication is division
Solution
counting numbers
29. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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30. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
each whole number can be uniquely decomposed into products of primes.
a + c = b + c
A number is divisible by 3
31. Is a symbol (usually a letter) that stands for a value that may vary.
One equal sign per line
Geometry
Cayley's Theorem
Variable
32. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
each whole number can be uniquely decomposed into products of primes.
The Distributive Property (Subtraction)
inline
Properties of Equality
33. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
4 + x = 12
A number is divisible by 9
Periodic Function
The Additive Identity Property
34. 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
The Distributive Property (Subtraction)
Variable
Equation
35. A way to measure how far away a given individual result is from the average result.
Division is not Associative
Standard Deviation
A number is divisible by 10
Equation
36. The study of shape from the perspective of being on the surface of the shape.
Intrinsic View
Associative Property of Multiplication:
left to right
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.
37. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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38. 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.
Torus
Multiplicative Inverse:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Hyperbolic Geometry
39. 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.
Spaceland
Products and Factors
Tone
bar graph
40. 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
Pigeonhole Principle
Irrational
The Additive Identity Property
set
41. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Distributive Property:
Spaceland
Factor Trees
Non-Orientability
42. (a · b) · c = a · (b · c)
Principal Curvatures
Non-Euclidian Geometry
Poincare Disk
Associative Property of Multiplication:
43. A graph in which every node is connected to every other node is called a complete graph.
inline
Complete Graph
Wave Equation
bar graph
44. Original Balance minus River Tam's Withdrawal is Current Balance
Unique Factorization Theorem
Comparison Property
a · c = b · c for c does not equal 0
B - 125 = 1200
45. A topological object that can be used to study the allowable states of a given system.
Euclid's Postulates
Configuration Space
prime factors
Galois Theory
46. If a and b are any whole numbers - then a
variable
Central Limit Theorem
Sign Rules for Division
Commutative Property of Multiplication
47. 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
Grouping Symbols
Non-Euclidian Geometry
Factor Trees
Extrinsic View
48. 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.
Factor Trees
Law of Large Numbers
Dividing both Sides of an Equation by the Same Quantity
A number is divisible by 3
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. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Cayley's Theorem
One equal sign per line
Commensurability