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CLEP General Math: Number Sense - Patterns - Algebraic Thinking

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. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.






2. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.






3. (a · b) · c = a · (b · c)






4. 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.






5. If a = b then






6. Cannot be written as a ratio of natural numbers.






7. 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






8. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.






9. 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.






10. If a whole number is not a prime number - then it is called a...






11. 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






12. This result says that the symmetries of geometric objects can be expressed as groups of permutations.

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13. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.






14. You must always solve the equation set up in the previous step.






15. The expression a/b means






16. A






17. Let a and b represent two whole numbers. Then - a + b = b + a.






18. Determines the likelihood of events that are not independent of one another.






19. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to






20. Index p radicand






21. 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.






22. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a






23. 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






24. 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.






25. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.






26. A(b + c) = a · b + a · c a(b - c) = a · b - a · c






27. 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.






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






29. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.






30. A number is divisible by 2






31. A topological invariant that relates a surface's vertices - edges - and faces.






32. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab






33. Aka The Osculating Circle - a way to measure the curvature of a line.






34. 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






35. (a






36. Let a - b - and c be any whole numbers. Then - a






37. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.






38. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones






39. 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






40. All integers are thus divided into three classes:






41. Einstein's famous theory - relates gravity to the curvature of spacetime.






42. 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






43. 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.






44. Has no factors other than 1 and itself






45. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.






46. 1. Find the prime factorizations of each number.






47. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even






48. 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






49. Collection of objects. list all the objects in the set and enclosing the list in curly braces.






50. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'