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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. Originally known as analysis situs






2. 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






3. Perform all additions and subtractions in the order presented






4. A






5. Writing Mathematical equations - arrange your work one equation






6. 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.






7. 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






8. 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.






9. 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






10. A topological object that can be used to study the allowable states of a given system.






11. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.

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12. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.






13. (a + b) + c = a + (b + c)






14. If a is any whole number - then a






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






16. Positive integers are






17. A · 1 = 1 · a = a






18. 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






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






20. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'






21. 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.






22. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.






23. 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






24. Index p radicand






25. (a






26. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.






27. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.






28. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)

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29. (a · b) · c = a · (b · c)






30. To describe and extend a numerical pattern






31. 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.






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






33. 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






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






35. An important part of problem solving is identifying






36. 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.






37. If a and b are any whole numbers - then a






38. 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.






39. If grouping symbols are nested






40. This method can create a flat map from a curved surface while preserving all angles in any features present.






41. 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 -






42. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.






43. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.






44. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values






45. ____________ 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






46. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.






47. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.






48. Are the fundamental building blocks of arithmetic.






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






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