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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. 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






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






3. 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.






4. If a = b then






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






6. 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.






7. A flat map of hyperbolic space.






8. A · 1 = 1 · a = a






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






10. Division by zero is undefined. Each of the expressions 6






11. A way to measure how far away a given individual result is from the average result.






12. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.






13. Index p radicand






14. The system that Euclid used in The Elements






15. 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.






16. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'






17. The study of shape from the perspective of being on the surface of the shape.






18. An important part of problem solving is identifying






19. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -






20. A factor tree is a way to visualize a number's






21. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called






22. Originally known as analysis situs






23. If a represents any whole number - then a






24. 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






25. Positive integers are






26. If a = b then






27. Is the shortest string that contains all possible permutations of a particular length from a given set.






28. The amount of displacement - as measured from the still surface line.






29. 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






30. Two equations if they have the same solution set.






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






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






33. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.






34. ____________ 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






35. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).






36. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.






37. If a is any whole number - then a






38. All integers are thus divided into three classes:






39. The state of appearing unchanged.






40. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that






41. The process of taking a complicated signal and breaking it into sine and cosine components.






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






43. 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.






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






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






46. Is a symbol (usually a letter) that stands for a value that may vary.






47. 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.'






48. 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.






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

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