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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. An important part of problem solving is identifying






2. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.






3. 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.'






4. 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.






5. 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






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






7. To describe and extend a numerical pattern






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






9. 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).






10. 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).






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






12. If a = b then






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






14. 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.






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






16. If a = b then






17. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.






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






19. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).






20. 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


21. If a represents any whole number - then a






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






23. Is a path that visits every node in a graph and ends where it began.






24. Positive integers are






25. 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.






26. A · 1/a = 1/a · a = 1






27. 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.






28. Requirements for Word Problem Solutions.






29. 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.






30. The expression a/b means






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


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






33. A flat map of hyperbolic space.






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






35. If a = b then






36. 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






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






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






39. Index p radicand






40. If grouping symbols are nested






41. An arrangement where order matters.






42. 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.






43. All integers are thus divided into three classes:






44. The fundamental theorem of arithmetic says that






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


46. 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.






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






48. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'






49. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.






50. 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