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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 algebraic 'sentence' containing an unknown quantity.






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






3. If a = b then






4. 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)






5. 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.






6. 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.'






7. 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.






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






9. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.






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






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






12. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.






13. A point in three-dimensional space requires three numbers to fix its location.






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






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






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






17. The surface of a standard 'donut shape'.






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






19. 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






20. The system that Euclid used in The Elements






21. 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






22. The study of shape from an external perspective.






23. A · b = b · a






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


25. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.






26. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator






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






28. 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






29. Perform all additions and subtractions in the order presented






30. 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






31. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.






32. 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.






33. 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.'






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






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


36. The expression a/b means






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






38. 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.






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






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






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






42. All integers are thus divided into three classes:






43. 4 more than a certain number is 12






44. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is






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






46. 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.






47. Originally known as analysis situs






48. 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.






49. 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).






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