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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. All integers are thus divided into three classes:






2. The inverse of multiplication






3. ____________ 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






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. 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






6. If a = b then






7. 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.






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

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






10. A flat map of hyperbolic space.






11. If a represents any whole number - then a






12. 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.






13. 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 -






14. 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






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






16. 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.






17. If its final digit is a 0 or 5.






18. Positive integers are






19. N = {1 - 2 - 3 - 4 - 5 - . . .}.






20. 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.






21. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t






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






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






24. 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.






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






26. 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






27. If a = b then






28. Negative






29. 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






30. Are the fundamental building blocks of arithmetic.






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






32. 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).






33. 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 -






34. Solving Equations






35. If grouping symbols are nested






36. Uses second derivatives to relate acceleration in space to acceleration in time.






37. The state of appearing unchanged.






38. 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.






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






40. An algebraic 'sentence' containing an unknown quantity.






41. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.






42. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or






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






44. 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






45. The system that Euclid used in The Elements






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






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






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






49. (a · b) · c = a · (b · c)






50. An arrangement where order matters.