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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. 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






2. Dimension is how mathematicians express the idea of degrees of freedom






3. 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.






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






5. If a = b then






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






7. 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.






8. 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.






9. Means approximately equal.






10. Multiplication is equivalent to






11. Negative






12. If a = b then






13. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.






14. 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






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






16. When writing mathematical statements - follow the mantra:






17. Arise from the attempt to measure all quantities with a common unit of measure.






18. 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.






19. 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






20. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.






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






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






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






24. If a is any whole number - then a






25. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar






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






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






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






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






30. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco






31. 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)






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






33. A flat map of hyperbolic space.






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






35. Mathematical statement that equates two mathematical expressions.






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






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






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






39. Writing Mathematical equations - arrange your work one equation






40. In the expression 3






41. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.






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






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






44. (a






45. 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






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






47. Requirements for Word Problem Solutions.






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






49. If grouping symbols are nested






50. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even