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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. A · 1/a = 1/a · a = 1






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






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






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






6. 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.






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






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






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






10. ____________ 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






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






12. To describe and extend a numerical pattern






13. 4 more than a certain number is 12






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






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






16. 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






17. 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.






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






19. An important part of problem solving is identifying






20. An arrangement where order matters.






21. Means approximately equal.






22. 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






23. If a = b then






24. Collection of objects. list all the objects in the set and enclosing the list in curly braces.






25. Requirements for Word Problem Solutions.






26. 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.






27. 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.






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






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






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






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






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






33. A + (-a) = (-a) + a = 0






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






35. 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.






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






37. 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.






38. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.






39. 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.






40. 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






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






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






43. The system that Euclid used in The Elements






44. If a - b - and c are any whole numbers - then a






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






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






47. If a represents any whole number - then a






48. The study of shape from an external perspective.






49. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.






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