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






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






3. The fundamental theorem of arithmetic says that






4. 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






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






6. A · 1/a = 1/a · a = 1






7. 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.'






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






9. All integers are thus divided into three classes:






10. 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.






11. ____________ 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






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






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






14. Has no factors other than 1 and itself






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






16. 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






17. 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






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






19. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.






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






21. 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).






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






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

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24. 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 -






25. 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.






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






27. Let a and b represent two whole numbers. Then - a + b = b + a.






28. 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.






29. A flat map of hyperbolic space.






30. If a is any whole number - then a






31. 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.






32. (a · b) · c = a · (b · c)






33. 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.






34. 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






35. 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






36. 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






37. 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.






38. Rules for Rounding - To round a number to a particular place - follow these steps:






39. If a = b then






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






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






42. 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.






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






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






45. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.






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






47. 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.






48. A number is divisible by 2






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






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