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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. 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.'






2. If a = b then






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






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






5. (a · b) · c = a · (b · c)






6. If its final digit is a 0.






7. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in






8. The study of shape from an external perspective.






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






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






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






12. Solving Equations






13. 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.






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






15. To describe and extend a numerical pattern






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






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






18. 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 -






19. 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






20. (a






21. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.






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






23. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.






24. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.






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






26. 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






27. 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






28. An important part of problem solving is identifying






29. Positive integers are






30. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina






31. 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






32. Has no factors other than 1 and itself






33. In the expression 3






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






35. 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.






36. 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.






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






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






39. 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.






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






41. All integers are thus divided into three classes:






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






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






44. 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.






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






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






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






48. If a = b then






49. A number is divisible by 2






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