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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 number is divisible by 2






2. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).






3. 4 more than a certain number is 12






4. A factor tree is a way to visualize a number's






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






6. 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






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






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






9. To describe and extend a numerical pattern






10. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).






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






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






13. 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.






14. An important part of problem solving is identifying






15. Positive integers are






16. 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






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






18. A






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






20. A flat map of hyperbolic space.






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






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






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






24. 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






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






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






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

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28. 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






29. (a · b) · c = a · (b · c)






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






31. An arrangement where order matters.






32. 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.






33. A · 1/a = 1/a · a = 1






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






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






36. The state of appearing unchanged.






37. 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.






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






39. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.






40. Has no factors other than 1 and itself






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






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






43. ____________ 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






44. 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






45. If a represents any whole number - then a






46. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.






47. 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






48. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.






49. × - ( )( ) - · - 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






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