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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. 1. Find the prime factorizations of each number.






2. 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.






3. A · 1 = 1 · a = a






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






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






6. 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.






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






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






9. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.






10. 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.






11. If a = b then






12. An important part of problem solving is identifying






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






14. 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)






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






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






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






18. Means approximately equal.






19. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).






20. Writing Mathematical equations - arrange your work one equation






21. Two equations if they have the same solution set.






22. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of






23. 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






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






25. A flat map of hyperbolic space.






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






27. Index p radicand






28. 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.






29. 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






30. 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.






31. If a = b then






32. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'






33. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.






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






35. (a






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






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






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






39. 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.






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

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






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






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






44. 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






45. In the expression 3






46. 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 -






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






48. 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.






49. Has no factors other than 1 and itself






50. 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.