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






2. 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






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






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






5. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.






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






7. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.






8. 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 -






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






11. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a






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






13. 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).






14. Writing Mathematical equations - arrange your work one equation






15. 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






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






17. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.






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






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






20. If a represents any whole number - then a






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






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

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23. If a = b then






24. 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.






25. A + 0 = 0 + a = a






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






27. 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.






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






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






30. The fundamental theorem of arithmetic says that






31. Solving Equations






32. All integers are thus divided into three classes:






33. A






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






35. 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).






36. Means approximately equal.






37. 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.






38. 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.






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






40. Are the fundamental building blocks of arithmetic.






41. 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.






42. A way to measure how far away a given individual result is from the average result.






43. Cannot be written as a ratio of natural numbers.






44. 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).






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






46. (a






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






48. 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.






49. (a · b) · c = a · (b · c)






50. 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







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