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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 expression a/b means






2. A flat map of hyperbolic space.






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






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






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

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






7. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.






8. 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






9. 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.






10. If a = b then






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






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






13. Division by zero is undefined. Each of the expressions 6






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






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






16. The state of appearing unchanged.






17. 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.






18. 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.'






19. 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






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






21. To describe and extend a numerical pattern






22. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is






23. 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.






24. Mathematical statement that equates two mathematical expressions.






25. If a = b then






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






27. (a · b) · c = a · (b · c)






28. 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






29. 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.






30. Solving Equations






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






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






33. 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.






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






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






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






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






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






39. ____________ 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






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






41. A number is divisible by 2






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






43. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.






44. The surface of a standard 'donut shape'.






45. Are the fundamental building blocks of arithmetic.






46. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.

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






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






49. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'






50. 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.