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






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






3. 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.






4. A · b = b · a






5. 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.






6. Multiplication is equivalent to






7. Perform all additions and subtractions in the order presented






8. 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.






9. Mathematical statement that equates two mathematical expressions.






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






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






12. If a = b then






13. If its final digit is a 0.






14. A · 1 = 1 · a = a






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






16. ____________ 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






17. 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).






18. 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.






19. Means approximately equal.






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






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






22. The system that Euclid used in The Elements






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






24. A · 1/a = 1/a · a = 1






25. 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.






26. 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






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






28. 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.






29. Solving Equations






30. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A

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






32. 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






33. If a represents any whole number - then a






34. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar






35. If a is any whole number - then a






36. If a = b then






37. 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.'






38. 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.






39. (a · b) · c = a · (b · c)






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






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






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

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43. Negative






44. A(b + c) = a · b + a · c a(b - c) = a · b - a · c






45. 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.






46. If grouping symbols are nested






47. The study of shape from an external perspective.






48. 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)






49. Is a symbol (usually a letter) that stands for a value that may vary.






50. 4 more than a certain number is 12