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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 topological invariant that relates a surface's vertices - edges - and faces.






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






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






4. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.






5. Multiplication is equivalent to






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






7. Solving Equations






8. 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






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






10. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'






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






12. Has no factors other than 1 and itself






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






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

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15. When writing mathematical statements - follow the mantra:






16. 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






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






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






19. × - ( )( ) - · - 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






20. 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.






21. Rules for Rounding - To round a number to a particular place - follow these steps:






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






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






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






25. 4 more than a certain number is 12






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






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






28. Add and subtract






29. The expression a/b means






30. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.






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






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






33. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.






34. If a represents any whole number - then a






35. 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.






36. 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).






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






38. 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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39. 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






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






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






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

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43. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.






44. 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.






45. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t






46. If a = b then






47. 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.






48. 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.






49. Original Balance minus River Tam's Withdrawal is Current Balance






50. An important part of problem solving is identifying