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






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






4. Requirements for Word Problem Solutions.






5. Positive integers are






6. A · 1 = 1 · a = a






7. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.






8. 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.'






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






10. Is the shortest string that contains all possible permutations of a particular length from a given set.






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






12. 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.'






13. 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






14. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones






15. 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.






16. 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






17. If its final digit is a 0.






18. Perform all additions and subtractions in the order presented






19. Are the fundamental building blocks of arithmetic.






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






21. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.






22. An important part of problem solving is identifying






23. 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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24. Add and subtract






25. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values






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






27. The fundamental theorem of arithmetic says that






28. ____________ 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






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






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






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






32. 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).






33. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.






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






35. If a represents any whole number - then a






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






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






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






39. The system that Euclid used in The Elements






40. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo






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






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

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






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






45. 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).






46. When writing mathematical statements - follow the mantra:






47. 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.






48. If a is any whole number - then a






49. 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.






50. A point in three-dimensional space requires three numbers to fix its location.