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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. If a = b then






2. Arise from the attempt to measure all quantities with a common unit of measure.






3. 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.






4. The state of appearing unchanged.






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






6. Originally known as analysis situs






7. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.






8. 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)






9. Add and subtract






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






11. Mathematical statement that equates two mathematical expressions.






12. 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.






13. 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.






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






15. A graph in which every node is connected to every other node is called a complete graph.






16. 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.






17. If a is any whole number - then a






18. 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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19. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called






20. Has no factors other than 1 and itself






21. 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.






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






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






24. 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






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






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






27. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com






28. Requirements for Word Problem Solutions.






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






30. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator






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

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






33. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco






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






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






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






37. 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.






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






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






40. (a






41. 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






42. 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






43. 4 more than a certain number is 12






44. 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.






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






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






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. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.






49. (a · b) · c = a · (b · c)






50. 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.'