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






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

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3. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.






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






5. 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.






6. Writing Mathematical equations - arrange your work one equation






7. A + b = b + a






8. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a






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






10. 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.






11. 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






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






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






14. 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.






15. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.






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






17. If a = b then






18. Multiplication is equivalent to






19. If a is any whole number - then a






20. If its final digit is a 0.






21. If grouping symbols are nested






22. 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.






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. 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






25. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -






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






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

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28. Means approximately equal.






29. 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






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






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






32. 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).






33. Mathematical statement that equates two mathematical expressions.






34. The system that Euclid used in The Elements






35. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -






36. 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






37. 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






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






39. 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.






40. × - ( )( ) - · - 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






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






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






43. To describe and extend a numerical pattern






44. 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






45. A · 1/a = 1/a · a = 1






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






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






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






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






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