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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. Let a - b - and c be any whole numbers. Then - a






2. Positive integers are






3. When writing mathematical statements - follow the mantra:






4. 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.






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






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






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






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






9. 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






10. 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






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






12. 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.






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






14. 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






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






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






17. 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.






18. If a = b then






19. 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.






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






21. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in






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






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






24. 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






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






26. ____________ 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






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






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






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






30. 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.






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






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






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






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






35. If a = b then






36. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab






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






38. Negative






39. An arrangement where order matters.






40. 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






41. 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.'






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






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






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






45. 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)






46. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.






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






48. Writing Mathematical equations - arrange your work one equation






49. 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.






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