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






3. 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






4. Has no factors other than 1 and itself






5. All integers are thus divided into three classes:






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






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

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8. (a · b) · c = a · (b · c)






9. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.






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






11. A flat map of hyperbolic space.






12. Originally known as analysis situs






13. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.






14. To describe and extend a numerical pattern






15. 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






16. 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






17. When writing mathematical statements - follow the mantra:






18. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t






19. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.






20. 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






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






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






23. 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)






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






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






26. 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






27. 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.






28. × - ( )( ) - · - 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






29. 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.






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






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






32. 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.






33. Perform all additions and subtractions in the order presented






34. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).






35. The state of appearing unchanged.






36. An arrangement where order matters.






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






38. 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






39. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.






40. 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.






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






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






43. 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).






44. 4 more than a certain number is 12






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






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






47. A number is divisible by 2






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






49. A + 0 = 0 + a = a






50. Mathematical statement that equates two mathematical expressions.