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






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






3. (a






4. Perform all additions and subtractions in the order presented






5. × - ( )( ) - · - 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






6. 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.






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. Means approximately equal.






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






10. Requirements for Word Problem Solutions.






11. Uses second derivatives to relate acceleration in space to acceleration in time.






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






13. 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).






14. If a = b then






15. 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.






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






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






18. The study of shape from the perspective of being on the surface of the shape.






19. A flat map of hyperbolic space.






20. 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.






21. A topological invariant that relates a surface's vertices - edges - and faces.






22. If its final digit is a 0 or 5.






23. If a = b then






24. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.






25. 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.






26. 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.






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

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






29. 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.'






30. A · 1 = 1 · a = a






31. 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






32. 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






33. The study of shape from an external perspective.






34. Originally known as analysis situs






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






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






37. 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






38. The fundamental theorem of arithmetic says that






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






40. If grouping symbols are nested






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






42. 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.






43. 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






44. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.






45. Mathematical statement that equates two mathematical expressions.






46. 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






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






48. The system that Euclid used in The Elements






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






50. Index p radicand