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CLEP College Algebra: Algebra Principles

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. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)






2. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its






3. Include composition and convolution






4. Operations can have fewer or more than






5. Are true for only some values of the involved variables: x2 - 1 = 4.






6. Are denoted by letters at the beginning - a - b - c - d - ...






7. Involve only one value - such as negation and trigonometric functions.






8. If a < b and c < 0






9. Are called the domains of the operation






10. In which the specific properties of vector spaces are studied (including matrices)






11. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






12. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.






13. Is Written as a






14. In which properties common to all algebraic structures are studied






15. Can be added and subtracted.






16. Symbols that denote numbers - is to allow the making of generalizations in mathematics






17. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction






18. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






19. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).






20. Is an equation involving integrals.






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






22. 1 - which preserves numbers: a^1 = a






23. Is a function of the form ? : V ? Y - where V ? X1






24. If a = b and b = c then a = c






25. Include the binary operations union and intersection and the unary operation of complementation.






26. The squaring operation only produces






27. An operation of arity k is called a






28. The value produced is called






29. The operation of exponentiation means ________________: a^n = a






30. The codomain is the set of real numbers but the range is the






31. Is an equation where the unknowns are required to be integers.






32. The values of the variables which make the equation true are the solutions of the equation and can be found through






33. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.






34. 1 - which preserves numbers: a






35. In which abstract algebraic methods are used to study combinatorial questions.






36. May not be defined for every possible value.






37. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






38. Can be combined using logic operations - such as and - or - and not.






39. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.






40. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po






41. If a < b and b < c






42. If it holds for all a and b in X that if a is related to b then b is related to a.






43. A + b = b + a






44. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.






45. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:






46. Is Written as ab or a^b






47. A






48. If a = b and c = d then a + c = b + d and ac = bd; that if a = b then a + c = b + c; that if two symbols are equal - then one can be substituted for the other.

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49. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi






50. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the







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