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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. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an






2. Is an equation involving a transcendental function of one of its variables.






3. The inner product operation on two vectors produces a






4. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.






5. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.






6. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym






7. The operation of multiplication means _______________: a






8. Subtraction ( - )






9. 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






10. 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)






11. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics






12. There are two common types of operations:






13. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).






14. Is called the type or arity of the operation






15. If a < b and c < 0






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






17. Can be combined using the function composition operation - performing the first rotation and then the second.






18. k-ary operation is a






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






20. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






21. The value produced is called






22. Logarithm (Log)






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






24. Will have two solutions in the complex number system - but need not have any in the real number system.






25. Is an equation of the form aX = b for a > 0 - which has solution






26. Is Written as a






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






28. In an equation with a single unknown - a value of that unknown for which the equation is true is called






29. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.






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






32. Include composition and convolution






33. Is an equation in which a polynomial is set equal to another polynomial.






34. 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






35. Is an action or procedure which produces a new value from one or more input values.






36. Is an algebraic 'sentence' containing an unknown quantity.






37. May not be defined for every possible value.






38. If a < b and c > 0






39. Is an equation in which the unknowns are functions rather than simple quantities.






40. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.






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






42. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






43. Is an equation involving integrals.






44. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called






45. Is Written as a + b






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






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






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






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






50. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)