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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. That 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.






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






3. 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)






4. 0 - which preserves numbers: a + 0 = a






5. 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'.






6. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:






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






8. Logarithm (Log)






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






10. Is an equation involving integrals.






11. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






12. Referring to the finite number of arguments (the value k)






13. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left






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






15. Division ( / )






16. 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.






17. Not associative






18. Include composition and convolution






19. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






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






21. k-ary operation is a






22. Is to add - subtract - multiply - or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated - the other side of the equation is the value of the variable.






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






24. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in






25. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.






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






27. The operation of multiplication means _______________: a






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






29. 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).






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






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






32. Letters from the beginning of the alphabet like a - b - c... often denote






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






34. Subtraction ( - )






35. 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






36. The squaring operation only produces






37. An operation of arity zero is simply an element of the codomain Y - called a






38. Is an equation of the form log`a^X = b for a > 0 - which has solution






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






40. The process of expressing the unknowns in terms of the knowns is called






41. Is Written as ab or a^b






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






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






44. A unary operation






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






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






47. Is called the type or arity of the operation






48. The values for which an operation is defined form a set called its






49. A + b = b + a






50. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of