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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. 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).






2. Are called the domains of the operation






3. b = b






4. Is an equation involving integrals.






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






6. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






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






8. If a < b and c < 0






9. Not associative






10. 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






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






12. Can be added and subtracted.






13. Is Written as a + b






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






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






16. Can be defined axiomatically up to an isomorphism






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






18. 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.






19. If a < b and b < c






20. A vector can be multiplied by a scalar to form another vector






21. 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)






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






23. The value produced is called






24. () 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.






25. 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






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






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






28. A binary operation






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






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






31. 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.






32. 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.






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






34. Not commutative a^b?b^a






35. Logarithm (Log)






36. May not be defined for every possible value.






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






38. Is an equation involving derivatives.






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






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






41. 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.






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






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






44. Is an equation of the form X^m/n = a - for m - n integers - which has solution






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






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






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






48. Applies abstract algebra to the problems of geometry






49. 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.






50. The values combined are called







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