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






2. 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)






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






4. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






5. 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






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






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






8. May not be defined for every possible value.






9. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).






10. The values combined are called






11. Can be defined axiomatically up to an isomorphism






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






13. 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'.






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






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






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






17. 0 - which preserves numbers: a + 0 = a






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






19. The value produced is called






20. Is Written as a






21. A






22. If a < b and b < c






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






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






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






26. 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






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






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






29. If a < b and c < d






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






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






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






33. b = b






34. Is Written as a + b






35. () 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.






36. 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.






37. Applies abstract algebra to the problems of geometry






38. Is called the codomain of the operation






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






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






41. 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






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






43. 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






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






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






46. k-ary operation is a






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






48. (a






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






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