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






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






3. 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.






4. 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






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






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






7. 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






8. 0 - which preserves numbers: a + 0 = a






9. Is algebraic equation of degree one






10. 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).






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






12. 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).






13. The operation of multiplication means _______________: a






14. () 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.






15. A binary operation






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






17. Operations can have fewer or more than






18. Is an equation involving derivatives.






19. 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)






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






21. Not commutative a^b?b^a






22. May not be defined for every possible value.






23. 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






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






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






26. The values combined are called






27. Can be added and subtracted.






28. (a






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






30. A






31. 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






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






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






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






35. 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.






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






37. Not associative






38. If a = b then b = a






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






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






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






42. If a < b and c > 0






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






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






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






46. Is an equation involving integrals.






47. Can be defined axiomatically up to an isomorphism






48. Subtraction ( - )






49. There are two common types of operations:






50. k-ary operation is a