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






2. k-ary operation is a






3. 1 - which preserves numbers: a






4. Is called the type or arity of the operation






5. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction






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






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






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






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






10. 0 - which preserves numbers: a + 0 = a






11. Not commutative a^b?b^a






12. 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






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






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






15. 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






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






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






18. A + b = b + a






19. Is an equation involving derivatives.






20. Involve only one value - such as negation and trigonometric functions.






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






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






23. 1 - which preserves numbers: a^1 = a






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






25. If a = b then b = a






26. Include composition and convolution






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






28. 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.






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. 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






31. If a < b and c < d






32. Is Written as a + b






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






34. 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






35. b = b






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






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






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






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






40. An operation of arity k is called a






41. The values combined are called






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






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






44. 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)






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






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






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






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






49. 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






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