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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. 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)






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






3. There are two common types of operations:






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






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






6. Is an action or procedure which produces a new value from one or more input values.






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






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






9. Can be defined axiomatically up to an isomorphism






10. Is algebraic equation of degree one






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






12. A unary operation






13. The operation of multiplication means _______________: a






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






15. Can be added and subtracted.






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






17. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.






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






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






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






21. The value produced is called






22. 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






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






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






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






26. The values of the variables which make the equation true are the solutions of the equation and can be found through






27. 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).






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






29. Logarithm (Log)






30. 0 - which preserves numbers: a + 0 = a






31. 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.






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






33. Applies abstract algebra to the problems of geometry






34. 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.






35. Subtraction ( - )






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






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






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






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






40. 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'.






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






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






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






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






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






46. Include composition and convolution






47. 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






48. 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






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






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







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