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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 multiplication means _______________: a






2. Are called the domains of the operation






3. 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.

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4. Not commutative a^b?b^a






5. Is Written as a






6. k-ary operation is a






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






8. 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.






9. 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.






10. Can be combined using the function composition operation - performing the first rotation and then the second.






11. If a = b then b = a






12. 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)






13. b = b






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






15. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






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






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






18. () 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.






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






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






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






22. 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.






23. A






24. 1 - which preserves numbers: a






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






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






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






28. Is algebraic equation of degree one






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






30. Can be defined axiomatically up to an isomorphism






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






32. 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).






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






34. The inner product operation on two vectors produces a






35. 0 - which preserves numbers: a + 0 = a






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






37. Is Written as a + b






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






39. A + b = b + a






40. 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






41. 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)






42. 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'.






43. 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






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






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






46. If a < b and c > 0






47. A unary operation






48. Is called the codomain of the operation






49. Subtraction ( - )






50. Operations can have fewer or more than