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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. In which abstract algebraic methods are used to study combinatorial questions.






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






3. 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.






4. 1 - which preserves numbers: a^1 = a






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






6. The operation of multiplication means _______________: a






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






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






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






10. Is Written as ab or a^b






11. Can be defined axiomatically up to an isomorphism






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






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






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






16. 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






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






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






19. 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






20. May not be defined for every possible value.






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






22. Operations can have fewer or more than






23. The values combined are called






24. A






25. 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'.






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






27. Not commutative a^b?b^a






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






29. If a < b and c < d






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






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






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






33. Applies abstract algebra to the problems of geometry






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






35. (a






36. 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).






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






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






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






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






41. A unary operation






42. 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)






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






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






45. The inner product operation on two vectors produces a






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






47. Subtraction ( - )






48. An operation of arity k is called a






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






50. If a = b then b = a